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News and updates, January 2007

Jan 31, 2007 (2nd)

By suberi / GGNFS-0.77.1-20060513-pentium4
(5·10¹⁵⁶-23)/9 = (5)₁₅₅3_<156> = C156
C156 = P49 · P108
P49 = 2560846149716872439579858329726586825671575032531_<49>
P108 = 216942183589192918421663964578069355218853581414103484953743923902937473987096413182058653625995214621863163_<108>

Number: 55553_156 N=555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553 ( 156 digits) SNFS difficulty: 156 digits. Divisors found: r1=2560846149716872439579858329726586825671575032531 (pp49) r2=216942183589192918421663964578069355218853581414103484953743923902937473987096413182058653625995214621863163 (pp108) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 62.22 hours. Scaled time: 37.96 units (timescale=0.610). Factorization parameters were as follows: n: 555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555553 m: 10000000000000000000000000000000 c5: 50 c0: -23 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, ) Primes: RFBsize:216816, AFBsize:217086, largePrimes:5742807 encountered Relations: rels:5740934, finalFF:571746 Max relations in full relation-set: 28 Initial matrix: 433967 x 571746 with sparse part having weight 48670665. Pruned matrix : 367071 x 369304 with weight 30938760. Total sieving time: 53.91 hours. Total relation processing time: 0.44 hours. Matrix solve time: 7.68 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 62.22 hours. --------- CPU info (if available) ----------

Jan 31, 2007

By Kurt Beschorner / GMP-ECM
(10¹⁰⁷⁵-1)/9 = (1)_1075<1075> = 41 · 173 · 271 · 431 · 21401 · 25601 · 1527791 · 182521213001_<12> · 1963506722254397_<16> · 2140992015395526641_<19> · 41398275939670867448911914339156680381343777006826487831_<56> · C840
C840 = P32 · C809
P32 = 28808518895110018881804272718751_<32>
C809 = [34711607481137779185343172568717063853649585607981256386198377523802955101674937658780544823861348911920227642123216535679247669103837522475155674109571330827877424273413589767269899876630170875051449423734879644153648797148657214133378174948653045435306621735367968242996150776676173929074851994253401369223360251902080671630146157701604684771369403136781086510374585437847110162407898647867517026085273167889611696348163648367323493946325384541861626251628996810055789736484792164758749290264880489129700245642965069450249435987606544165556441089849084572024845424821961153276851461743602388067096595478280474790653411469219889993269156750027876209726144359277423206345399199574980124591526006741368479442403172140074454806048167074796407295825522453850061099531834063042167111891660292294188880701000618751_<809>]
(10¹³³⁹-1)/9 = (1)_1339<1339> = 53 · 79 · 1031 · 2948479 · 7034077 · 265371653 · 376778533 · 134914656772016146559_<21> · 153211620887015423991278431667808361439217294295901387715486473457925534859044796980526236853_<93> · C1189
C1189 = P34 · C1155
P34 = 9493900906734104973632584503630517_<34>
C1155 = [632491207186448318890356683644297741034601907694816173005638750740737186940122497932594560862737202522189814350559651835868449534354515462709460091660741392814285242480113401500238396839063375106786760174836622425912148172669874591463607503550390352096721622033738764417670476128739126566593652232366036313115036262621351370531942058662970675263252135456180530041111456576490840059497947547656297180150865169781921026697092535326559189090901016073621062270288251905350095113048701395892474088679773730180957620791457786874975077274963046507870295886492068449779576980621429573621987926862106957358529979871749003078012483311918918056897022178680906927333023672650547467196330473015376365169819270298135302424463054955275154178508872212669165606005556186097344135313836949668943436468735757706714806656076555645025638238949490301337481793952710831287244059417539551759685294285676541444031993261039619459300689558717767780552414413207728044156319556290785341776021015215167915759238562759219794577748280605771163176444321516668102067580717790586331168633043863180135666797505171251204514617530287681136978427097385346931445452216068468197848426615040752671_<1155>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 30, 2007 (3rd)

By Wataru Sakai / GGNFS-0.77.1-20060513-pentium4
(2·10¹⁹²-11)/9 = (2)₁₉₁1_<192> = C192
C192 = P51 · P141
P51 = 558618399051833370115786772061914616637233905518207_<51>
P141 = 397806843812179113084158478278673278462548559737123328190563207638690256907455600564416540019096658258610880726309405139019884843047677986803_<141>

