Since June 16, 2000

STUDIO KAMADA

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Index

1. Introduction
2. Last update
3. News and updates
4. Wanted
5. Records
6. Contributors
7. Forms
8. Factor Table Search
   
9. Factor tables
   Repunit (1)_w | Near-repdigit (R)_wD | Near-repdigit D(R)_w | Near-repdigit Palindrome (R)_wD(R)_w | Plateau and Depression D(R)_wD | Generalized quasi-repdigit D(R)_wE
10. Implementations
11. Related links

1. Introduction

This page contains the factor tables and pertinent informations of repunit, near-repdigit, plateau and depression and generalized quasi-repdigit numbers. See Forms for more details.

2. Last update

Dec 24, 2008 00:16 JST

3. News and updates

Dec 24, 2008

By Serge Batalov / GMP-ECM 6.2.1
(38·10²⁰⁵+61)/9 = 4(2)₂₀₄9_<206> = 7 · 996172031694311_<15> · C190
C190 = P39 · C152
P39 = 604708101318908926128095438473785832727_<39>
C152 = [10012970019827499748751154328820037782074317676296066223065340785954584373285105326974194401949500349014357279371189711576864463523554910181915957776451_<152>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3954599440 Step 1 took 16015ms Step 2 took 15053ms ********** Factor found in step 2: 604708101318908926128095438473785832727 Found probable prime factor of 39 digits: 604708101318908926128095438473785832727 Composite cofactor has 152 digits

Dec 23, 2008 (8th)

By Serge Batalov / GMP-ECM 6.2.1, Msieve-1.39
(38·10¹²⁹+61)/9 = 4(2)₁₂₈9_<130> = 113 · 212476189 · 206782920150614243_<18> · C102
C102 = P31 · P72
P31 = 6877800995261078438976596986477_<31>
P72 = 123648287482431227866137204018035742921025020239320352409776567579513327_<72>

Factor found in step 1: 6877800995261078438976596986477

(38·10¹⁵¹+61)/9 = 4(2)₁₅₀9_<152> = 7 · 1117 · 20743 · 192637 · 82137278791_<11> · C128
C128 = P29 · P99
P29 = 56185303161233834414804494597_<29>
P99 = 292829995865447732444269891383468434429946313251210428873631095088198685156325342448697256025078463_<99>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=3917450993 Step 1 took 9731ms Step 2 took 10584ms ********** Factor found in step 2: 56185303161233834414804494597 Found probable prime factor of 29 digits: 56185303161233834414804494597 Probable prime cofactor 292829995865447732444269891383468434429946313251210428873631095088198685156325342448697256025078463 has 99 digits

(13·10¹⁴⁵-7)/3 = 4(3)₁₄₄1_<146> = 3709 · 3847 · 2170109 · C133
C133 = P32 · C101
P32 = 39052045075867533488696837658421_<32>
C101 = [35835853124155232087376837262708155018312446867976450226551174108265579054212486580985798592914115673_<101>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2266195174 Step 1 took 9764ms Step 2 took 10698ms ********** Factor found in step 2: 39052045075867533488696837658421 Found probable prime factor of 32 digits: 39052045075867533488696837658421 Composite cofactor has 101 digits

(13·10¹⁸⁶-7)/3 = 4(3)₁₈₅1_<187> = 29 · 41 · 1723 · 2881969280353873_<16> · C165
C165 = P34 · C132
P34 = 2267180036234447141280701752917889_<34>
C132 = [323727512032728409566065549304498685213258027853771402670265835962965506247762803100126933161757433369766377101984695411470824717509_<132>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=980914334 Step 1 took 13664ms Step 2 took 13602ms ********** Factor found in step 2: 2267180036234447141280701752917889 Found probable prime factor of 34 digits: 2267180036234447141280701752917889 Composite cofactor has 132 digits

(13·10¹⁹⁴-7)/3 = 4(3)₁₉₃1_<195> = 3881 · 4040009 · 12429749 · 4005775577929_<13> · C165
C165 = P32 · C133
P32 = 66007507859850270736596089399561_<32>
C133 = [8409183178583936583030174346844415915814492342050749419119294169308338808320971385476178209350780286513505479940764510332776202970919_<133>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=230614363 Step 1 took 13630ms Step 2 took 13457ms ********** Factor found in step 2: 66007507859850270736596089399561 Found probable prime factor of 32 digits: 66007507859850270736596089399561 Composite cofactor 8409183178583936583030174346844415915814492342050749419119294169308338808320971385476178209350780286513505479940764510332776202970919 has 133 digits

(38·10¹⁸⁰+61)/9 = 4(2)₁₇₉9_<181> = 11² · 193 · 2125621 · 9206214079_<10> · 61673945456472526189_<20> · C141
C141 = P32 · P109
P32 = 37615930741760579786512667771617_<32>
P109 = 3982519964961393426250352239850021980260372565021485335616685544317069003492639457212340339450474841652800179_<109>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1328187747 Step 1 took 11835ms Step 2 took 11587ms ********** Factor found in step 2: 37615930741760579786512667771617 Found probable prime factor of 32 digits: 37615930741760579786512667771617 Probable prime cofactor 3982519964961393426250352239850021980260372565021485335616685544317069003492639457212340339450474841652800179 has 109 digits

(38·10¹⁷⁵+61)/9 = 4(2)₁₇₄9_<176> = 7 · 48661 · C171
C171 = P31 · C140
P31 = 1740394642983557583386337035393_<31>
C140 = [71222018811833964655417651567953033432448526235056638873220031832622185237876237006720634532335848847765089902608605674576837157124980845239_<140>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=205899236 Step 1 took 13705ms ********** Factor found in step 1: 1740394642983557583386337035393 Found probable prime factor of 31 digits: 1740394642983557583386337035393 Composite cofactor has 140 digits

(13·10²⁰⁴-7)/3 = 4(3)₂₀₃1_<205> = 119179 · 279991 · 11574691 · 21512664293_<11> · C177
C177 = P32 · P146
P32 = 26308325916731982485427287860457_<32>
P146 = 19823551780928035006602671905281634246612561791914656475871110593336489297213306083897826212562111916418038463405766923512493202714696938292099769_<146>

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=1594125605 Step 1 took 16110ms Step 2 took 14725ms ********** Factor found in step 2: 26308325916731982485427287860457 Found probable prime factor of 32 digits: 26308325916731982485427287860457 Probable prime cofactor has 146 digits

(13·10¹⁹³-7)/3 = 4(3)₁₉₂1_<194> = 151 · 10209190744703_<14> · C179
C179 = P31 · C148
P31 = 7709568588244219307028066227297_<31>
C148 = [3646059534317701069724515171275791765391252664992167269599666190068435969269326867841860958544963686066522189227458537555849678015726858695874479291_<148>]

Using B1=3000000, B2=11414255590, polynomial Dickson(12), sigma=2528423854 Step 1 took 15951ms Step 2 took 14697ms ********** Factor found in step 2: 7709568588244219307028066227297 Found probable prime factor of 31 digits: 7709568588244219307028066227297 Composite cofactor has 148 digits

(13·10¹²⁵-7)/3 = 4(3)₁₂₄1_<126> = 17 · 19 · 137 · 3943 · 80849611 · C110
C110 = P39 · P71
P39 = 756960282992795240590601586497232434921_<39>
P71 = 40580855963552503455078830310304821124582047703016518551277824518526757_<71>

SNFS difficulty: 126 digits. Divisors found: r1=756960282992795240590601586497232434921 (pp39) r2=40580855963552503455078830310304821124582047703016518551277824518526757 (pp71) Version: Msieve-1.39 Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.951). Factorization parameters were as follows: n: 30718096214260565396870102557694086018037165181434351721059131933001350211212314245444509148935415858799681197 m: 10000000000000000000000000 deg: 5 c5: 13 c0: -7 skew: 0.88 type: snfs lss: 1 rlim: 890000 alim: 890000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 890000/890000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [445000, 695001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 125763 x 125999 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,890000,890000,26,26,49,49,2.3,2.3,50000 total time: 1.30 hours.

Dec 23, 2008 (7th)

By Sinkiti Sibata / Msieve
(38·10¹⁵⁵+43)/9 = 4(2)₁₅₄7_<156> = 13 · 648404825447551_<15> · C140
C140 = P62 · P78
P62 = 68502326768501726934975760518634987979255867421670311224348881_<62>
P78 = 731216821236048149998573343592774757206363666972266538567208965878323259710609_<78>

Number: 42227_155 N=50090053626936883206705630949905665484857244831913664200001658149686866574332055065172584204637245327813337676459217261678272501746512978529 ( 140 digits) SNFS difficulty: 156 digits. Divisors found: r1=68502326768501726934975760518634987979255867421670311224348881 r2=731216821236048149998573343592774757206363666972266538567208965878323259710609 Version: Total time: 32.15 hours. Scaled time: 82.43 units (timescale=2.564). Factorization parameters were as follows: name: 42227_155 n: 50090053626936883206705630949905665484857244831913664200001658149686866574332055065172584204637245327813337676459217261678272501746512978529 m: 10000000000000000000000000000000 deg: 5 c5: 38 c0: 43 skew: 1.03 type: snfs lss: 1 rlim: 2800000 alim: 2800000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2800000/2800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1400000, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 560105 x 560353 Total sieving time: 32.15 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,2800000,2800000,27,27,50,50,2.4,2.4,100000 total time: 32.15 hours. --------- CPU info (if available) ----------

(37·10¹⁵⁶+17)/9 = 4(1)₁₅₅3_<157> = 3³ · 29 · 10189769 · 13778351 · 2556268457_<10> · C131
C131 = P34 · P97
P34 = 3797525954125859456188033584306947_<34>
P97 = 3852375905322761719761070474805539193083531228124173816698883017752530486655049572263981171562611_<97>

Number: 42227_156 N=14629497485512292314226146150939449758591397444048985543210067506643763064342654028641902815319618485210777765254764855395452758617 ( 131 digits) SNFS difficulty: 158 digits. Divisors found: r1=3797525954125859456188033584306947 r2=3852375905322761719761070474805539193083531228124173816698883017752530486655049572263981171562611 Version: Total time: 30.38 hours. Scaled time: 60.50 units (timescale=1.991). Factorization parameters were as follows: name: 42227_156 n: 14629497485512292314226146150939449758591397444048985543210067506643763064342654028641902815319618485210777765254764855395452758617 m: 20000000000000000000000000000000 deg: 5 c5: 185 c0: 272 skew: 1.08 type: snfs lss: 1 rlim: 3100000 alim: 3100000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3100000/3100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1550000, 2650001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 579590 x 579838 Total sieving time: 30.38 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000 total time: 30.38 hours. --------- CPU info (if available) ----------

(38·10¹¹¹+61)/9 = 4(2)₁₁₀9_<112> = 11339154493_<11> · 7499477233123_<13> · C89
C89 = P37 · P52
P37 = 7397064209141958485367330886373433809_<37>
P52 = 6712279544020820708812321814113647261175372549034179_<52>

Tue Dec 23 17:27:13 2008 Msieve v. 1.39 Tue Dec 23 17:27:13 2008 random seeds: 7cbef738 6f66a5b2 Tue Dec 23 17:27:13 2008 factoring 49651162776832117853392950700141070758766904970016036759288163519498755604332466735157811 (89 digits) Tue Dec 23 17:27:14 2008 searching for 15-digit factors Tue Dec 23 17:27:16 2008 commencing quadratic sieve (89-digit input) Tue Dec 23 17:27:16 2008 using multiplier of 11 Tue Dec 23 17:27:16 2008 using 32kb Intel Core sieve core Tue Dec 23 17:27:16 2008 sieve interval: 32 blocks of size 32768 Tue Dec 23 17:27:16 2008 processing polynomials in batches of 7 Tue Dec 23 17:27:16 2008 using a sieve bound of 1556189 (58842 primes) Tue Dec 23 17:27:16 2008 using large prime bound of 124495120 (26 bits) Tue Dec 23 17:27:16 2008 using double large prime bound of 372626841652480 (42-49 bits) Tue Dec 23 17:27:16 2008 using trial factoring cutoff of 49 bits Tue Dec 23 17:27:16 2008 polynomial 'A' values have 11 factors Tue Dec 23 18:38:03 2008 59083 relations (15371 full + 43712 combined from 629948 partial), need 58938 Tue Dec 23 18:38:04 2008 begin with 645319 relations Tue Dec 23 18:38:04 2008 reduce to 144756 relations in 9 passes Tue Dec 23 18:38:04 2008 attempting to read 144756 relations Tue Dec 23 18:38:06 2008 recovered 144756 relations Tue Dec 23 18:38:06 2008 recovered 124039 polynomials Tue Dec 23 18:38:06 2008 attempting to build 59083 cycles Tue Dec 23 18:38:06 2008 found 59083 cycles in 5 passes Tue Dec 23 18:38:06 2008 distribution of cycle lengths: Tue Dec 23 18:38:06 2008 length 1 : 15371 Tue Dec 23 18:38:06 2008 length 2 : 11272 Tue Dec 23 18:38:06 2008 length 3 : 10572 Tue Dec 23 18:38:06 2008 length 4 : 7903 Tue Dec 23 18:38:06 2008 length 5 : 5658 Tue Dec 23 18:38:06 2008 length 6 : 3490 Tue Dec 23 18:38:06 2008 length 7 : 2178 Tue Dec 23 18:38:06 2008 length 9+: 2639 Tue Dec 23 18:38:06 2008 largest cycle: 20 relations Tue Dec 23 18:38:07 2008 matrix is 58842 x 59083 (14.7 MB) with weight 3621608 (61.30/col) Tue Dec 23 18:38:07 2008 sparse part has weight 3621608 (61.30/col) Tue Dec 23 18:38:07 2008 filtering completed in 3 passes Tue Dec 23 18:38:07 2008 matrix is 55011 x 55075 (13.8 MB) with weight 3403270 (61.79/col) Tue Dec 23 18:38:07 2008 sparse part has weight 3403270 (61.79/col) Tue Dec 23 18:38:08 2008 saving the first 48 matrix rows for later Tue Dec 23 18:38:08 2008 matrix is 54963 x 55075 (10.5 MB) with weight 2875828 (52.22/col) Tue Dec 23 18:38:08 2008 sparse part has weight 2420144 (43.94/col) Tue Dec 23 18:38:08 2008 matrix includes 64 packed rows Tue Dec 23 18:38:08 2008 using block size 22030 for processor cache size 1024 kB Tue Dec 23 18:38:08 2008 commencing Lanczos iteration Tue Dec 23 18:38:08 2008 memory use: 9.3 MB Tue Dec 23 18:38:29 2008 lanczos halted after 871 iterations (dim = 54961) Tue Dec 23 18:38:29 2008 recovered 17 nontrivial dependencies Tue Dec 23 18:38:29 2008 prp37 factor: 7397064209141958485367330886373433809 Tue Dec 23 18:38:29 2008 prp52 factor: 6712279544020820708812321814113647261175372549034179 Tue Dec 23 18:38:29 2008 elapsed time 01:11:16

(38·10¹⁵⁷+43)/9 = 4(2)₁₅₆7_<158> = 3833 · 5659 · C151
C151 = P59 · P92
P59 = 91465142275684836616097261496147067070594607462692509039543_<59>
P92 = 21281731504266448543814676309892699432806272010865082270499088002856980384586766615972344087_<92>

Number: 42227_157 N=1946536599910654994557048257147197041338131628011548883606705701794496211816949357822976664975587383170602105211092084740339931779936681520738685232241 ( 151 digits) SNFS difficulty: 159 digits. Divisors found: r1=91465142275684836616097261496147067070594607462692509039543 r2=21281731504266448543814676309892699432806272010865082270499088002856980384586766615972344087 Version: Total time: 34.06 hours. Scaled time: 85.63 units (timescale=2.514). Factorization parameters were as follows: name:42227_157 n: 1946536599910654994557048257147197041338131628011548883606705701794496211816949357822976664975587383170602105211092084740339931779936681520738685232241 m: 20000000000000000000000000000000 deg: 5 c5: 475 c0: 172 skew: 0.82 type: snfs lss: 1 rlim: 3100000 alim: 3100000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3100000/3100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1550000, 2850001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 522055 x 522303 Total sieving time: 34.06 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,3100000,3100000,27,27,50,50,2.4,2.4,100000 total time: 34.06 hours. --------- CPU info (if available) ----------