Number: 22221_192 N=222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 ( 192 digits) SNFS difficulty: 192 digits. Divisors found: r1=558618399051833370115786772061914616637233905518207 (pp51) r2=397806843812179113084158478278673278462548559737123328190563207638690256907455600564416540019096658258610880726309405139019884843047677986803 (pp141) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 2650.61 hours. Scaled time: 3353.02 units (timescale=1.265). Factorization parameters were as follows: n: 222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222221 m: 100000000000000000000000000000000000000 c5: 200 c0: -11 skew: 1 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 30100001) Primes: RFBsize:501962, AFBsize:503807, largePrimes:7704137 encountered Relations: rels:8480417, finalFF:1132965 Max relations in full relation-set: 28 Initial matrix: 1005834 x 1132965 with sparse part having weight 156672342. Pruned matrix : 922746 x 927839 with weight 141023585. Total sieving time: 2579.02 hours. Total relation processing time: 2.88 hours. Matrix solve time: 68.25 hours. Time per square root: 0.45 hours. Prototype def-par.txt line would be: snfs,192,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 2650.61 hours. --------- CPU info (if available) ----------

Jan 30, 2007 (2nd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(52·10¹⁵²-7)/9 = 5(7)_152<153> = 1621 · 50957 · C145
C145 = P67 · P79
P67 = 2709042073446592170792934274741551206028921382492321254041066670097_<67>
P79 = 2582011769442852651209968987523621441279428819480352551729492154606092853851153_<79>

Number: trial N=6994778517554969842395789230498133434609117309353844380649105034970307763784602289934718310510036879660349374148178058000442508521116536194071841 ( 145 digits) SNFS difficulty: 154 digits. Divisors found: r1=2709042073446592170792934274741551206028921382492321254041066670097 (pp67) r2=2582011769442852651209968987523621441279428819480352551729492154606092853851153 (pp79) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 62.87 hours. Scaled time: 32.76 units (timescale=0.521). Factorization parameters were as follows: n: 6994778517554969842395789230498133434609117309353844380649105034970307763784602289934718310510036879660349374148178058000442508521116536194071841 m: 2000000000000000000000000000000 c5: 325 c0: -14 skew: 1 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2400001) Primes: RFBsize:176302, AFBsize:176488, largePrimes:5582957 encountered Relations: rels:5444690, finalFF:406954 Max relations in full relation-set: 0 Initial matrix: 352856 x 406954 with sparse part having weight 35869280. Pruned matrix : 334041 x 335869 with weight 26580813. Total sieving time: 51.60 hours. Total relation processing time: 0.49 hours. Matrix solve time: 10.36 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: snfs,154,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 62.87 hours. --------- CPU info (if available) ----------

Jan 30, 2007

By anonymous / GMP-ECM B1=1000000
(5·10¹⁹⁷-41)/9 = (5)₁₉₆1_<197> = 3³ · 113 · 7057 · 98731 · 180990319 · 2368810349_<10> · 112482036837773_<15> · 5364655462624710751_<19> · C135
C135 = P32 · P103
P32 = 11964267951850715104560344952589_<32>
P103 = 8443351287853077133602447796951347937273196183236859341898751751641591112408103384212454905661287831579_<103>

Jan 29, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
(14·10¹⁷⁵-41)/9 = 1(5)₁₇₄1_<176> = 11 · 43 · C173
C173 = P46 · P128
P46 = 1971848954400133691125566917937107287858416479_<46>
P128 = 16678260045126227226173832334535265219726130696522534014568395028983269564908150799866271813714347853920132775969907902330680553_<128>

Number: 15551_175 N=32887009631195677707305614282358468404980032887009631195677707305614282358468404980032887009631195677707305614282358468404980032887009631195677707305614282358468404980032887 ( 173 digits) SNFS difficulty: 176 digits. Divisors found: r1=1971848954400133691125566917937107287858416479 (pp46) r2=16678260045126227226173832334535265219726130696522534014568395028983269564908150799866271813714347853920132775969907902330680553 (pp128) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 390.89 hours. Scaled time: 238.83 units (timescale=0.611). Factorization parameters were as follows: name: 15551_175 n: 32887009631195677707305614282358468404980032887009631195677707305614282358468404980032887009631195677707305614282358468404980032887009631195677707305614282358468404980032887 m: 100000000000000000000000000000000000 c5: 14 c0: -41 skew: 4 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 11300001) Primes: RFBsize:501962, AFBsize:502607, largePrimes:6474994 encountered Relations: rels:6944147, finalFF:1127040 Max relations in full relation-set: 0 Initial matrix: 1004635 x 1127040 with sparse part having weight 69379171. Pruned matrix : 898670 x 903757 with weight 54223156. Total sieving time: 335.51 hours. Total relation processing time: 1.06 hours. Matrix solve time: 53.90 hours. Time per square root: 0.42 hours. Prototype def-par.txt line would be: snfs,176,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 390.89 hours. --------- CPU info (if available) ----------

Jan 28, 2007

By anonymous / GMP-ECM B1=250000
(28·10¹⁷⁰+17)/9 = 3(1)₁₆₉3_<171> = C171
C171 = P40 · C132
P40 = 1364116464566141004805456799576331094877_<40>
C132 = [228067851383980179396737331050460171350301360191884615279312516244379676595735991540084639749089760281280334949498526496536231019869_<132>]

Jan 27, 2007 (5th)

By anonymous / GMP-ECM B1=250000
(2·10¹⁶⁴-11)/9 = (2)₁₆₃1_<164> = 3 · 7 · C163
C163 = P28 · P135
P28 = 2705744860522788636251121991_<28>
P135 = 391094176557577793883311466250837928124679378240286597104225549984604139382887743727588795990566928192149494732283550828037750266209311_<135>
(89·10¹⁶⁶+1)/9 = 9(8)₁₆₅9_<167> = 3 · 7 · C166
C166 = P31 · C136
P31 = 2145267415169671460471822733293_<31>
C136 = [2195061872331785564833392556541334193678898931031362398283536977263473924321435784902869096812578999064592069887228245952439930289418313_<136>]

Jan 27, 2007 (4th)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(14·10¹⁵²-41)/9 = 1(5)₁₅₁1_<153> = 151 · 973057 · 847196941648551132106333324010269_<33> · C112
C112 = P36 · P77
P36 = 108123011159930669845571642420238883_<36>
P77 = 11557603368746529230971013510751174250574322894480256454543811212283540578959_<77>

Number: trial N=1249642878021033284825168208794036075612473963907528490275936932677995158635356633750195668907903252864903462797 ( 112 digits) SNFS difficulty: 153 digits. Divisors found: r1=108123011159930669845571642420238883 (pp36) r2=11557603368746529230971013510751174250574322894480256454543811212283540578959 (pp77) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 47.63 hours. Scaled time: 26.15 units (timescale=0.549). Factorization parameters were as follows: n: 1249642878021033284825168208794036075612473963907528490275936932677995158635356633750195668907903252864903462797 m: 1000000000000000000000000000000 c5: 1400 c0: -41 skew: 1 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176059, largePrimes:5528339 encountered Relations: rels:5432457, finalFF:410172 Max relations in full relation-set: 0 Initial matrix: 352428 x 410172 with sparse part having weight 28109504. Pruned matrix : 318706 x 320532 with weight 20499291. Total sieving time: 39.98 hours. Total relation processing time: 0.37 hours. Matrix solve time: 6.94 hours. Time per square root: 0.34 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 47.63 hours. --------- CPU info (if available) ----------

Jan 27, 2007 (3rd)

By Shaopu Lin / Msieve v. 1.16
2·10¹⁷⁹-9 = 1(9)₁₇₈1_<180> = 11 · 109 · 1531 · 197084090167072070444501_<24> · 30192185167289557139962813541_<29> · 11175180923359872868625684424731_<32> · C91
C91 = P44 · P47
P44 = 38745744185364135989275373176013064492968519_<44>
P47 = 42287395639301185430766513250585783292869637311_<47>