(13·10¹¹⁶-7)/3 = 4(3)₁₁₅1_<117> = 41 · 105225587 · C108
C108 = P47 · P61
P47 = 20912340313401736804695249831314117167056127139_<47>
P61 = 4803018351672359716761183080233491333287524164537900935628787_<61>

Number: 43331_116 N=100442354301686248318155650268889154362152020216994424474504576240621884645894815542260238572668695980350393 ( 108 digits) SNFS difficulty: 118 digits. Divisors found: r1=20912340313401736804695249831314117167056127139 r2=4803018351672359716761183080233491333287524164537900935628787 Version: Total time: 1.52 hours. Scaled time: 3.02 units (timescale=1.991). Factorization parameters were as follows: name: 43331_116 n: 100442354301686248318155650268889154362152020216994424474504576240621884645894815542260238572668695980350393 m: 200000000000000000000000 deg: 5 c5: 65 c0: -112 skew: 1.11 type: snfs lss: 1 rlim: 660000 alim: 660000 lpbr: 25 lpba: 25 mfbr: 45 mfba: 45 rlambda: 2.2 alambda: 2.2 Factor base limits: 660000/660000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 45/45 Sieved rational special-q in [330000, 530001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 68965 x 69199 Total sieving time: 1.52 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,660000,660000,25,25,45,45,2.2,2.2,50000 total time: 1.52 hours. --------- CPU info (if available) ----------

(38·10¹²²+61)/9 = 4(2)₁₂₁9_<123> = 3 · 11 · 13 · 1447 · 8190245732611_<13> · 42734715820119503_<17> · C88
C88 = P38 · P51
P38 = 17894098175364997990374216358774504223_<38>
P51 = 108599467479248166102092723780312641021472824805237_<51>

Tue Dec 23 18:47:15 2008 Msieve v. 1.39 Tue Dec 23 18:47:15 2008 random seeds: 160947d4 cef27f46 Tue Dec 23 18:47:15 2008 factoring 1943289532866025046805189916901455945080339390486360112365850271499631585958241209015851 (88 digits) Tue Dec 23 18:47:16 2008 searching for 15-digit factors Tue Dec 23 18:47:17 2008 commencing quadratic sieve (88-digit input) Tue Dec 23 18:47:17 2008 using multiplier of 19 Tue Dec 23 18:47:17 2008 using 32kb Intel Core sieve core Tue Dec 23 18:47:17 2008 sieve interval: 24 blocks of size 32768 Tue Dec 23 18:47:17 2008 processing polynomials in batches of 9 Tue Dec 23 18:47:17 2008 using a sieve bound of 1506511 (57333 primes) Tue Dec 23 18:47:17 2008 using large prime bound of 120520880 (26 bits) Tue Dec 23 18:47:17 2008 using double large prime bound of 351489263807840 (42-49 bits) Tue Dec 23 18:47:17 2008 using trial factoring cutoff of 49 bits Tue Dec 23 18:47:17 2008 polynomial 'A' values have 11 factors Tue Dec 23 19:37:18 2008 57729 relations (16066 full + 41663 combined from 603363 partial), need 57429 Tue Dec 23 19:37:19 2008 begin with 619429 relations Tue Dec 23 19:37:19 2008 reduce to 138258 relations in 10 passes Tue Dec 23 19:37:19 2008 attempting to read 138258 relations Tue Dec 23 19:37:21 2008 recovered 138258 relations Tue Dec 23 19:37:21 2008 recovered 115980 polynomials Tue Dec 23 19:37:21 2008 attempting to build 57729 cycles Tue Dec 23 19:37:21 2008 found 57729 cycles in 5 passes Tue Dec 23 19:37:21 2008 distribution of cycle lengths: Tue Dec 23 19:37:21 2008 length 1 : 16066 Tue Dec 23 19:37:21 2008 length 2 : 11406 Tue Dec 23 19:37:21 2008 length 3 : 10192 Tue Dec 23 19:37:21 2008 length 4 : 7446 Tue Dec 23 19:37:21 2008 length 5 : 5239 Tue Dec 23 19:37:21 2008 length 6 : 3296 Tue Dec 23 19:37:21 2008 length 7 : 1905 Tue Dec 23 19:37:21 2008 length 9+: 2179 Tue Dec 23 19:37:21 2008 largest cycle: 19 relations Tue Dec 23 19:37:21 2008 matrix is 57333 x 57729 (13.8 MB) with weight 3385288 (58.64/col) Tue Dec 23 19:37:21 2008 sparse part has weight 3385288 (58.64/col) Tue Dec 23 19:37:22 2008 filtering completed in 3 passes Tue Dec 23 19:37:22 2008 matrix is 52973 x 53036 (12.7 MB) with weight 3125748 (58.94/col) Tue Dec 23 19:37:22 2008 sparse part has weight 3125748 (58.94/col) Tue Dec 23 19:37:22 2008 saving the first 48 matrix rows for later Tue Dec 23 19:37:22 2008 matrix is 52925 x 53036 (9.3 MB) with weight 2584488 (48.73/col) Tue Dec 23 19:37:22 2008 sparse part has weight 2112719 (39.84/col) Tue Dec 23 19:37:22 2008 matrix includes 64 packed rows Tue Dec 23 19:37:22 2008 using block size 21214 for processor cache size 1024 kB Tue Dec 23 19:37:23 2008 commencing Lanczos iteration Tue Dec 23 19:37:23 2008 memory use: 8.5 MB Tue Dec 23 19:37:40 2008 lanczos halted after 838 iterations (dim = 52924) Tue Dec 23 19:37:41 2008 recovered 17 nontrivial dependencies Tue Dec 23 19:37:42 2008 prp38 factor: 17894098175364997990374216358774504223 Tue Dec 23 19:37:42 2008 prp51 factor: 108599467479248166102092723780312641021472824805237 Tue Dec 23 19:37:42 2008 elapsed time 00:50:27

(13·10¹¹⁹-7)/3 = 4(3)₁₁₈1_<120> = 23 · 127 · C117
C117 = P48 · P70
P48 = 113514518603811468544415778265029062834435682901_<48>
P70 = 1306890282973394626750519136011642653347252960413338529753654668995311_<70>

Number: 43331_119 N=148351021339723838867967591007645783407508844003195252767317128837156225037087755334930959716991897751911445851877211 ( 117 digits) SNFS difficulty: 121 digits. Divisors found: r1=113514518603811468544415778265029062834435682901 r2=1306890282973394626750519136011642653347252960413338529753654668995311 Version: Total time: 2.19 hours. Scaled time: 4.38 units (timescale=1.997). Factorization parameters were as follows: name: 43331_119 n: 148351021339723838867967591007645783407508844003195252767317128837156225037087755334930959716991897751911445851877211 m: 1000000000000000000000000 deg: 5 c5: 13 c0: -70 skew: 1.40 type: snfs lss: 1 rlim: 730000 alim: 730000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 730000/730000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [365000, 665001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 87580 x 87818 Total sieving time: 2.19 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,730000,730000,25,25,46,46,2.2,2.2,50000 total time: 2.19 hours. --------- CPU info (if available) ----------

(38·10¹²⁴+61)/9 = 4(2)₁₂₃9_<125> = 11 · 47² · 383 · 170711 · 1500390189343255882395007_<25> · C89
C89 = P41 · P48
P41 = 63555308651323802072448928885255075100069_<41>
P48 = 278699608001282959114888883431789684547614379749_<48>

Tue Dec 23 20:12:21 2008 Msieve v. 1.39 Tue Dec 23 20:12:21 2008 random seeds: 7df503ec db120c14 Tue Dec 23 20:12:21 2008 factoring 17712839607524491181194896261236888181051603158412905861666362722760429830774699542102681 (89 digits) Tue Dec 23 20:12:22 2008 searching for 15-digit factors Tue Dec 23 20:12:24 2008 commencing quadratic sieve (89-digit input) Tue Dec 23 20:12:24 2008 using multiplier of 1 Tue Dec 23 20:12:24 2008 using 32kb Intel Core sieve core Tue Dec 23 20:12:24 2008 sieve interval: 30 blocks of size 32768 Tue Dec 23 20:12:24 2008 processing polynomials in batches of 7 Tue Dec 23 20:12:24 2008 using a sieve bound of 1546837 (58547 primes) Tue Dec 23 20:12:24 2008 using large prime bound of 123746960 (26 bits) Tue Dec 23 20:12:24 2008 using double large prime bound of 368605688486800 (42-49 bits) Tue Dec 23 20:12:24 2008 using trial factoring cutoff of 49 bits Tue Dec 23 20:12:24 2008 polynomial 'A' values have 11 factors Tue Dec 23 21:02:17 2008 58671 relations (16518 full + 42153 combined from 614508 partial), need 58643 Tue Dec 23 21:02:18 2008 begin with 631026 relations Tue Dec 23 21:02:19 2008 reduce to 139761 relations in 11 passes Tue Dec 23 21:02:19 2008 attempting to read 139761 relations Tue Dec 23 21:02:20 2008 recovered 139761 relations Tue Dec 23 21:02:20 2008 recovered 112916 polynomials Tue Dec 23 21:02:20 2008 attempting to build 58671 cycles Tue Dec 23 21:02:21 2008 found 58671 cycles in 6 passes Tue Dec 23 21:02:21 2008 distribution of cycle lengths: Tue Dec 23 21:02:21 2008 length 1 : 16518 Tue Dec 23 21:02:21 2008 length 2 : 11650 Tue Dec 23 21:02:21 2008 length 3 : 10419 Tue Dec 23 21:02:21 2008 length 4 : 7564 Tue Dec 23 21:02:21 2008 length 5 : 5203 Tue Dec 23 21:02:21 2008 length 6 : 3267 Tue Dec 23 21:02:21 2008 length 7 : 1916 Tue Dec 23 21:02:21 2008 length 9+: 2134 Tue Dec 23 21:02:21 2008 largest cycle: 19 relations Tue Dec 23 21:02:21 2008 matrix is 58547 x 58671 (13.9 MB) with weight 3403013 (58.00/col) Tue Dec 23 21:02:21 2008 sparse part has weight 3403013 (58.00/col) Tue Dec 23 21:02:21 2008 filtering completed in 3 passes Tue Dec 23 21:02:21 2008 matrix is 53864 x 53928 (12.9 MB) with weight 3170121 (58.78/col) Tue Dec 23 21:02:21 2008 sparse part has weight 3170121 (58.78/col) Tue Dec 23 21:02:22 2008 saving the first 48 matrix rows for later Tue Dec 23 21:02:22 2008 matrix is 53816 x 53928 (9.1 MB) with weight 2584186 (47.92/col) Tue Dec 23 21:02:22 2008 sparse part has weight 2066484 (38.32/col) Tue Dec 23 21:02:22 2008 matrix includes 64 packed rows Tue Dec 23 21:02:22 2008 using block size 21571 for processor cache size 1024 kB Tue Dec 23 21:02:22 2008 commencing Lanczos iteration Tue Dec 23 21:02:22 2008 memory use: 8.4 MB Tue Dec 23 21:02:40 2008 lanczos halted after 853 iterations (dim = 53814) Tue Dec 23 21:02:40 2008 recovered 16 nontrivial dependencies Tue Dec 23 21:02:41 2008 prp41 factor: 63555308651323802072448928885255075100069 Tue Dec 23 21:02:41 2008 prp48 factor: 278699608001282959114888883431789684547614379749 Tue Dec 23 21:02:41 2008 elapsed time 00:50:20

(38·10¹²³+61)/9 = 4(2)₁₂₂9_<124> = 59 · 29050033885209937_<17> · C106
C106 = P38 · P68
P38 = 90758930904109184231531507553783048527_<38>
P68 = 27142700885477796848302781645863411898017548539507764956042342567569_<68>

Number: 42229_123 N=2463442514215982536119131591935078249728878201624727560526653267928776465809352361520806512445821303420863 ( 106 digits) SNFS difficulty: 125 digits. Divisors found: r1=90758930904109184231531507553783048527 r2=27142700885477796848302781645863411898017548539507764956042342567569 Version: Total time: 1.88 hours. Scaled time: 4.84 units (timescale=2.575). Factorization parameters were as follows: name: 42229_123 n: 2463442514215982536119131591935078249728878201624727560526653267928776465809352361520806512445821303420863 m: 5000000000000000000000000 deg: 5 c5: 304 c0: 1525 skew: 1.38 type: snfs lss: 1 rlim: 880000 alim: 880000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 880000/880000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [440000, 640001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 111021 x 111261 Total sieving time: 1.88 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,125,5,0,0,0,0,0,0,0,0,880000,880000,26,26,46,46,2.3,2.3,50000 total time: 1.88 hours. --------- CPU info (if available) ----------

(38·10¹³¹+61)/9 = 4(2)₁₃₀9_<132> = 3 · 661 · C129
C129 = P62 · P68
P62 = 18931593415430636447428825920870807172531523070990639092291417_<62>
P68 = 11246857801195903571673445644347018389968064581167169333729364888739_<68>

Number: 42229_131 N=212920939093405054070712164509441362694010197792346052557852860424721241665265871014736370258306718215946657701574494312769653163 ( 129 digits) SNFS difficulty: 132 digits. Divisors found: r1=18931593415430636447428825920870807172531523070990639092291417 r2=11246857801195903571673445644347018389968064581167169333729364888739 Version: Total time: 3.43 hours. Scaled time: 7.84 units (timescale=2.282). Factorization parameters were as follows: name: 42229_131 n: 212920939093405054070712164509441362694010197792346052557852860424721241665265871014736370258306718215946657701574494312769653163 m: 100000000000000000000000000 deg: 5 c5: 380 c0: 61 skew: 0.69 type: snfs lss: 1 rlim: 1130000 alim: 1130000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1130000/1130000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [565000, 1015001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 159415 x 159663 Total sieving time: 3.43 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,132,5,0,0,0,0,0,0,0,0,1130000,1130000,26,26,47,47,2.3,2.3,50000 total time: 3.43 hours. --------- CPU info (if available) ----------

(38·10¹²⁵+61)/9 = 4(2)₁₂₄9_<126> = 3⁴ · 23789 · C120
C120 = P48 · P72
P48 = 375555149263134842089555204601763364829365781719_<48>
P72 = 583453381194914039518484879886709379205169265358315351203669660340202799_<72>

Number: 42229_125 N=219118921662736653480897241240879679435937152310888693873048609053267290890344184505974190904823332197951341875626831481 ( 120 digits) SNFS difficulty: 126 digits. Divisors found: r1=375555149263134842089555204601763364829365781719 r2=583453381194914039518484879886709379205169265358315351203669660340202799 Version: Total time: 2.23 hours. Scaled time: 4.43 units (timescale=1.991). Factorization parameters were as follows: name: 42229_125 n: 219118921662736653480897241240879679435937152310888693873048609053267290890344184505974190904823332197951341875626831481 m: 10000000000000000000000000 deg: 5 c5: 38 c0: 61 skew: 1.10 type: snfs lss: 1 rlim: 900000 alim: 900000 lpbr: 26 lpba: 26 mfbr: 46 mfba: 46 rlambda: 2.3 alambda: 2.3 Factor base limits: 900000/900000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 46/46 Sieved rational special-q in [450000, 700001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 123791 x 124029 Total sieving time: 2.23 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,126,5,0,0,0,0,0,0,0,0,900000,900000,26,26,46,46,2.3,2.3,50000 total time: 2.23 hours. --------- CPU info (if available) ----------

(13·10¹⁷⁴-7)/3 = 4(3)₁₇₃1_<175> = 2661733 · 2981915448269_<13> · 57373034177700817_<17> · 210183647146556081_<18> · 1886441303582244311116568671646101_<34> · C89
C89 = P37 · P53
P37 = 1154850117862112282943626662349224241_<37>
P53 = 20781965619296732780146962236360397468436031673870679_<53>

ue Dec 23 21:17:52 2008 Msieve v. 1.39 Tue Dec 23 21:17:52 2008 random seeds: 9d7994a0 f4a4cbfc Tue Dec 23 21:17:52 2008 factoring 24000055444851197132978321002485393490269394924989129370986539182893234062802945405929639 (89 digits) Tue Dec 23 21:17:53 2008 searching for 15-digit factors Tue Dec 23 21:17:54 2008 commencing quadratic sieve (89-digit input) Tue Dec 23 21:17:54 2008 using multiplier of 39 Tue Dec 23 21:17:54 2008 using 32kb Intel Core sieve core Tue Dec 23 21:17:54 2008 sieve interval: 30 blocks of size 32768 Tue Dec 23 21:17:54 2008 processing polynomials in batches of 7 Tue Dec 23 21:17:54 2008 using a sieve bound of 1545007 (58667 primes) Tue Dec 23 21:17:54 2008 using large prime bound of 123600560 (26 bits) Tue Dec 23 21:17:54 2008 using double large prime bound of 367821176096160 (42-49 bits) Tue Dec 23 21:17:54 2008 using trial factoring cutoff of 49 bits Tue Dec 23 21:17:54 2008 polynomial 'A' values have 12 factors Tue Dec 23 22:28:02 2008 58882 relations (15618 full + 43264 combined from 622557 partial), need 58763 Tue Dec 23 22:28:03 2008 begin with 638175 relations Tue Dec 23 22:28:03 2008 reduce to 143131 relations in 9 passes Tue Dec 23 22:28:03 2008 attempting to read 143131 relations Tue Dec 23 22:28:05 2008 recovered 143131 relations Tue Dec 23 22:28:05 2008 recovered 124085 polynomials Tue Dec 23 22:28:05 2008 attempting to build 58882 cycles Tue Dec 23 22:28:05 2008 found 58881 cycles in 5 passes Tue Dec 23 22:28:05 2008 distribution of cycle lengths: Tue Dec 23 22:28:05 2008 length 1 : 15618 Tue Dec 23 22:28:05 2008 length 2 : 11396 Tue Dec 23 22:28:05 2008 length 3 : 10604 Tue Dec 23 22:28:05 2008 length 4 : 7945 Tue Dec 23 22:28:05 2008 length 5 : 5461 Tue Dec 23 22:28:05 2008 length 6 : 3495 Tue Dec 23 22:28:05 2008 length 7 : 2019 Tue Dec 23 22:28:05 2008 length 9+: 2343 Tue Dec 23 22:28:05 2008 largest cycle: 17 relations Tue Dec 23 22:28:06 2008 matrix is 58667 x 58881 (14.2 MB) with weight 3480054 (59.10/col) Tue Dec 23 22:28:06 2008 sparse part has weight 3480054 (59.10/col) Tue Dec 23 22:28:06 2008 filtering completed in 3 passes Tue Dec 23 22:28:06 2008 matrix is 54828 x 54892 (13.3 MB) with weight 3262907 (59.44/col) Tue Dec 23 22:28:06 2008 sparse part has weight 3262907 (59.44/col) Tue Dec 23 22:28:06 2008 saving the first 48 matrix rows for later Tue Dec 23 22:28:06 2008 matrix is 54780 x 54892 (8.1 MB) with weight 2523354 (45.97/col) Tue Dec 23 22:28:06 2008 sparse part has weight 1787841 (32.57/col) Tue Dec 23 22:28:06 2008 matrix includes 64 packed rows Tue Dec 23 22:28:06 2008 using block size 21956 for processor cache size 1024 kB Tue Dec 23 22:28:07 2008 commencing Lanczos iteration Tue Dec 23 22:28:07 2008 memory use: 8.0 MB Tue Dec 23 22:28:24 2008 lanczos halted after 868 iterations (dim = 54778) Tue Dec 23 22:28:24 2008 recovered 17 nontrivial dependencies Tue Dec 23 22:28:24 2008 prp37 factor: 1154850117862112282943626662349224241 Tue Dec 23 22:28:24 2008 prp53 factor: 20781965619296732780146962236360397468436031673870679 Tue Dec 23 22:28:24 2008 elapsed time 01:10:32

Dec 23, 2008 (6th)

By Jo Yeong Uk / GGNFS / Msieve v1.39
(38·10¹⁵⁸+7)/9 = 4(2)₁₅₇3_<159> = 3 · 41 · 227 · 457 · 719 · 11692937714243057_<17> · C133
C133 = P60 · P74
P60 = 261684502017364426401172993314582377543873715761538550838501_<60>
P74 = 15040538615515346545319103996178595611693408558594037216409591162891195973_<74>

I've used Greg Childer's x64 binaries that is about 30% faster. Number: 42223_158 N=3935875857674073259892366744726611131660458011927081245662043080032693008432327787653104908465235028172227775906183483719689864556473 ( 133 digits) SNFS difficulty: 161 digits. Divisors found: r1=261684502017364426401172993314582377543873715761538550838501 r2=15040538615515346545319103996178595611693408558594037216409591162891195973 Version: Total time: 16.42 hours. Scaled time: 39.20 units (timescale=2.387). Factorization parameters were as follows: n: 3935875857674073259892366744726611131660458011927081245662043080032693008432327787653104908465235028172227775906183483719689864556473 m: 100000000000000000000000000000000 deg: 5 c5: 19 c0: 350 skew: 1.79 type: snfs lss: 1 rlim: 3400000 alim: 3400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.4 alambda: 2.4 Factor base limits: 3400000/3400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved rational special-q in [1700000, 3100001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9164673 Max relations in full relation-set: Initial matrix: Pruned matrix : 657541 x 657789 Total sieving time: 14.77 hours. Total relation processing time: 0.62 hours. Matrix solve time: 0.95 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,3400000,3400000,27,27,51,51,2.4,2.4,100000 total time: 16.42 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(13·10¹⁶³-7)/3 = 4(3)₁₆₂1_<164> = 23 · 181 · 201977806379599_<15> · 256380435467453624357_<21> · 3848836599303511776161_<22> · C104
C104 = P40 · P65
P40 = 2484322471920498002597770188046418572961_<40>
P65 = 21022759073577810522071683163551125750312379421937000260369560979_<65>

Number: 43331_163 N=52227312788259904783285448177771151215979194504591185340103120146351292794322523024425734515127250088819 ( 104 digits) Divisors found: r1=2484322471920498002597770188046418572961 r2=21022759073577810522071683163551125750312379421937000260369560979 Version: Total time: 3.98 hours. Scaled time: 9.53 units (timescale=2.391). Factorization parameters were as follows: name: 43331_163 n: 52227312788259904783285448177771151215979194504591185340103120146351292794322523024425734515127250088819 skew: 22078.67 # norm 5.99e+14 c5: 21240 c4: -1497386772 c3: -38425098620186 c2: 845882405351926079 c1: 8026727642520429063354 c0: 1072508182475386490862336 # alpha -6.69 Y1: 84046748929 Y0: -75536254703912113145 # Murphy_E 2.05e-09 # M 14288233827694019863237397998856850064401035115600452898033582468342007884707128037624699464864009909031 type: gnfs rlim: 1500000 alim: 1500000 lpbr: 26 lpba: 26 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 50/50 Sieved algebraic special-q in [750000, 1500001) Primes: rational ideals reading, algebraic ideals reading, Relations: 5069392 Max relations in full relation-set: Initial matrix: Pruned matrix : 241075 x 241323 Total sieving time: 3.46 hours. Total relation processing time: 0.36 hours. Matrix solve time: 0.12 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: gnfs,103,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,1500000,1500000,26,26,50,50,2.6,2.6,50000 total time: 3.98 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 23, 2008 (5th)

By Robert Backstrom / GGNFS, Msieve, GMP-ECM
(13·10¹⁰⁶-7)/3 = 4(3)₁₀₅1_<107> = 41 · 13774823 · 49522433 · C91
C91 = P32 · P59
P32 = 57847164065344667246749592041001_<32>
P59 = 26783551748975471064496580057189581449979924547068814782949_<59>

Number: n N=1549352512275633183368088459353775952136320751322520942606357553923121412953602781723691949 ( 91 digits) SNFS difficulty: 107 digits. Divisors found: r1=57847164065344667246749592041001 (pp32) r2=26783551748975471064496580057189581449979924547068814782949 (pp59) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.65 hours. Scaled time: 1.18 units (timescale=1.829). Factorization parameters were as follows: name: KA_4_3_105_1 n: 1549352512275633183368088459353775952136320751322520942606357553923121412953602781723691949 type: snfs skew: 0.56 deg: 5 c5: 130 c0: -7 m: 1000000000000000000000 rlim: 450000 alim: 450000 lpbr: 28 lpba: 28 mfbr: 56 mfba: 56 rlambda: 2.5 alambda: 2.5 qintsize: 2000 Factor base limits: 450000/450000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 56/56 Sieved algebraic special-q in [225000, 271001) Primes: RFBsize:37706, AFBsize:37704, largePrimes:4143192 encountered Relations: rels:3498691, finalFF:97136 Max relations in full relation-set: 48 Initial matrix: 75477 x 97136 with sparse part having weight 10956977. Pruned matrix : 70519 x 70960 with weight 5601496. Total sieving time: 0.56 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.02 hours. Total square root time: 0.01 hours, sqrts: 1. Prototype def-par.txt line would be: snfs,107,5,0,0,0,0,0,0,0,0,450000,450000,28,28,56,56,2.5,2.5,50000 total time: 0.65 hours. --------- CPU info (if available) ----------

(38·10¹¹⁶+61)/9 = 4(2)₁₁₅9_<117> = 3² · 11 · 13 · 6271 · 7643257 · 44775959 · 883573237 · C87
C87 = P40 · P47
P40 = 4242755187407345742527427668930198334521_<40>
P47 = 40776679208206304454293512576431198414080057327_<47>

Tue Dec 23 18:19:00 2008 Tue Dec 23 18:19:00 2008 Tue Dec 23 18:19:00 2008 Msieve v. 1.39 Tue Dec 23 18:19:00 2008 random seeds: 96cc2620 f2dff84d Tue Dec 23 18:19:00 2008 factoring 173005467235862557859424523342614033694193668612191137256544163118007289277935603085367 (87 digits) Tue Dec 23 18:19:01 2008 searching for 15-digit factors Tue Dec 23 18:19:02 2008 commencing quadratic sieve (87-digit input) Tue Dec 23 18:19:02 2008 using multiplier of 7 Tue Dec 23 18:19:02 2008 using 64kb Opteron sieve core Tue Dec 23 18:19:02 2008 sieve interval: 10 blocks of size 65536 Tue Dec 23 18:19:02 2008 processing polynomials in batches of 11 Tue Dec 23 18:19:02 2008 using a sieve bound of 1480243 (56254 primes) Tue Dec 23 18:19:02 2008 using large prime bound of 118419440 (26 bits) Tue Dec 23 18:19:02 2008 using double large prime bound of 340534638927600 (41-49 bits) Tue Dec 23 18:19:02 2008 using trial factoring cutoff of 49 bits Tue Dec 23 18:19:02 2008 polynomial 'A' values have 11 factors Tue Dec 23 18:48:34 2008 56642 relations (16217 full + 40425 combined from 588342 partial), need 56350 Tue Dec 23 18:48:34 2008 begin with 604559 relations Tue Dec 23 18:48:34 2008 reduce to 134247 relations in 11 passes Tue Dec 23 18:48:34 2008 attempting to read 134247 relations Tue Dec 23 18:48:35 2008 recovered 134247 relations Tue Dec 23 18:48:35 2008 recovered 109821 polynomials Tue Dec 23 18:48:35 2008 attempting to build 56642 cycles Tue Dec 23 18:48:36 2008 found 56642 cycles in 5 passes Tue Dec 23 18:48:36 2008 distribution of cycle lengths: Tue Dec 23 18:48:36 2008 length 1 : 16217 Tue Dec 23 18:48:36 2008 length 2 : 11293 Tue Dec 23 18:48:36 2008 length 3 : 10010 Tue Dec 23 18:48:36 2008 length 4 : 7280 Tue Dec 23 18:48:36 2008 length 5 : 5006 Tue Dec 23 18:48:36 2008 length 6 : 3000 Tue Dec 23 18:48:36 2008 length 7 : 1762 Tue Dec 23 18:48:36 2008 length 9+: 2074 Tue Dec 23 18:48:36 2008 largest cycle: 17 relations Tue Dec 23 18:48:36 2008 matrix is 56254 x 56642 (12.9 MB) with weight 3166386 (55.90/col) Tue Dec 23 18:48:36 2008 sparse part has weight 3166386 (55.90/col) Tue Dec 23 18:48:37 2008 filtering completed in 3 passes Tue Dec 23 18:48:37 2008 matrix is 51309 x 51373 (11.8 MB) with weight 2892193 (56.30/col) Tue Dec 23 18:48:37 2008 sparse part has weight 2892193 (56.30/col) Tue Dec 23 18:48:37 2008 saving the first 48 matrix rows for later Tue Dec 23 18:48:37 2008 matrix is 51261 x 51373 (7.7 MB) with weight 2276433 (44.31/col) Tue Dec 23 18:48:37 2008 sparse part has weight 1699820 (33.09/col) Tue Dec 23 18:48:37 2008 matrix includes 64 packed rows Tue Dec 23 18:48:37 2008 using block size 20549 for processor cache size 1024 kB Tue Dec 23 18:48:37 2008 commencing Lanczos iteration Tue Dec 23 18:48:37 2008 memory use: 7.5 MB Tue Dec 23 18:48:51 2008 lanczos halted after 812 iterations (dim = 51259) Tue Dec 23 18:48:51 2008 recovered 16 nontrivial dependencies Tue Dec 23 18:48:52 2008 prp40 factor: 4242755187407345742527427668930198334521 Tue Dec 23 18:48:52 2008 prp47 factor: 40776679208206304454293512576431198414080057327 Tue Dec 23 18:48:52 2008 elapsed time 00:29:52

(13·10¹³⁴-7)/3 = 4(3)₁₃₃1_<135> = 8849 · 48271117 · 8224435209442541_<16> · 423468662193971749903_<21> · C87
C87 = P32 · P55
P32 = 69478828398569728593459721798867_<32>
P55 = 4192380641004827675507764758323249935285647811508989127_<55>

Tue Dec 23 19:41:18 2008 Tue Dec 23 19:41:18 2008 Tue Dec 23 19:41:18 2008 Msieve v. 1.39 Tue Dec 23 19:41:18 2008 random seeds: baed84ac 587f7957 Tue Dec 23 19:41:18 2008 factoring 291281695137860183482012662507685449765126395405237570140944533477572342538205183919109 (87 digits) Tue Dec 23 19:41:18 2008 searching for 15-digit factors Tue Dec 23 19:41:19 2008 commencing quadratic sieve (87-digit input) Tue Dec 23 19:41:19 2008 using multiplier of 29 Tue Dec 23 19:41:19 2008 using 64kb Opteron sieve core Tue Dec 23 19:41:19 2008 sieve interval: 10 blocks of size 65536 Tue Dec 23 19:41:19 2008 processing polynomials in batches of 11 Tue Dec 23 19:41:19 2008 using a sieve bound of 1489667 (56642 primes) Tue Dec 23 19:41:19 2008 using large prime bound of 119173360 (26 bits) Tue Dec 23 19:41:19 2008 using double large prime bound of 344447000754720 (42-49 bits) Tue Dec 23 19:41:19 2008 using trial factoring cutoff of 49 bits Tue Dec 23 19:41:19 2008 polynomial 'A' values have 11 factors Tue Dec 23 20:13:40 2008 56750 relations (16023 full + 40727 combined from 592860 partial), need 56738 Tue Dec 23 20:13:40 2008 begin with 608883 relations Tue Dec 23 20:13:41 2008 reduce to 135001 relations in 8 passes Tue Dec 23 20:13:41 2008 attempting to read 135001 relations Tue Dec 23 20:13:42 2008 recovered 135001 relations Tue Dec 23 20:13:42 2008 recovered 113426 polynomials Tue Dec 23 20:13:42 2008 attempting to build 56750 cycles Tue Dec 23 20:13:42 2008 found 56750 cycles in 6 passes Tue Dec 23 20:13:42 2008 distribution of cycle lengths: Tue Dec 23 20:13:42 2008 length 1 : 16023 Tue Dec 23 20:13:42 2008 length 2 : 11360 Tue Dec 23 20:13:42 2008 length 3 : 9954 Tue Dec 23 20:13:42 2008 length 4 : 7463 Tue Dec 23 20:13:42 2008 length 5 : 5058 Tue Dec 23 20:13:42 2008 length 6 : 3100 Tue Dec 23 20:13:42 2008 length 7 : 1796 Tue Dec 23 20:13:42 2008 length 9+: 1996 Tue Dec 23 20:13:42 2008 largest cycle: 19 relations Tue Dec 23 20:13:42 2008 matrix is 56642 x 56750 (13.3 MB) with weight 3250880 (57.28/col) Tue Dec 23 20:13:42 2008 sparse part has weight 3250880 (57.28/col) Tue Dec 23 20:13:43 2008 filtering completed in 3 passes Tue Dec 23 20:13:43 2008 matrix is 52021 x 52085 (12.3 MB) with weight 3026197 (58.10/col) Tue Dec 23 20:13:43 2008 sparse part has weight 3026197 (58.10/col) Tue Dec 23 20:13:43 2008 saving the first 48 matrix rows for later Tue Dec 23 20:13:43 2008 matrix is 51973 x 52085 (8.6 MB) with weight 2442834 (46.90/col) Tue Dec 23 20:13:43 2008 sparse part has weight 1949032 (37.42/col) Tue Dec 23 20:13:43 2008 matrix includes 64 packed rows Tue Dec 23 20:13:43 2008 using block size 20834 for processor cache size 1024 kB Tue Dec 23 20:13:44 2008 commencing Lanczos iteration Tue Dec 23 20:13:44 2008 memory use: 8.0 MB Tue Dec 23 20:13:59 2008 lanczos halted after 823 iterations (dim = 51967) Tue Dec 23 20:13:59 2008 recovered 13 nontrivial dependencies Tue Dec 23 20:14:00 2008 prp32 factor: 69478828398569728593459721798867 Tue Dec 23 20:14:00 2008 prp55 factor: 4192380641004827675507764758323249935285647811508989127 Tue Dec 23 20:14:00 2008 elapsed time 00:32:42

(13·10¹⁰⁹-7)/3 = 4(3)₁₀₈1_<110> = 17 · 137 · 977 · C104
C104 = P31 · P73
P31 = 3407814690944317539762588740159_<31>
P73 = 5588330392801960092177439750747650769278886747644606354321657148324217573_<73>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 19043994410441148270827281371648092179964575240551285550193450360143908141146468972425614524063478614107 (104 digits) Using B1=714000, B2=696728352, polynomial Dickson(3), sigma=1623556616 Step 1 took 4969ms Step 2 took 2609ms ********** Factor found in step 2: 3407814690944317539762588740159 Found probable prime factor of 31 digits: 3407814690944317539762588740159 Probable prime cofactor 5588330392801960092177439750747650769278886747644606354321657148324217573 has 73 digits

(38·10¹⁰⁹+61)/9 = 4(2)₁₀₈9_<110> = 7 · 199 · 881 · 580373 · C98
C98 = P44 · P55
P44 = 26751738096440014307990911916120465357207011_<44>
P55 = 2215923985067384009560418171449180919028006614390617771_<55>

Number: n N=59279818090142310194468555816137740448324236376809698473858515326593093225915093020485675422392481 ( 98 digits) SNFS difficulty: 111 digits. Divisors found: Wed Dec 24 00:30:23 2008 prp44 factor: 26751738096440014307990911916120465357207011 Wed Dec 24 00:30:23 2008 prp55 factor: 2215923985067384009560418171449180919028006614390617771 Wed Dec 24 00:30:23 2008 elapsed time 00:05:05 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 0.65 hours. Scaled time: 1.20 units (timescale=1.828). Factorization parameters were as follows: name: KA_4_2_108_9 n: 59279818090142310194468555816137740448324236376809698473858515326593093225915093020485675422392481 type: snfs skew: 1.74 deg: 5 c5: 19 c0: 305 m: 10000000000000000000000 rlim: 450000 alim: 450000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 5000 Factor base limits: 450000/450000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 275001) Primes: RFBsize:37706, AFBsize:37830, largePrimes:4770991 encountered Relations: rels:3870829, finalFF:81071 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 105623 hash collisions in 3950766 relations Msieve: matrix is 89786 x 90033 (23.6 MB) Total sieving time: 0.60 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,111,5,0,0,0,0,0,0,0,0,450000,450000,29,29,58,58,2.5,2.5,50000 total time: 0.65 hours. --------- CPU info (if available) ----------

Dec 23, 2008 (4th)

By Sinkiti Sibata / Msieve
(38·10¹⁴⁹+43)/9 = 4(2)₁₄₈7_<150> = 13 · 113453640491_<12> · C138
C138 = P39 · P47 · P53
P39 = 123132274553465756860058461410327710779_<39>
P47 = 27267256871151239064440712042018508774862667557_<47>
P53 = 85264047995684401299884905037961478641338880822995323_<53>

Number: 42227_149 N=286272281242565584871308935586551398963328947291933211769489506901789407053841847782020315712273819190869798534111037762948452697250984669 ( 138 digits) SNFS difficulty: 151 digits. Divisors found: r1=123132274553465756860058461410327710779 r2=27267256871151239064440712042018508774862667557 r3=85264047995684401299884905037961478641338880822995323 Version: Total time: 17.03 hours. Scaled time: 33.49 units (timescale=1.967). Factorization parameters were as follows: name: 42227_149 n: 286272281242565584871308935586551398963328947291933211769489506901789407053841847782020315712273819190869798534111037762948452697250984669 m: 1000000000000000000000000000000 deg: 5 c5: 19 c0: 215 skew: 1.62 type: snfs lss: 1 rlim: 2300000 alim: 2300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1150000, 1750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 326210 x 326458 Total sieving time: 17.03 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2300000,2300000,27,27,49,49,2.4,2.4,100000 total time: 17.03 hours. --------- CPU info (if available) ----------

Dec 23, 2008 (3rd)

By Serge Batalov / GMP-ECM 6.2.1
(38·10¹⁷⁹+43)/9 = 4(2)₁₇₈7_<180> = 13 · 190548791 · C171
C171 = P32 · C139
P32 = 83693711822605989870189783269927_<32>
C139 = [2036567026754301909068906536670007279613488322697273803941595712633680899678332169392476463478230146670448373216770032371376154711024549247_<139>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=28284232 Step 1 took 50467ms Step 2 took 24270ms ********** Factor found in step 2: 83693711822605989870189783269927 Found probable prime factor of 32 digits: 83693711822605989870189783269927 Composite cofactor has 139 digits

(38·10¹⁹⁵+43)/9 = 4(2)₁₉₄7_<196> = 3 · 1409 · 36583 · 2631581 · C182
C182 = P37 · P145
P37 = 1110098676846052025875562910419707159_<37>
P145 = 9346547020444687949473270005207416033036409081717352834060726263287081343511433873690747964630107753834169432220989123151666306482271859585653093_<145>

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=3282926492 Step 1 took 58616ms Step 2 took 26203ms ********** Factor found in step 2: 1110098676846052025875562910419707159 Found probable prime factor of 37 digits: 1110098676846052025875562910419707159 Probable prime cofactor has 145 digits

Dec 23, 2008 (2nd)

By Robert Backstrom / GMP-ECM
(11·10¹⁶⁶-17)/3 = 3(6)₁₆₅1_<167> = 31 · 9645541 · C159
C159 = P40 · P120
P40 = 1116427148631667120168455525371131408601_<40>
P120 = 109838035390645973298719203114797829250387790912028941879398460215801086922957023513075842014334465944683742916668887991_<120>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 122626164662483025347743472836949508140489448044728201240835654816634849691809178531191224129656978175172463918374192254346624590463586353818380837812123010591 (159 digits) Using B1=2860000, B2=4281671950, polynomial Dickson(6), sigma=2445717877 Step 1 took 37615ms Step 2 took 13651ms ********** Factor found in step 2: 1116427148631667120168455525371131408601 Found probable prime factor of 40 digits: 1116427148631667120168455525371131408601 Probable prime cofactor 109838035390645973298719203114797829250387790912028941879398460215801086922957023513075842014334465944683742916668887991 has 120 digits

Dec 23, 2008

Factorizations of 422...229 and Factorizations of 433...331 have been extended up to n=205. Unknown factors of the composite numbers that appeared newly are probably 30-digit or more.

Dec 22, 2008 (5th)

By Jo Yeong Uk / GMP-ECM, Msieve
(37·10¹⁹⁰+53)/9 = 4(1)₁₈₉7_<191> = 59 · 33366083669_<11> · 1038688946123696607997710239_<28> · 228822554008790119385212155709949_<33> · C119
C119 = P37 · P41 · P42
P37 = 6700559039122072293901319740648826129_<37>
P41 = 94122795556702802098640504555138641771009_<41>
P42 = 139319457310594504389225773069331905769337_<42>

GMP-ECM 6.2.1 [powered by GMP 4.2.3] [ECM] Input number is 87865347299839227077677777536365983116150872999131750437968032584396075641901842890425376739301590272179304048017141257 (119 digits) Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=2495475907 Step 1 took 13322ms Step 2 took 9282ms ********** Factor found in step 2: 6700559039122072293901319740648826129 Found probable prime factor of 37 digits: 6700559039122072293901319740648826129 Composite cofactor 13113136797515870136423584090069674988260781902340888649157796440990324986327751033 has 83 digits Mon Dec 22 22:59:56 2008 Mon Dec 22 22:59:56 2008 Mon Dec 22 22:59:56 2008 Msieve v. 1.39 Mon Dec 22 22:59:56 2008 random seeds: 5344db90 d0343cf0 Mon Dec 22 22:59:56 2008 factoring 13113136797515870136423584090069674988260781902340888649157796440990324986327751033 (83 digits) Mon Dec 22 22:59:57 2008 searching for 15-digit factors Mon Dec 22 22:59:58 2008 commencing quadratic sieve (83-digit input) Mon Dec 22 22:59:58 2008 using multiplier of 1 Mon Dec 22 22:59:58 2008 using VC8 32kb sieve core Mon Dec 22 22:59:58 2008 sieve interval: 12 blocks of size 32768 Mon Dec 22 22:59:58 2008 processing polynomials in batches of 17 Mon Dec 22 22:59:58 2008 using a sieve bound of 1357919 (52059 primes) Mon Dec 22 22:59:58 2008 using large prime bound of 124928548 (26 bits) Mon Dec 22 22:59:58 2008 using trial factoring cutoff of 27 bits Mon Dec 22 22:59:58 2008 polynomial 'A' values have 10 factors Mon Dec 22 23:15:29 2008 52266 relations (26562 full + 25704 combined from 277983 partial), need 52155 Mon Dec 22 23:15:29 2008 begin with 304545 relations Mon Dec 22 23:15:29 2008 reduce to 74683 relations in 2 passes Mon Dec 22 23:15:29 2008 attempting to read 74683 relations Mon Dec 22 23:15:30 2008 recovered 74683 relations Mon Dec 22 23:15:30 2008 recovered 66029 polynomials Mon Dec 22 23:15:30 2008 attempting to build 52266 cycles Mon Dec 22 23:15:30 2008 found 52266 cycles in 1 passes Mon Dec 22 23:15:30 2008 distribution of cycle lengths: Mon Dec 22 23:15:30 2008 length 1 : 26562 Mon Dec 22 23:15:30 2008 length 2 : 25704 Mon Dec 22 23:15:30 2008 largest cycle: 2 relations Mon Dec 22 23:15:30 2008 matrix is 52059 x 52266 (7.7 MB) with weight 1591401 (30.45/col) Mon Dec 22 23:15:30 2008 sparse part has weight 1591401 (30.45/col) Mon Dec 22 23:15:30 2008 filtering completed in 3 passes Mon Dec 22 23:15:30 2008 matrix is 37218 x 37282 (6.0 MB) with weight 1276780 (34.25/col) Mon Dec 22 23:15:30 2008 sparse part has weight 1276780 (34.25/col) Mon Dec 22 23:15:30 2008 saving the first 48 matrix rows for later Mon Dec 22 23:15:30 2008 matrix is 37170 x 37282 (4.8 MB) with weight 1060890 (28.46/col) Mon Dec 22 23:15:30 2008 sparse part has weight 894883 (24.00/col) Mon Dec 22 23:15:30 2008 matrix includes 64 packed rows Mon Dec 22 23:15:30 2008 using block size 14912 for processor cache size 4096 kB Mon Dec 22 23:15:30 2008 commencing Lanczos iteration Mon Dec 22 23:15:30 2008 memory use: 4.5 MB Mon Dec 22 23:15:35 2008 lanczos halted after 589 iterations (dim = 37168) Mon Dec 22 23:15:35 2008 recovered 15 nontrivial dependencies Mon Dec 22 23:15:35 2008 prp41 factor: 94122795556702802098640504555138641771009 Mon Dec 22 23:15:35 2008 prp42 factor: 139319457310594504389225773069331905769337 Mon Dec 22 23:15:35 2008 elapsed time 00:15:39

Dec 22, 2008 (4th)

By Serge Batalov / GMP-ECM 6.2.1
(38·10¹⁷⁶+43)/9 = 4(2)₁₇₅7_<177> = 7 · 953 · 18013 · 276447312401475563_<18> · C152
C152 = P36 · C116
P36 = 178756426448137413914826142437964919_<36>
C116 = [71103349768243348700450905945142994417179643820598258646824953982535526988209326934630523825762360058327976339721717_<116>]

Using B1=11000000, B2=35133391030, polynomial Dickson(12), sigma=1342266695 Step 1 took 43401ms Step 2 took 21416ms ********** Factor found in step 2: 178756426448137413914826142437964919 Found probable prime factor of 36 digits: 178756426448137413914826142437964919 Composite cofactor has 116 digits

Dec 22, 2008 (3rd)

By Jo Yeong Uk / GGNFS-0.77.1-20050930-nocona, Msieve v1.39
(38·10¹⁵⁶+7)/9 = 4(2)₁₅₅3_<157> = 1571 · 20627 · 161999 · 31370407 · C137
C137 = P40 · P97
P40 = 3151311867708119352908892784260206809733_<40>
P97 = 8135888003589561713984004929583919997606982433878122227315798705604256568191678963555861658276451_<97>

Number: 42223_156 N=25638720420055904175047718597666401571261026682120717702745767511977789529191792514452212244210202584659272309033290926661594350071497583 ( 137 digits) SNFS difficulty: 157 digits. Divisors found: r1=3151311867708119352908892784260206809733 r2=8135888003589561713984004929583919997606982433878122227315798705604256568191678963555861658276451 Version: Total time: 17.75 hours. Scaled time: 42.36 units (timescale=2.387). Factorization parameters were as follows: n: 25638720420055904175047718597666401571261026682120717702745767511977789529191792514452212244210202584659272309033290926661594350071497583 m: 10000000000000000000000000000000 deg: 5 c5: 380 c0: 7 skew: 0.45 type: snfs lss: 1 rlim: 3000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1500000, 2600001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8115178 Max relations in full relation-set: Initial matrix: Pruned matrix : 565574 x 565822 Total sieving time: 16.58 hours. Total relation processing time: 0.41 hours. Matrix solve time: 0.68 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000 total time: 17.75 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

(35·10¹⁸⁶-17)/9 = 3(8)₁₈₅7_<187> = 157 · 24359 · 61381 · 8547631 · 741825421 · 12281370259_<11> · 1354976246545216979406271187005039_<34> · C117
C117 = P43 · P74
P43 = 5120353883635458429190544130895666258719013_<43>
P74 = 30662425523328166855980476520758336325858134810791000702868819091594477883_<74>

Number: 38887_186 N=157002469610056383002517699709502160585077480848188350871607152214104956824868980051866840757039680270434992140089479 ( 117 digits) Divisors found: r1=5120353883635458429190544130895666258719013 r2=30662425523328166855980476520758336325858134810791000702868819091594477883 Version: Total time: 22.72 hours. Scaled time: 54.15 units (timescale=2.384). Factorization parameters were as follows: name: 38887_186 n: 157002469610056383002517699709502160585077480848188350871607152214104956824868980051866840757039680270434992140089479 skew: 90503.15 # norm 3.19e+16 c5: 7200 c4: -1050000632 c3: 784336535541926 c2: 6556944883925153517 c1: -2168736184919240296891976 c0: 307461253102532191921522760 # alpha -7.15 Y1: 2113994864537 Y0: -29357272872032918557839 # Murphy_E 4.67e-10 # M 22297279247945908317688117096806927032070203219509894621581388695827552723266532914832455914310598281190746054030867 type: gnfs rlim: 3300000 alim: 3300000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 qintsize: 75000 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 52/52 Sieved algebraic special-q in [1650000, 2925001) Primes: rational ideals reading, algebraic ideals reading, Relations: 9009334 Max relations in full relation-set: Initial matrix: Pruned matrix : 505641 x 505889 Polynomial selection time: 1.73 hours. Total sieving time: 19.51 hours. Total relation processing time: 0.70 hours. Matrix solve time: 0.67 hours. Time per square root: 0.10 hours. Prototype def-par.txt line would be: gnfs,116,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3300000,3300000,27,27,52,52,2.4,2.4,75000 total time: 22.72 hours. --------- CPU info (if available) ---------- Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Intel(R) Core(TM)2 Quad CPU Q6700 @ 2.66GHz stepping 0b Memory: 8047068k/8912896k available (2460k kernel code, 339224k reserved, 1251k data, 196k init) Calibrating delay using timer specific routine.. 5347.60 BogoMIPS (lpj=2673803) Calibrating delay using timer specific routine.. 5344.76 BogoMIPS (lpj=2672384) Calibrating delay using timer specific routine.. 5497.76 BogoMIPS (lpj=2748880) Calibrating delay using timer specific routine.. 5344.69 BogoMIPS (lpj=2672347)

Dec 22, 2008 (2nd)

By Sinkiti Sibata / GGNFS, Msieve
(38·10¹⁵⁰+43)/9 = 4(2)₁₄₉7_<151> = 3 · 5404033 · 1315507653822793_<16> · 1793543806775351758201343_<25> · C105
C105 = P46 · P59
P46 = 1474436240860335083889521243713798444857541487_<46>
P59 = 74863559958939232893634955690188665701792653148056199268121_<59>

Number: 42227_150 N=110381545923280664073717632487428289003590698192574383665984937129689496720053069202801052883676794035927 ( 105 digits) Divisors found: r1=1474436240860335083889521243713798444857541487 (pp46) r2=74863559958939232893634955690188665701792653148056199268121 (pp59) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 15.61 hours. Scaled time: 7.37 units (timescale=0.472). Factorization parameters were as follows: name: 42227_150 n: 110381545923280664073717632487428289003590698192574383665984937129689496720053069202801052883676794035927 skew: 13420.60 # norm 9.52e+14 c5: 107460 c4: -360905256 c3: -62359547385495 c2: -486725426096074673 c1: 4105199284466708023171 c0: -86832314907525862615335 # alpha -6.88 Y1: 67446069691 Y0: -63435188891743035196 # Murphy_E 1.97e-09 # M 69240885770336502168462731026371669070686911436648784413026709589522938575061457362992740606116577231612 type: gnfs rlim: 2500000 alim: 2500000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 150000 Factor base limits: 2500000/2500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1250000, 2150001) Primes: RFBsize:183072, AFBsize:182694, largePrimes:4397803 encountered Relations: rels:4492136, finalFF:486116 Max relations in full relation-set: 28 Initial matrix: 365843 x 486116 with sparse part having weight 33668090. Pruned matrix : 267920 x 269813 with weight 16505009. Total sieving time: 13.47 hours. Total relation processing time: 0.27 hours. Matrix solve time: 1.68 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2500000,2500000,26,26,49,49,2.6,2.6,150000 total time: 15.61 hours. --------- CPU info (if available) ----------

(38·10¹⁴⁰+43)/9 = 4(2)₁₃₉7_<141> = 7 · 2039 · 16902410577105783452297695849_<29> · C109
C109 = P44 · P66
P44 = 12699265945218353733988416402502984096925867_<44>
P66 = 137815655861186307456994950037515633314473360940130795156807220753_<66>

Number: 42227_140 N=1750157665195895484648268135865022403532332639214085226117860426329641105594587945290563927802167775344917851 ( 109 digits) SNFS difficulty: 141 digits. Divisors found: r1=12699265945218353733988416402502984096925867 r2=137815655861186307456994950037515633314473360940130795156807220753 Version: Total time: 10.29 hours. Scaled time: 20.61 units (timescale=2.003). Factorization parameters were as follows: name: 42227_140 n: 1750157665195895484648268135865022403532332639214085226117860426329641105594587945290563927802167775344917851 m: 10000000000000000000000000000 deg: 5 c5: 38 c0: 43 skew: 1.03 type: snfs lss: 1 rlim: 1600000 alim: 1600000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1600000/1600000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [800000, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 255864 x 256112 Total sieving time: 10.29 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,141,5,0,0,0,0,0,0,0,0,1600000,1600000,26,26,48,48,2.3,2.3,100000 total time: 10.29 hours. --------- CPU info (if available) ----------

(38·10¹⁴⁴+43)/9 = 4(2)₁₄₃7_<145> = 3³ · 31 · 1606157397847_<13> · C130
C130 = P59 · P71
P59 = 43754364299985865542408997922500687052406885856436424436163_<59>
P71 = 71780445327028706891060593598257035580865296056623661966850183987404811_<71>

Number: 42227_144 N=3140707754454032100209047495164969064451607130248949747422702757390517541777485585989335253410516591681046770886049171734308580193 ( 130 digits) SNFS difficulty: 146 digits. Divisors found: r1=43754364299985865542408997922500687052406885856436424436163 r2=71780445327028706891060593598257035580865296056623661966850183987404811 Version: Total time: 10.43 hours. Scaled time: 20.90 units (timescale=2.003). Factorization parameters were as follows: name: 42227_144 n: 3140707754454032100209047495164969064451607130248949747422702757390517541777485585989335253410516591681046770886049171734308580193 m: 100000000000000000000000000000 deg: 5 c5: 19 c0: 215 skew: 1.62 type: snfs lss: 1 rlim: 1920000 alim: 1920000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1920000/1920000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [960000, 1960001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 262590 x 262838 Total sieving time: 10.43 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,1920000,1920000,26,26,49,49,2.3,2.3,100000 total time: 10.43 hours. --------- CPU info (if available) ----------

(38·10¹⁴⁶+43)/9 = 4(2)₁₄₅7_<147> = 7² · 9222235349_<10> · 81823735257070026169067_<23> · C113
C113 = P54 · P59
P54 = 324669516616670697087399863175104643086264125364574157_<54>
P59 = 35171265133319275701635037151479684144701079965460533176633_<59>

Number: 42227_146 N=11419037649631533302730167351422803394561213724399974201383070218486899102995497193219122768932079190766508073381 ( 113 digits) SNFS difficulty: 148 digits. Divisors found: r1=324669516616670697087399863175104643086264125364574157 r2=35171265133319275701635037151479684144701079965460533176633 Version: Total time: 13.24 hours. Scaled time: 31.31 units (timescale=2.366). Factorization parameters were as follows: name: 42227_146 n: 11419037649631533302730167351422803394561213724399974201383070218486899102995497193219122768932079190766508073381 m: 200000000000000000000000000000 deg: 5 c5: 95 c0: 344 skew: 1.29 type: snfs lss: 1 rlim: 2100000 alim: 2100000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1050000, 2750001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 362115 x 362360 Total sieving time: 13.24 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,2100000,2100000,26,26,49,49,2.3,2.3,100000 total time: 13.24 hours. --------- CPU info (if available) ----------

Dec 22, 2008

By Robert Backstrom / GGNFS, Msieve
(37·10¹⁸⁶+71)/9 = 4(1)₁₈₅9_<187> = 3² · 59² · C183
C183 = P47 · P136
P47 = 55044224415250538928921553264661339723266003429_<47>
P136 = 2383970764021785908203194996945240916853952320935449385966474798602815965953926289351897727903544055041607935420772339895475891591817859_<136>

Number: n N=131223821734211468962019570082387280510425200648316611162536662871815605704334996683938558878710176230045999269402506020336145779026177379141086887902936930994002716687768875837438511 ( 183 digits) SNFS difficulty: 187 digits. Divisors found: Mon Dec 22 05:04:18 2008 prp47 factor: 55044224415250538928921553264661339723266003429 Mon Dec 22 05:04:18 2008 prp136 factor: 2383970764021785908203194996945240916853952320935449385966474798602815965953926289351897727903544055041607935420772339895475891591817859 Mon Dec 22 05:04:19 2008 elapsed time 06:55:19 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20051202-athlon Total time: 93.76 hours. Scaled time: 192.30 units (timescale=2.051). Factorization parameters were as follows: name: KA_4_1_185_9 n: 131223821734211468962019570082387280510425200648316611162536662871815605704334996683938558878710176230045999269402506020336145779026177379141086887902936930994002716687768875837438511 type: snfs skew: 0.72 deg: 5 c5: 370 c0: 71 m: 10000000000000000000000000000000000000 rlim: 8800000 alim: 8800000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8800000/8800000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 5700001) Primes: RFBsize:590006, AFBsize:589651, largePrimes:33470457 encountered Relations: rels:31004910, finalFF:1017105 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 7398741 hash collisions in 38005293 relations Msieve: matrix is 1645242 x 1645490 (446.2 MB) Total sieving time: 91.92 hours. Total relation processing time: 1.84 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,187,5,0,0,0,0,0,0,0,0,8800000,8800000,29,29,58,58,2.5,2.5,100000 total time: 93.76 hours. --------- CPU info (if available) ----------

(2·10¹⁸⁶+7)/9 = (2)₁₈₅3_<186> = 61 · 7247 · C180
C180 = P64 · P117
P64 = 1000296869048935293617966311639974939939901074399500816397239041_<64>
P117 = 502539820663756223904404112395960972646821102101410044844975062438931281776309797410654017639319069448362694337047509_<117>

Number: n N=502689009182368786229739433665535365051501745713256638071202379327618261987938982602687425711989861768062809986319318615101833482757641312792455040123379990413720594892227246598869 ( 180 digits) SNFS difficulty: 186 digits. Divisors found: Mon Dec 22 17:13:51 2008 prp64 factor: 1000296869048935293617966311639974939939901074399500816397239041 Mon Dec 22 17:13:51 2008 prp117 factor: 502539820663756223904404112395960972646821102101410044844975062438931281776309797410654017639319069448362694337047509 Mon Dec 22 17:13:51 2008 elapsed time 03:54:27 (Msieve 1.39 - dependency 1) Version: GGNFS-0.77.1-20050930-k8 Total time: 45.86 hours. Scaled time: 92.19 units (timescale=2.010). Factorization parameters were as follows: name: KA_2_185_3 n: 502689009182368786229739433665535365051501745713256638071202379327618261987938982602687425711989861768062809986319318615101833482757641312792455040123379990413720594892227246598869 type: snfs skew: 0.81 deg: 5 c5: 20 c0: 7 m: 10000000000000000000000000000000000000 rlim: 8500000 alim: 8500000 lpbr: 29 lpba: 29 mfbr: 58 mfba: 58 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 8500000/8500000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 58/58 Sieved special-q in [100000, 6750001) Primes: RFBsize:571119, AFBsize:570202, largePrimes:34438043 encountered Relations: rels:31297614, finalFF:904990 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Msieve: found 3087212 hash collisions in 32883378 relations Msieve: matrix is 1657566 x 1657814 (456.2 MB) Total sieving time: 45.11 hours. Total relation processing time: 0.76 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,8500000,8500000,29,29,58,58,2.5,2.5,100000 total time: 45.86 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU1: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU2: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 CPU3: Intel(R) Core(TM)2 Quad CPU Q9550 @ 2.83GHz stepping 07 Memory: 3321556k/3407296k available (2912k kernel code, 84428k reserved, 1794k data, 1544k init, 2502088k highmem) Calibrating delay loop (skipped), value calculated using timer frequency.. 5660.98 BogoMIPS (lpj=2830490) Calibrating delay using timer specific routine.. 5660.89 BogoMIPS (lpj=2830449) Calibrating delay using timer specific routine.. 5660.91 BogoMIPS (lpj=2830457) Calibrating delay using timer specific routine.. 5660.92 BogoMIPS (lpj=2830462) Total of 4 processors activated (22643.71 BogoMIPS).

4. Wanted

See Wanted.

5. Records

See Records.

6. Contributors

Alexander Mkrtychyan, Anton Korobeynikov, Bryan Koen, Cedric Vonck, Chris Monico, Erik Branger, Greg Childers, honeycrack7, Hugo Platzer, JMB, Jo Yeong Uk, Julien Peter Benney, Justin Card, Kenichiro Yamaguchi, Kenji Ibusuki, Maksym Voznyy, Markus Tervooren, matsui, Michael Peterson, Nechaev Sergey, Naoki Yamamoto, Patrick Keller, Phil Carmody, Philippe Strohl, Robert Backstrom, Samuel Chong, Sander Hoogendoorn, Serge Batalov, Shaopu Lin, Shusuke Kubota, Sinkiti Sibata, suberi, Takahiro Nohara, Tetsuya Kobayashi, Thomas Womack, Tomoya Adachi, Tyler Cadigan, Wataru Sakai, Wojciech Florek, Yoichi Hanatani .

Unnamed results were factored by Makoto Kamada and anonymous contributors, except 11...11 (Repunit) and 100...001.

Thank you for many contributions. Our factor tables are dependent on contributions. Contributions of factors are welcome.

Contribution and reservation page is now available. To submit or reserve factors, click the buttons added to each tables.

Contributions by e-mails are also acceptable.

7. Forms

Repunit

(1)_w

Near-repdigit

(R)_wD

Single digit D ∈ { 1, 3, 7, 9 }
Repeated digit R ∈ { 1, 2, 3, 4, 5, 6, 7, 8, 9 }
D≠R and gcd(D, R) = 1

D(R)_w

Single digit D ∈ { 1, 2, 3, 4, 5, 6, 7, 8, 9 }
Repeated digit R ∈ { 1, 3, 7, 9 }
D≠R and gcd(D, R) = 1

Near-repdigit Palindrome

(R)_wD(R)_w

Single digit D ∈ { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
Repeated digit R ∈ { 1, 3, 7, 9 }
D≠R and gcd(D, R) = 1

Plateau and Depression

D(R)_wD

Single digit D ∈ { 1, 3, 7, 9 }
Repeated digit R ∈ { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
D≠R and gcd(D, R) = 1

D<R

Plateau ('台地' in Japanese)

D>R

Depression ('窪地' in Japanese)

Generalized quasi-repdigit

D(R)_wE

Single digit D ∈ { 1, 2, 3, 4, 5, 6, 7, 8, 9 }
Single digit E ∈ { 1, 3, 7, 9 }
Repeated digit R ∈ { 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 }
D≠E, D≠R, E≠R and gcd(D, E, R) = 1 and gcd(D+E, R, 9) = 1

8. Factor Table Search

Examples

• Search composite numbers which has 105 digits or less.
• Search numbers which was factored by GGNFS.
• Search numbers which was factored by gnfs.
• Search numbers whose second largest factor has 70 digits or more.
• Search prime numbers.

9. Factor tables

Representations

number_<xxx>

Subscript <xxx> is length of adjacent number.

[number_<xxx>]

Numbers in square brackets are definitely composite and not factorized yet.

Near-repdigit (R)wD
Number	General term	Room	Condition	Status / Not factored	Last update
11...113	(10n+17)/9	14.33%	n≤200	184, 187, 188, 189, 192, 193, 195, 199 (8/200)	Dec 14, 2008
11...117	(10n+53)/9	16.19%	n≤200	183, 184, 185, 186, 189, 194, 196 (7/200)	Oct 23, 2008
11...119	(10n+71)/9	15.44%	n≤200	171, 176, 177, 178, 179, 183, 188, 189, 190, 191, 193, 195, 199, 200 (14/200)	Dec 9, 2008
22...221	(2·10n-11)/9	16.84%	n≤200	174, 175, 176, 179, 183, 185, 186, 187, 188, 189, 191, 196, 199, 200 (14/200)	Oct 11, 2008
22...223	(2·10n+7)/9	23.92%	n≤200	171, 173, 174, 175, 176, 179, 182, 184, 189, 193, 195, 196, 198, 199, 200 (15/200)	Dec 22, 2008
22...227	(2·10n+43)/9	13.19%	n≤200	171, 179, 183, 184, 185, 186, 189, 190, 192, 194, 197, 199, 200 (13/200)	Sep 27, 2008
22...229	(2·10n+61)/9	14.02%	n≤200	171, 180, 181, 182, 183, 184, 186, 189, 191, 194, 195, 196, 198, 199, 200 (15/200)	Oct 3, 2008
33...331	(10n-7)/3	34.06%	n≤200	182, 183, 189, 190, 196, 199, 200 (7/200)	Nov 6, 2008
33...337	(10n+11)/3	15.23%	n≤200	173, 174, 178, 179, 180, 184, 185, 186, 187, 191, 192, 193, 194, 196, 197, 198, 199, 200 (18/200)	Dec 11, 2008
44...441	(4·10n-31)/9	16.25%	n≤200	172, 174, 175, 176, 180, 181, 185, 195, 196, 197, 198, 200 (12/200)	Oct 11, 2008
44...443	(4·10n-13)/9	14.66%	n≤200	170, 172, 175, 176, 178, 179, 180, 184, 185, 188, 189, 191, 193, 195, 196, 197, 198, 200 (18/200)	Oct 22, 2008
44...447	(4·10n+23)/9	14.05%	n≤200	178, 181, 183, 184, 185, 188, 192, 193, 195, 196, 197, 199, 200 (13/200)	Dec 7, 2008
44...449	(4·10n+41)/9	16.53%	n≤200	174, 176, 178, 179, 180, 183, 184, 186, 188, 189, 190, 191, 193, 199, 200 (15/200)	Oct 2, 2008
55...551	(5·10n-41)/9	16.91%	n≤200	180, 181, 183, 184, 187, 189, 190, 192, 196, 198, 199, 200 (12/200)	Nov 16, 2008
55...553	(5·10n-23)/9	14.82%	n≤200	176, 178, 179, 182, 187, 188, 192, 193, 196, 200 (10/200)	Nov 5, 2008
55...557	(5·10n+13)/9	16.11%	n≤200	174, 175, 176, 179, 180, 181, 182, 183, 185, 187, 188, 191, 192, 193, 194, 198, 200 (17/200)	Oct 22, 2008
55...559	(5·10n+31)/9	11.42%	n≤200	173, 174, 179, 180, 181, 182, 183, 184, 190, 191, 194, 196 (12/200)	Dec 7, 2008
66...661	(2·10n-17)/3	31.84%	n≤200	171, 172, 174, 175, 176, 183, 186, 190, 193, 194, 195, 197, 200 (13/200)	Oct 30, 2008
66...667	(2·10n+1)/3	27.28%	n≤200	172, 176, 180, 183, 186, 187, 189, 191, 195, 198, 200 (11/200)	Dec 7, 2008
77...771	(7·10n-61)/9	21.08%	n≤200	170, 178, 179, 181, 182, 187, 189, 190, 191, 193, 194, 195, 197, 198 (14/200)	Nov 23, 2008
77...773	(7·10n-43)/9	18.49%	n≤200	169, 179, 180, 186, 188, 195, 197, 199, 200 (9/200)	Aug 8, 2008
77...779	(7·10n+11)/9	12.22%	n≤200	171, 177, 178, 180, 181, 183, 185, 187, 191, 192, 193, 194, 196, 199, 200 (15/200)	Nov 11, 2008
88...881	(8·10n-71)/9	15.92%	n≤200	171, 173, 176, 179, 180, 182, 184, 187, 188, 191, 193, 196, 197, 198, 199 (15/200)	Oct 23, 2008
88...883	(8·10n-53)/9	24.96%	n≤200	170, 172, 174, 176, 177, 179, 181, 182, 184, 185, 186, 189, 194, 195, 196, 197, 199 (17/200)	Sep 24, 2008
88...887	(8·10n-17)/9	18.49%	n≤200	173, 180, 181, 182, 183, 184, 187, 188, 189, 196, 198, 200 (12/200)	Dec 15, 2008
88...889	(8·10n+1)/9	12.94%	n≤250	182, 184, 188, 191, 193, 196, 199, 202, 203, 205, 206, 208, 214, 218, 220, 221, 224, 227, 229, 232, 235, 236, 238, 239, 242, 244, 248 (27/250)	Dec 18, 2008
99...991	10n-9	18.02%	n≤250	201, 211, 213, 215, 217, 221, 229, 231, 235, 241, 243, 245, 247 (13/250)	Oct 24, 2008
99...997	10n-3	21.47%	n≤200	178, 181, 183, 186, 189, 192, 193, 195, 196, 198, 199 (11/200)	Jul 17, 2008

Near-repdigit D(R)w
Number	General term	Room	Condition	Status / Not factored	Last update
133...33	(4·10n-1)/3	12.05%	n≤250	203, 209, 211, 213, 215, 219, 221, 227, 229, 231, 237, 239, 241, 245, 247, 249 (16/250)	Sep 6, 2008
177...77	(16·10n-7)/9	24.35%	n≤200	169, 171, 174, 176, 178, 180, 184, 188, 189, 190, 193, 194, 197, 198, 199 (15/200)	Dec 7, 2008
199...99	2·10n-1	27.85%	n≤200	168, 170, 174, 175, 176, 180, 181, 183, 189, 190, 191, 192, 193, 195, 196, 197, 199, 200 (18/200)	Oct 22, 2008
211...11	(19·10n-1)/9	22.37%	n≤200	176, 178, 179, 183, 184, 185, 188, 189, 192, 194, 195, 196, 197, 200 (14/200)	Oct 22, 2008
233...33	(7·10n-1)/3	34.05%	n≤200	173, 175, 177, 179, 182, 183, 185, 186, 187, 189, 191, 193, 194, 197, 199, 200 (16/200)	Aug 23, 2008
277...77	(25·10n-7)/9	19.45%	n≤200	170, 175, 177, 179, 181, 182, 183, 184, 187, 190, 192, 193, 195, 196, 197, 198, 199 (17/200)	Mar 10, 2008
299...99	3·10n-1	21.47%	n≤200	169, 171, 172, 174, 176, 177, 178, 180, 182, 191, 192, 195, 197, 198, 199 (15/200)	Oct 3, 2008
311...11	(28·10n-1)/9	19.45%	n≤200	170, 172, 175, 176, 177, 178, 180, 181, 182, 184, 187, 188, 194, 196, 197, 198, 199, 200 (18/200)	Jul 28, 2008
377...77	(34·10n-7)/9	4.822%	n≤200	170, 173, 174, 175, 177, 178, 179, 180, 184, 185, 186, 189, 191, 192, 197, 198 (16/200)	Dec 15, 2008
411...11	(37·10n-1)/9	11.07%	n≤200	173, 174, 177, 178, 183, 184, 185, 187, 189, 190, 191, 193, 198, 199 (14/200)	Dec 11, 2008
433...33	(13·10n-1)/3	25.94%	n≤200	168, 173, 176, 177, 179, 180, 181, 182, 184, 187, 189, 190, 192, 193, 194, 195, 196, 198, 200 (19/200)	Nov 6, 2008
477...77	(43·10n-7)/9	18.49%	n≤200	168, 170, 172, 178, 179, 181, 182, 184 (8/200)	Dec 18, 2008
499...99	5·10n-1	27.85%	n≤200	172, 173, 174, 177, 179, 180, 181, 182, 183, 185, 186, 187, 189, 191, 193, 197, 198, 199 (18/200)	Oct 2, 2008
511...11	(46·10n-1)/9	14.82%	n≤200	175, 176, 179, 180, 183, 184, 187, 188, 190, 192, 196, 197 (12/200)	Aug 9, 2008
533...33	(16·10n-1)/3	13.22%	n≤250	181, 183, 185, 187, 189, 191, 193, 195, 197, 199, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 235, 237, 243 (23/250)	Nov 11, 2008
577...77	(52·10n-7)/9	19.9%	n≤200	170, 171, 173, 176, 178, 182, 185, 188, 190, 191, 192, 195, 198, 200 (14/200)	Oct 13, 2008
599...99	6·10n-1	27.43%	n≤200	172, 174, 176, 177, 179, 180, 188, 190, 191, 192, 193, 195, 196, 199 (14/200)	Nov 9, 2008
611...11	(55·10n-1)/9	16.84%	n≤200	175, 177, 179, 183, 185, 186, 188, 189, 194, 196, 197, 198 (12/200)	Oct 7, 2008
677...77	(61·10n-7)/9	21.08%	n≤200	171, 176, 183, 184, 185, 189, 190, 191, 194, 196, 197, 200 (12/200)	Oct 23, 2008
711...11	(64·10n-1)/9	7.078%	n≤250	205, 211, 227, 233, 245 (5/250)	Dec 2, 2008
733...33	(22·10n-1)/3	17.6%	n≤200	172, 173, 179, 180, 183, 185, 186, 188, 190, 191, 192, 194, 197, 198, 199 (15/200)	Jul 11, 2008
799...99	8·10n-1	24.47%	n≤250	205, 217, 220, 223, 224, 226, 227, 230, 233, 235, 236, 239, 241, 244, 245, 248 (16/250)	Sep 6, 2008
811...11	(73·10n-1)/9	19.8%	n≤200	173, 179, 181, 188, 190, 191, 192, 195, 199, 200 (10/200)	Sep 30, 2008
833...33	(25·10n-1)/3	12.05%	n≤250	203, 205, 207, 211, 213, 215, 217, 221, 225, 227, 229, 233, 235, 239, 243, 245, 247, 249 (18/250)	Nov 7, 2008
877...77	(79·10n-7)/9	24.92%	n≤200	170, 177, 184, 185, 186, 188, 189, 190, 192, 193, 194, 195, 197, 198, 199 (15/200)	Nov 23, 2008
899...99	9·10n-1	18.02%	n≤250	171, 181, 185, 187, 189, 191, 197, 201, 203, 205, 207, 209, 211, 215, 217, 219, 221, 225, 229, 231, 235, 237, 241, 243, 245, 247, 249 (27/250)	Dec 7, 2008
911...11	(82·10n-1)/9	16.91%	n≤200	167, 172, 176, 177, 178, 180, 181, 182, 183, 188, 189, 191, 194, 198 (14/200)	Oct 22, 2008
977...77	(88·10n-7)/9	22.68%	n≤200	173, 175, 177, 179, 181, 182, 185, 187, 188, 189, 191, 193, 197, 198, 200 (15/200)	Oct 22, 2008

Generalized quasi-repdigit D(R)wE
Number	General term	Room	Condition	Status / Not factored	Last update
100...003	10n+3	20.74%	n≤250	189, 194, 195, 200, 201, 203, 205, 212, 216, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 233, 234, 236, 239, 240, 241, 242, 243, 244, 245, 247, 248, 250 (36/250)	Dec 16, 2008
100...007	10n+7	29.23%	n≤200	178, 180, 181, 182, 183, 189, 191, 192, 194, 196, 198, 199, 200 (13/200)	Oct 23, 2008
100...009	10n+9	29.15%	n≤200	176, 179, 182, 183, 186, 190, 195, 196, 198 (9/200)	Oct 23, 2008
122...223	(11·10n+7)/9	12.22%	n≤200	171, 178, 180, 181, 182, 183, 188, 189, 190, 192, 194, 196, 197, 199, 200 (15/200)	Oct 6, 2008
122...227	(11·10n+43)/9	17.11%	n≤200	172, 177, 178, 182, 183, 185, 186, 187, 188, 190, 191, 192, 194, 199 (14/200)	Nov 5, 2008
122...229	(11·10n+61)/9	16.45%	n≤200	174, 176, 181, 183, 188, 189, 190, 191, 193, 194, 195, 196, 197, 199 (14/200)	Aug 9, 2008
133...337	(4·10n+11)/3	20.08%	n≤200	171, 172, 174, 179, 182, 183, 185, 189, 191, 193, 194, 195, 197, 200 (14/200)	Oct 22, 2008
133...339	(4·10n+17)/3	21.03%	n≤200	171, 172, 173, 174, 178, 179, 180, 181, 183, 185, 188, 189, 191, 193, 197, 199 (16/200)	Oct 30, 2008
144...443	13·(10n-1)/9	See 11...11 (Repunit).
144...447	(13·10n+23)/9	22.46%	n≤200	172, 175, 176, 177, 179, 180, 186, 189, 190, 191, 192, 196, 197 (13/200)	Oct 18, 2008
144...449	(13·10n+41)/9	25.17%	n≤200	170, 171, 173, 180, 183, 184, 185, 186, 188, 190, 192, 194, 197, 198, 200 (15/200)	Nov 24, 2008
155...553	(14·10n-23)/9	16.9%	n≤200	174, 176, 177, 182, 184, 186, 187, 188, 191, 194, 195, 196, 197, 198 (14/200)	Dec 4, 2008
155...557	(14·10n+13)/9	16.26%	n≤200	171, 172, 173, 175, 176, 177, 180, 182, 186, 187, 188, 189, 190, 192, 194, 195, 196 (17/200)	Oct 22, 2008
155...559	(14·10n+31)/9	20.76%	n≤200	172, 173, 178, 181, 185, 187, 189, 191, 193, 197, 199, 200 (12/200)	Oct 22, 2008
166...663	(5·10n-11)/3	17.6%	n≤200	171, 178, 179, 180, 182, 183, 184, 185, 186, 191, 192, 194, 195, 196, 197, 200 (16/200)	Nov 10, 2008
166...667	(5·10n+1)/3	27.28%	n≤200	173, 176, 177, 179, 180, 182, 183, 184, 187, 188, 190, 191, 194, 197, 198 (15/200)	Aug 23, 2008
166...669	(5·10n+7)/3	26.81%	n≤200	175, 176, 180, 183, 192, 194, 196, 199, 200 (9/200)	Aug 31, 2008
177...773	(16·10n-43)/9	12.37%	n≤200	174, 175, 179, 182, 183, 186, 189, 197, 198, 200 (10/200)	Oct 11, 2008
177...779	(16·10n+11)/9	13.36%	n≤200	174, 175, 182, 185, 189, 191, 192, 193, 194, 197, 199, 200 (12/200)	Dec 11, 2008
188...883	(17·10n-53)/9	12.61%	n≤200	167, 172, 175, 177, 179, 180, 181, 184, 188, 192, 193, 194, 195, 196 (14/200)	Oct 2, 2008
188...887	17·(10n-1)/9	See 11...11 (Repunit).
188...889	(17·10n+1)/9	14.34%	n≤200	172, 175, 176, 177, 178, 180, 182, 186, 187, 190, 191, 193, 194, 196, 197, 198, 199 (17/200)	Nov 24, 2008
199...993	2·10n-7	29.08%	n≤200	173, 179, 181, 182, 190, 191, 193, 194, 195, 196, 197, 199 (12/200)	Oct 11, 2008
199...997	2·10n-3	24.32%	n≤200	172, 177, 178, 179, 183, 185, 187, 193, 195, 196, 197, 200 (12/200)	Jun 30, 2008
200...001	2·10n+1	See 66...667.
200...003	2·10n+3	23.69%	n≤200	177, 179, 180, 181, 182, 186, 190, 191, 192, 193, 194, 196, 198, 199, 200 (15/200)	Jul 6, 2008
200...007	2·10n+7	See 22...223.
200...009	2·10n+9	8.764%	n≤200	171, 178, 179, 180, 181, 183, 185, 186, 189, 191, 193, 194, 195, 196, 197, 200 (16/200)	Oct 30, 2008
211...113	(19·10n+17)/9	23.75%	n≤200	174, 183, 186, 187, 188, 189, 191, 193, 194, 196, 197 (11/200)	Oct 22, 2008
211...117	(19·10n+53)/9	9.81%	n≤200	174, 178, 180, 185, 186, 188, 189, 191, 192, 195, 199 (11/200)	Nov 7, 2008
211...119	(19·10n+71)/9	10.11%	n≤200	169, 170, 171, 172, 174, 179, 180, 182, 183, 185, 186, 188, 189, 191, 192, 194, 195, 196, 198, 199, 200 (21/200)	Jul 20, 2008
233...331	7·(10n-1)/3	See 11...11 (Repunit).
233...337	(7·10n+11)/3	See 77...779.
233...339	(7·10n+17)/3	30.12%	n≤200	175, 176, 181, 186, 188, 190, 191, 192, 193, 194, 196, 197 (12/200)	Jun 30, 2008
244...441	(22·10n-31)/9	22.62%	n≤200	168, 170, 175, 176, 177, 178, 181, 187, 189, 190, 191, 195, 196, 198 (14/200)	Oct 22, 2008
244...443	(22·10n-13)/9	19.31%	n≤205	167, 175, 180, 181, 188, 189, 193, 194, 197, 198, 201, 203, 205 (13/205)	Nov 24, 2008
244...447	(22·10n+23)/9	13.6%	n≤205	172, 173, 179, 182, 185, 186, 187, 189, 190, 192, 193, 195, 196, 197, 198, 200, 201, 203 (18/205)	Dec 9, 2008
244...449	(22·10n+41)/9	12.7%	n≤205	175, 177, 178, 179, 185, 188, 190, 191, 192, 193, 194, 199, 200, 202, 205 (15/205)	Oct 11, 2008
255...551	(23·10n-41)/9	23.03%	n≤205	171, 174, 175, 181, 182, 184, 187, 191, 192, 193, 194, 197, 199, 200, 202, 205 (16/205)	Nov 14, 2008
255...553	23·(10n-1)/9	See 11...11 (Repunit).
255...557	(23·10n+13)/9	22.46%	n≤205	172, 175, 176, 177, 181, 182, 185, 190, 192, 193, 194, 195, 196, 199 (14/205)	Nov 6, 2008
255...559	(23·10n+31)/9	9.389%	n≤205	172, 173, 175, 176, 178, 179, 180, 182, 183, 185, 188, 189, 190, 191, 192, 194, 195, 197, 198, 199, 200, 201, 202, 205 (24/205)	Dec 7, 2008
266...661	(8·10n-17)/3	See 88...887.
266...663	(8·10n-11)/3	29.28%	n≤205	173, 175, 177, 178, 181, 182, 183, 184, 185, 189, 190, 191, 193, 194, 195, 198, 199, 200, 201, 202, 204, 205 (22/205)	Nov 1, 2008
266...667	(8·10n+1)/3	See 88...889.
266...669	(8·10n+7)/3	26.77%	n≤200	174, 180, 182, 183, 184, 187, 195, 197, 198 (9/200)	Nov 6, 2008
277...771	(25·10n-61)/9	13.86%	n≤205	174, 175, 176, 178, 179, 180, 181, 183, 186, 187, 188, 192, 193, 198, 200, 201 (16/205)	Nov 1, 2008
277...773	(25·10n-43)/9	19.99%	n≤205	174, 175, 178, 187, 188, 190, 191, 192, 193, 194, 196, 198, 199, 200, 201, 204 (16/205)	Dec 9, 2008
277...779	(25·10n+11)/9	20.71%	n≤205	169, 173, 174, 175, 176, 178, 179, 180, 182, 186, 187, 188, 189, 190, 193, 195, 198, 199, 201, 203 (20/205)	Oct 22, 2008
288...881	(26·10n-71)/9	19.34%	n≤205	173, 174, 175, 177, 178, 179, 180, 184, 185, 188, 189, 190, 191, 196, 200, 202, 204 (17/205)	Nov 24, 2008
288...883	(26·10n-53)/9	16.04%	n≤205	177, 178, 179, 182, 183, 184, 187, 188, 190, 191, 192, 194, 199, 200, 201, 203, 205 (17/205)	Nov 5, 2008
288...887	(26·10n-17)/9	15.52%	n≤205	184, 186, 189, 191, 194, 195, 198, 199, 200, 201, 202, 205 (12/205)	Oct 30, 2008
288...889	(26·10n+1)/9	16.11%	n≤205	174, 175, 176, 177, 180, 182, 183, 184, 185, 186, 187, 190, 191, 192, 196, 198, 199, 200, 201, 202, 203, 204, 205 (23/205)	Nov 11, 2008
299...991	3·(10n-3)	See 99...997.
299...993	3·10n-7	22.39%	n≤200	176, 180, 188, 191, 193, 194, 195, 196, 197, 198 (10/200)	Oct 23, 2008
299...997	3·(10n-1)	See 11...11 (Repunit).
300...001	3·10n+1	20.74%	n≤200	170, 173, 174, 175, 176, 182, 183, 193, 194, 195, 196, 197, 200 (13/200)	Sep 8, 2008
300...007	3·10n+7	19.75%	n≤200	171, 173, 178, 180, 182, 183, 187, 188, 189, 190, 192, 195, 196, 198, 199, 200 (16/200)	Nov 6, 2008
311...117	(28·10n+53)/9	8.885%	n≤205	171, 176, 178, 180, 181, 184, 190, 191, 195, 196, 198, 199, 201, 202, 203, 204 (16/205)	Nov 19, 2008
311...119	(28·10n+71)/9	11.69%	n≤205	170, 172, 175, 176, 183, 187, 188, 190, 192, 194, 195, 198, 199, 200, 203, 204, 205 (17/205)	Dec 9, 2008
322...221	(29·10n-11)/9	15.93%	n≤205	168, 169, 170, 171, 173, 174, 175, 180, 181, 184, 186, 187, 188, 189, 194, 195, 196, 197, 199, 200, 202, 203, 205 (23/205)	Nov 29, 2008
322...227	(29·10n+43)/9	5.946%	n≤205	112, 167, 169, 170, 171, 174, 177, 182, 183, 185, 186, 187, 189, 191, 194, 195, 198, 200, 202, 203, 204, 205 (22/205)	Dec 20, 2008
322...229	(29·10n+61)/9	16.37%	n≤205	170, 171, 173, 175, 177, 178, 179, 181, 182, 185, 188, 189, 191, 196, 199, 203, 204 (17/205)	Dec 8, 2008
344...441	31·(10n-1)/9	See 11...11 (Repunit).
344...447	(31·10n+23)/9	9.39%	n≤205	169, 170, 173, 174, 178, 179, 180, 181, 183, 186, 187, 188, 189, 191, 193, 194, 196, 197, 198, 201, 203 (21/205)	Nov 24, 2008
344...449	(31·10n+41)/9	18.68%	n≤205	168, 170, 174, 175, 177, 181, 182, 183, 187, 188, 190, 193, 194, 196, 197, 198, 201, 202, 204 (19/205)	Dec 17, 2008
355...551	(32·10n-41)/9	17.15%	n≤205	169, 174, 176, 179, 180, 184, 185, 189, 191, 192, 195, 199, 200, 202 (14/205)	Dec 7, 2008
355...557	(32·10n+13)/9	11.14%	n≤205	165, 169, 174, 178, 179, 181, 182, 183, 184, 185, 186, 190, 192, 194, 196, 197, 198, 199, 203, 204, 205 (21/205)	Dec 5, 2008
355...559	(32·10n+31)/9	17.58%	n≤205	165, 167, 168, 169, 170, 172, 175, 182, 183, 184, 187, 190, 191, 192, 196, 197, 198, 203, 205 (19/205)	Dec 5, 2008
366...661	(11·10n-17)/3	23.95%	n≤205	171, 174, 179, 180, 182, 186, 187, 189, 190, 192, 194, 200, 202, 203 (14/205)	Dec 23, 2008
366...667	(11·10n+1)/3	15.23%	n≤205	162, 165, 167, 175, 176, 178, 179, 181, 183, 184, 185, 186, 188, 189, 190, 193, 195, 197, 198, 199, 200, 203, 204, 205 (24/205)	Dec 5, 2008
377...771	(34·10n-61)/9	17.59%	n≤205	164, 170, 172, 176, 179, 184, 187, 191, 192, 193, 194, 195, 196, 197, 201, 204, 205 (17/205)	Dec 10, 2008
377...779	(34·10n+11)/9	23.95%	n≤205	162, 166, 168, 169, 172, 174, 176, 178, 179, 182, 183, 185, 187, 188, 189, 191, 193, 197, 199, 200, 201, 203, 204, 205 (24/205)	Dec 17, 2008
388...881	(35·10n-71)/9	19.26%	n≤205	169, 172, 173, 174, 176, 181, 183, 184, 185, 186, 190, 194, 195, 197, 198, 201, 202, 204, 205 (19/205)	Dec 8, 2008
388...887	(35·10n-17)/9	4.822%	n≤205	162, 164, 165, 167, 173, 175, 177, 183, 185, 188, 190, 195, 197, 198, 199, 200, 201, 202, 204 (19/205)	Dec 22, 2008
388...889	(35·10n+1)/9	23.92%	n≤205	164, 165, 171, 172, 175, 176, 178, 181, 182, 185, 186, 190, 195, 196, 197, 198, 200, 201, 202, 205 (20/205)	Dec 19, 2008
399...991	4·10n-9	9.384%	n≤250	177, 189, 191, 193, 203, 205, 207, 209, 211, 213, 217, 219, 221, 225, 235, 237, 239, 243, 245, 247, 249 (21/250)	Nov 12, 2008
399...997	4·10n-3	13.11%	n≤200	174, 177, 181, 184, 185, 186, 188, 189, 190, 191, 192, 193, 199, 200 (14/200)	Jul 2, 2008
400...001	4·10n+1	14.86%	n≤250	178, 182, 187, 189, 198, 202, 203, 206, 207, 209, 210, 211, 213, 215, 217, 219, 222, 225, 226, 227, 231, 233, 235, 237, 238, 239, 243, 245, 246, 247, 250 (31/250)	Nov 21, 2008
400...003	4·10n+3	18.95%	n≤200	171, 179, 189, 190, 191, 193, 195, 199, 200 (9/200)	Oct 6, 2008
400...007	4·10n+7	9.442%	n≤200	170, 171, 174, 176, 178, 179, 184, 186, 187, 188, 192, 193, 196, 197, 199 (15/200)	Nov 24, 2008
400...009	4·10n+9	21.55%	n≤200	176, 181, 184, 186, 190, 197, 198, 199 (8/200)	Oct 15, 2008
411...113	(37·10n+17)/9	16.22%	n≤205	163, 167, 170, 171, 172, 175, 176, 178, 179, 181, 183, 184, 185, 186, 187, 188, 189, 191, 192, 193, 194, 197, 198, 199, 202, 204, 205 (27/205)	Dec 24, 2008
411...117	(37·10n+53)/9	18.94%	n≤205	160, 162, 169, 170, 174, 175, 180, 181, 182, 183, 184, 185, 191, 192, 193, 194, 195, 196, 197, 198, 202, 203, 204, 205 (24/205)	Dec 23, 2008
411...119	(37·10n+71)/9	7.878%	n≤205	159, 161, 163, 164, 167, 170, 185, 187, 188, 189, 190, 194, 195, 196, 197, 204 (16/205)	Dec 22, 2008
422...221	(38·10n-11)/9	15.98%	n≤205	169, 171, 172, 173, 174, 176, 179, 180, 182, 186, 190, 193, 194, 196, 197, 198, 199, 201, 202, 203, 204, 205 (22/205)	Dec 21, 2008
422...223	(38·10n+7)/9	17.87%	n≤205	168, 173, 175, 177, 178, 179, 180, 184, 186, 187, 188, 190, 192, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204 (23/205)	Dec 23, 2008
422...227	(38·10n+43)/9	12.03%	n≤205	145, 153, 158, 163, 164, 165, 170, 171, 172, 174, 176, 179, 180, 182, 185, 186, 187, 190, 191, 193, 194, 199, 200, 201, 202 (25/205)	Dec 24, 2008
422...229	(38·10n+61)/9	4.748%	n≤205	132, 133, 136, 137, 139, 140, 143, 144, 145, 146, 147, 154, 156, 160, 164, 166, 170, 171, 172, 174, 175, 179, 183, 184, 186, 187, 188, 189, 193, 195, 197, 201, 202, 203, 204, 205 (36/205)	Dec 24, 2008
433...331	(13·10n-7)/3	27.27%	n≤205	124, 126, 129, 135, 136, 138, 139, 140, 145, 149, 152, 154, 156, 157, 159, 161, 162, 165, 166, 167, 172, 173, 175, 176, 180, 181, 183, 184, 186, 187, 192, 193, 194, 195, 200, 201, 203 (37/205)	Dec 24, 2008
433...337	(13·10n+11)/3	21%	n≤100	Completed up to n=100. (Jan 2, 2005)	Jul 11, 2008
433...339	(13·10n+17)/3	27.28%	n≤100	Completed up to n=100. (Jan 2, 2005)	Jul 11, 2008
455...551	41·(10n-1)/9	See 11...11 (Repunit).
455...553	(41·10n-23)/9	23.02%	n≤100	Completed up to n=100. (Jan 2, 2005)	Jul 11, 2008
455...557	(41·10n+13)/9	25.17%	n≤100	Completed up to n=100. (Jan 2, 2005)	Jul 10, 2008
455...559	(41·10n+31)/9	18.68%	n≤100	Completed up to n=100. (Jan 2, 2005)	Jul 11, 2008
466...661	(14·10n-17)/3	20.22%	n≤100	Completed up to n=100. (Jan 2, 2005)	Jul 11, 2008
466...663	(14·10n-11)/3	35.52%	n≤100	Completed up to n=100. (Jan 2, 2005)	Jul 11, 2008
466...667	(14·10n+1)/3	26.81%	n≤100	Completed up to n=100. (Jan 2, 2005)	Jul 11, 2008
466...669	7·(2·10n+1)/3	See 66...667.
477...771	(43·10n-61)/9	12.76%	n≤100	Completed up to n=100. (Dec 3, 2004)	Jul 10, 2008
477...773	43·(10n-1)/9	See 11...11 (Repunit).
477...779	(43·10n+11)/9	17.11%	n≤100	Completed up to n=100. (Dec 3, 2004)	Jul 11, 2008
488...881	(44·10n-71)/9	2.163%	n≤100	Completed up to n=100. (Dec 3, 2004)	Oct 20, 2008
488...883	(44·10n-53)/9	18.8%	n≤100	Completed up to n=100. (Jan 3, 2005)	Jul 11, 2008
488...887	(44·10n-17)/9	14.28%	n≤100	Completed up to n=100. (Jan 3, 2005)	Jul 10, 2008
488...889	(44·10n+1)/9	20.71%	n≤100	Completed up to n=100. (Jan 3, 2005)	Jul 11, 2008
499...991	5·10n-9	21.43%	n≤200	168, 175, 176, 177, 178, 181, 182, 183, 186, 187, 188, 192, 193, 195, 196, 200 (16/200)	Oct 22, 2008
499...993	5·10n-7	25%	n≤200	170, 172, 174, 177, 183, 184, 185, 187, 191, 192, 195, 198 (12/200)	Nov 19, 2008
499...997	5·10n-3	27.43%	n≤200	170, 173, 175, 176, 181, 183, 185, 187, 188, 189, 190, 191, 193, 194, 195, 197, 200 (17/200)	Oct 30, 2008
500...001	5·10n+1	See 166...667.
500...003	5·10n+3	24.96%	n≤200	169, 171, 174, 177, 178, 182, 184, 190, 193, 194, 195, 197, 199, 200 (14/200)	Jul 5, 2008
500...007	5·10n+7	See 166...669.
500...009	5·10n+9	27.25%	n≤200	168, 169, 171, 172, 173, 176, 177, 180, 181, 182, 183, 184, 185, 188, 190, 193, 197, 198, 199, 200 (20/200)	Dec 10, 2008
511...113	(46·10n+17)/9	13.67%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 11, 2008
511...117	(46·10n+53)/9	6.304%	n≤100	Completed up to n=100. (Dec 3, 2004)	Oct 14, 2008
511...119	(46·10n+71)/9	16.88%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 10, 2008
522...221	(47·10n-11)/9	16.06%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 11, 2008
522...223	(47·10n+7)/9	19.33%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 11, 2008
522...227	(47·10n+43)/9	22.34%	n≤100	Completed up to n=100. (Nov 29, 2004)	Jul 11, 2008
522...229	(47·10n+61)/9	20.59%	n≤100	Completed up to n=100. (Nov 29, 2004)	Jul 11, 2008
533...331	(16·10n-7)/3	See 177...77.
533...337	(16·10n+11)/3	See 177...779.
533...339	(16·10n+17)/3	12.58%	n≤100	Completed up to n=100. (Dec 3, 2004)	Jul 10, 2008
544...441	(49·10n-31)/9	21.99%	n≤100	Completed up to n=100. (Jan 6, 2005)	Jul 10, 2008
544...443	(49·10n-13)/9	20.1%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 10, 2008
544...447	(49·10n+23)/9	18.42%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 11, 2008
544...449	(49·10n+41)/9	24.32%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 11, 2008
566...661	51·(10n-1)/9	See 11...11 (Repunit).
566...663	(17·10n-11)/3	23.95%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 11, 2008
566...667	(17·10n+1)/3	See 188...889.
566...669	(17·10n+7)/3	30.12%	n≤100	Completed up to n=100. (Dec 3, 2004)	Dec 2, 2007
577...771	(52·10n-61)/9	21.48%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 11, 2008
577...773	(52·10n-43)/9	18.64%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 11, 2008
577...779	(52·10n+11)/9	14.64%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 10, 2008
588...881	(53·10n-71)/9	16.28%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 11, 2008
588...883	53·(10n-1)/9	See 11...11 (Repunit).
588...887	(53·10n-17)/9	12.61%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 11, 2008
588...889	(53·10n+1)/9	16.19%	n≤100	Completed up to n=100. (Dec 4, 2004)	Jul 11, 2008
599...991	3·(2·10n-3)	See 199...997.
599...993	6·10n-7	23.73%	n≤200	173, 174, 177, 178, 181, 182, 186, 187, 188, 191, 192, 195, 198, 199, 200 (15/200)	Oct 22, 2008
599...997	3·(2·10n-1)	See 199...99.
600...001	6·10n+1	24.96%	n≤200	177, 180, 181, 182, 185, 192, 194, 195, 198 (9/200)	Dec 12, 2008
600...007	6·10n+7	26.59%	n≤200	170, 174, 175, 177, 181, 184, 186, 189, 190, 191, 193, 196, 197, 198, 199 (15/200)	Oct 23, 2008
611...113	(55·10n+17)/9	23.95%	n≤100	Completed up to n=100. (Jan 6, 2005)	Jul 11, 2008
611...117	(55·10n+53)/9	9.76%	n≤100	Completed up to n=100. (Dec 4, 2004)	Jul 10, 2008
611...119	(55·10n+71)/9	13.03%	n≤100	Completed up to n=100. (Jan 4, 2005)	Jul 11, 2008
622...221	(56·10n-11)/9	21.94%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 11, 2008
622...223	7·(8·10n+1)/9	See 88...889.
622...227	(56·10n+43)/9	5.836%	n≤100	Completed up to n=100. (Nov 29, 2004)	Oct 14, 2008
622...229	(56·10n+61)/9	5.258%	n≤100	Completed up to n=100. (Jan 5, 2005)	Oct 14, 2008
633...331	(19·10n-7)/3	29.14%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 11, 2008
633...337	(19·10n+11)/3	29.27%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jan 2, 2008
644...441	(58·10n-31)/9	10.5%	n≤100	Completed up to n=100. (Jan 5, 2005)	Nov 2, 2008
644...443	(58·10n-13)/9	25.34%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 10, 2008
644...447	(58·10n+23)/9	24.69%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 11, 2008
644...449	(58·10n+41)/9	6.289%	n≤100	Completed up to n=100. (Jan 5, 2005)	Oct 14, 2008
655...551	(59·10n-41)/9	17.09%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 11, 2008
655...553	(59·10n-23)/9	24.64%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 11, 2008
655...557	(59·10n+13)/9	17.07%	n≤100	Completed up to n=100. (Dec 6, 2004)	Jul 11, 2008
655...559	(59·10n+31)/9	14.81%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 11, 2008
677...771	61·(10n-1)/9	See 11...11 (Repunit).
677...773	(61·10n-43)/9	12.76%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 11, 2008
677...779	(61·10n+11)/9	16.45%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 11, 2008
688...881	(62·10n-71)/9	14.56%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 11, 2008
688...883	(62·10n-53)/9	17.98%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 11, 2008
688...887	(62·10n-17)/9	14.17%	n≤100	Completed up to n=100. (Jan 5, 2005)	Jul 11, 2008
688...889	(62·10n+1)/9	11.43%	n≤100	Completed up to n=100. (Dec 6, 2004)	Jul 11, 2008
699...991	7·10n-9	31.06%	n≤200	173, 177, 179, 183, 185, 187, 188, 189, 192, 193, 195 (11/200)	Dec 2, 2008
699...997	7·10n-3	22.39%	n≤200	170, 180, 182, 184, 186, 188, 189, 192, 195, 196, 197, 198, 199 (13/200)	Aug 6, 2008
700...001	7·10n+1	29.23%	n≤200	172, 175, 177, 180, 181, 184, 185, 186, 191, 193, 195, 196, 197, 199 (14/200)	Sep 24, 2008
700...003	7·10n+3	19.75%	n≤200	173, 179, 180, 181, 183, 184, 186, 194, 195, 196, 197, 198 (12/200)	Nov 24, 2008
700...009	7·10n+9	30.71%	n≤200	167, 169, 180, 183, 185, 186, 190, 193, 194, 197, 198, 200 (12/200)	Nov 25, 2008
711...113	(64·10n+17)/9	9.586%	n≤100	Completed up to n=100. (Jan 6, 2005)	Oct 15, 2008
711...119	(64·10n+71)/9	19.54%	n≤100	Completed up to n=100. (Jan 6, 2005)	Jul 11, 2008
722...221	(65·10n-11)/9	19.31%	n≤100	Completed up to n=100. (Dec 6, 2004)	Jul 11, 2008
722...223	(65·10n+7)/9	16.26%	n≤100	Completed up to n=100. (Dec 6, 2004)	Jul 11, 2008
722...229	(65·10n+61)/9	14.54%	n≤100	Completed up to n=100. (Jan 6, 2005)	Jul 11, 2008
733...331	(22·10n-7)/3	33.58%	n≤100	Completed up to n=100. (Jan 6, 2005)	Dec 6, 2007
733...339	(22·10n+17)/3	17.09%	n≤100	Completed up to n=100. (Jan 6, 2005)	Jul 11, 2008
744...441	(67·10n-31)/9	18.26%	n≤100	Completed up to n=100. (Dec 6, 2004)	Jul 11, 2008
744...443	(67·10n-13)/9	10.83%	n≤100	Completed up to n=100. (Jan 6, 2005)	Oct 15, 2008
744...449	(67·10n+41)/9	13.55%	n≤100	Completed up to n=100. (Dec 6, 2004)	Jul 11, 2008
755...551	(68·10n-41)/9	16.63%	n≤100	Completed up to n=100. (Jan 6, 2005)	Jul 11, 2008
755...553	(68·10n-23)/9	13.94%	n≤100	Completed up to n=100. (Dec 6, 2004)	Jul 11, 2008
755...559	(68·10n+31)/9	14.29%	n≤100	Completed up to n=100. (Nov 29, 2004)	Jul 11, 2008
766...661	(23·10n-17)/3	25.67%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
766...663	(23·10n-11)/3	22.6%	n≤100	Completed up to n=100. (Jan 7, 2005)	Dec 2, 2007
766...669	(23·10n+7)/3	29.69%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
788...881	71·(10n-1)/9	See 11...11 (Repunit).
788...883	(71·10n-53)/9	16.28%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
788...889	(71·10n+1)/9	15.44%	n≤100	Completed up to n=100. (Dec 6, 2004)	Jul 11, 2008
799...991	8·10n-9	21.51%	n≤200	177, 180, 186, 188, 189, 190, 191, 193, 196, 197 (10/200)	Aug 30, 2008
799...993	8·10n-7	22.88%	n≤200	170, 173, 176, 178, 180, 185, 187, 190, 192, 193, 196, 197, 198, 199, 200 (15/200)	Sep 24, 2008
800...001	8·10n+1	See 88...889.
800...003	8·10n+3	13.93%	n≤200	173, 174, 178, 179, 180, 182, 183, 184, 186, 188, 190, 191, 192, 193, 195, 196, 197, 198, 199, 200 (20/200)	Nov 26, 2008
800...007	8·10n+7	See 266...669.
800...009	8·10n+9	26.88%	n≤200	170, 173, 178, 179, 191, 192, 193, 195, 196 (9/200)	Dec 11, 2008
811...113	(73·10n+17)/9	14.47%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
811...117	(73·10n+53)/9	12.02%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
811...119	(73·10n+71)/9	19.12%	n≤100	Completed up to n=100. (Jan 6, 2005)	Jul 11, 2008
822...221	(74·10n-11)/9	15.27%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
822...223	(74·10n+7)/9	20.73%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
822...227	(74·10n+43)/9	11.11%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
822...229	(74·10n+61)/9	14%	n≤100	Completed up to n=100. (Jan 6, 2005)	Jul 11, 2008
833...331	(25·10n-7)/3	See 277...77.
833...337	(25·10n+11)/3	See 277...779.
833...339	(25·10n+17)/3	22.4%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
844...441	(76·10n-31)/9	20.55%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
844...443	(76·10n-13)/9	16.55%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
844...447	(76·10n+23)/9	9.231%	n≤100	Completed up to n=100. (Jan 6, 2005)	Jul 11, 2008
844...449	(76·10n+41)/9	11.06%	n≤100	Completed up to n=100. (Jan 7, 2005)	Jul 11, 2008
855...551	(77·10n-41)/9	11.44%	n≤100	Completed up to n=100. (Dec 6, 2004)	Jul 11, 2008
855...553	(77·10n-23)/9	16.89%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
855...557	(77·10n+13)/9	20.51%	n≤100	Completed up to n=100. (Dec 6, 2004)	Jul 10, 2008
855...559	(77·10n+31)/9	20.28%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
866...661	(26·10n-17)/3	See 288...887.
866...663	(26·10n-11)/3	25.11%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
866...667	(26·10n+1)/3	See 288...889.
866...669	(26·10n+7)/3	14.08%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
877...771	(79·10n-61)/9	11.06%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
877...773	(79·10n-43)/9	12.41%	n≤100	Completed up to n=100. (Nov 29, 2004)	Jul 11, 2008
877...779	(79·10n+11)/9	21.13%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
899...991	9·(10n-1)	See 11...11 (Repunit).
899...993	9·10n-7	31.06%	n≤200	172, 175, 176, 177, 179, 183, 185, 186, 187, 188, 189, 190, 193, 195, 197, 198, 200 (17/200)	Oct 22, 2008
899...997	3·(3·10n-1)	See 299...99.
900...001	9·10n+1	29.15%	n≤200	168, 175, 176, 178, 179, 181, 182, 185, 187, 188, 191, 195, 196, 198, 199, 200 (16/200)	Nov 28, 2008
900...007	9·10n+7	30.71%	n≤200	172, 178, 181, 187, 188, 190, 193, 194, 195, 196, 197, 198 (12/200)	Nov 22, 2008
911...113	(82·10n+17)/9	0%	n≤100	Completed up to n=100. (Dec 7, 2004)	Jul 11, 2008
911...117	(82·10n+53)/9	12.48%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
922...221	(83·10n-11)/9	14.73%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
922...223	(83·10n+7)/9	15.42%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
922...227	(83·10n+43)/9	17.44%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
933...331	7·(4·10n-1)/3	See 133...33.
933...337	(28·10n+11)/3	24.8%	n≤100	Completed up to n=100. (Dec 1, 2004)	Jul 11, 2008
944...441	(85·10n-31)/9	14.17%	n≤100	Completed up to n=100. (Dec 7, 2004)	Jul 11, 2008
944...443	(85·10n-13)/9	15.52%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
944...447	(85·10n+23)/9	13.67%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
955...551	(86·10n-41)/9	17.09%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
955...553	(86·10n-23)/9	11.35%	n≤100	Completed up to n=100. (Nov 29, 2004)	Jul 11, 2008
955...557	(86·10n+13)/9	10.94%	n≤100	Completed up to n=100. (Jan 8, 2005)	Oct 17, 2008
966...661	(29·10n-17)/3	33%	n≤100	Completed up to n=100. (Jan 6, 2005)	Jul 11, 2008
966...667	(29·10n+1)/3	22.15%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
977...771	(88·10n-61)/9	14.85%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
977...773	(88·10n-43)/9	15.39%	n≤100	Completed up to n=100. (Dec 7, 2004)	Jul 11, 2008
988...881	(89·10n-71)/9	14.16%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
988...883	(89·10n-53)/9	15.69%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008
988...887	(89·10n-17)/9	25.49%	n≤100	Completed up to n=100. (Jan 8, 2005)	Jul 11, 2008

10. Implementations

• GGNFS - SourceForge.net: GGNFS suite
• GMP-ECM - InriaGforge: GMP-ECM (Elliptic Curve Method): Project Info
• Msieve - Integer Factorization Source Code (Jason Papadopoulos)
• PFGW - primeform : User group for PFGW & PrimeForm programs
• Primo - Primo - Primality Proving

11. Related links

• Bob Backstrom - Sydney PCUG, Web Design, Large Factors, Digital Photos, Electronics (Bob Backstrom)
• Factorizations of Repunit Numbers of the form (10^n-1)/9 (Kurt Beschorner)
• Factor Tables (Richard Brent)
• Plateau and Depression Primes (Patrick De Geest)
• Factoring and Prime Identification (Torbjörn Granlund)
• Factorizations of Repunit Numbers (Yousuke Koide)
• Factorizations of Cyclotomic Numbers (Hisanori Mishima)
• GGNFS - A Number Field Sieve implementation (Chris Monico)
• Factorizations of values of the cyclotomic polynomials Phi_n(z) evaluated at z=10 (Alfred Reich)
• The Cunningham Project (Sam Wagstaff)
• The ECMNET Project (Paul Zimmermann)
• Factorizations of bⁿ±1, b=2,3,5,6,7,10,11,12 Up to High Powers Third Edition (AMS Online Books)
• Open Directory - Science: Math: Number Theory: Factoring (dmoz)