Fri Jan 26 22:27:14 2007 Fri Jan 26 22:27:14 2007 Fri Jan 26 22:27:14 2007 Msieve v. 1.16 Fri Jan 26 22:27:14 2007 random seeds: a6eb1203 b5238d3a Fri Jan 26 22:27:14 2007 factoring 1638456613705646625512724389739829497429579295062517050049568260367385691018719269270812409 (91 digits) Fri Jan 26 22:27:14 2007 using multiplier of 41 Fri Jan 26 22:27:14 2007 sieve interval: 9 blocks of size 65536 Fri Jan 26 22:27:14 2007 processing polynomials in batches of 6 Fri Jan 26 22:27:14 2007 using a sieve bound of 1648483 (62353 primes) Fri Jan 26 22:27:14 2007 using large prime bound of 145066504 (27 bits) Fri Jan 26 22:27:14 2007 using double large prime bound of 490705292959992 (42-49 bits) Fri Jan 26 22:27:14 2007 using trial factoring cutoff of 51 bits Fri Jan 26 22:27:14 2007 polynomial 'A' values have 12 factors Sat Jan 27 01:15:16 2007 62806 relations (17263 full + 45543 combined from 679877 partial), need 62449 Sat Jan 27 01:15:17 2007 begin with 697140 relations Sat Jan 27 01:15:19 2007 reduce to 149952 relations in 11 passes Sat Jan 27 01:15:19 2007 attempting to read 149952 relations Sat Jan 27 01:15:21 2007 recovered 149952 relations Sat Jan 27 01:15:21 2007 recovered 133574 polynomials Sat Jan 27 01:15:21 2007 attempting to build 62806 cycles Sat Jan 27 01:15:21 2007 found 62806 cycles in 5 passes Sat Jan 27 01:15:21 2007 distribution of cycle lengths: Sat Jan 27 01:15:21 2007 length 1 : 17263 Sat Jan 27 01:15:21 2007 length 2 : 12770 Sat Jan 27 01:15:21 2007 length 3 : 11417 Sat Jan 27 01:15:21 2007 length 4 : 8177 Sat Jan 27 01:15:21 2007 length 5 : 5706 Sat Jan 27 01:15:21 2007 length 6 : 3337 Sat Jan 27 01:15:21 2007 length 7 : 1922 Sat Jan 27 01:15:21 2007 length 9+: 2214 Sat Jan 27 01:15:21 2007 largest cycle: 18 relations Sat Jan 27 01:15:22 2007 matrix is 62353 x 62806 with weight 3655627 (avg 58.21/col) Sat Jan 27 01:15:22 2007 filtering completed in 4 passes Sat Jan 27 01:15:22 2007 matrix is 60789 x 60853 with weight 3464835 (avg 56.94/col) Sat Jan 27 01:15:23 2007 saving the first 48 matrix rows for later Sat Jan 27 01:15:23 2007 matrix is 60741 x 60853 with weight 2679405 (avg 44.03/col) Sat Jan 27 01:15:23 2007 matrix includes 32 packed rows Sat Jan 27 01:17:20 2007 lanczos halted after 962 iterations Sat Jan 27 01:17:20 2007 recovered 17 nontrivial dependencies Sat Jan 27 01:17:23 2007 prp44 factor: 38745744185364135989275373176013064492968519 Sat Jan 27 01:17:23 2007 prp47 factor: 42287395639301185430766513250585783292869637311 Sat Jan 27 01:17:23 2007 elapsed time 02:50:09

(7·10¹⁸⁵-61)/9 = (7)₁₈₄1_<185> = 15869070719_<11> · 221773283827_<12> · 277298503527337722497_<21> · 6105120015064145026321_<22> · 148620272450318305620892247_<27> · C95
C95 = P45 · P51
P45 = 224862363761607190215772027417022972537690791_<45>
P51 = 390623396058772295453140324659480039189781576841383_<51>

Sat Jan 27 01:39:07 2007 Sat Jan 27 01:39:07 2007 Sat Jan 27 01:39:07 2007 Msieve v. 1.16 Sat Jan 27 01:39:07 2007 random seeds: 423f607f 2ef68dad Sat Jan 27 01:39:07 2007 factoring 87836500178362012339391534087557870391705073829131196795608369383843280519245566419346506803953 (95 digits) Sat Jan 27 01:39:07 2007 using multiplier of 33 Sat Jan 27 01:39:07 2007 sieve interval: 9 blocks of size 65536 Sat Jan 27 01:39:07 2007 processing polynomials in batches of 6 Sat Jan 27 01:39:07 2007 using a sieve bound of 2190817 (81176 primes) Sat Jan 27 01:39:07 2007 using large prime bound of 328622550 (28 bits) Sat Jan 27 01:39:07 2007 using double large prime bound of 2138233886692800 (43-51 bits) Sat Jan 27 01:39:07 2007 using trial factoring cutoff of 55 bits Sat Jan 27 01:39:07 2007 polynomial 'A' values have 12 factors Sat Jan 27 08:17:49 2007 81535 relations (20590 full + 60945 combined from 1191119 partial), need 81272 Sat Jan 27 08:17:51 2007 begin with 1211709 relations Sat Jan 27 08:17:53 2007 reduce to 208204 relations in 10 passes Sat Jan 27 08:17:53 2007 attempting to read 208204 relations Sat Jan 27 08:17:56 2007 recovered 208204 relations Sat Jan 27 08:17:56 2007 recovered 193380 polynomials Sat Jan 27 08:17:57 2007 attempting to build 81535 cycles Sat Jan 27 08:17:57 2007 found 81535 cycles in 6 passes Sat Jan 27 08:17:57 2007 distribution of cycle lengths: Sat Jan 27 08:17:57 2007 length 1 : 20590 Sat Jan 27 08:17:57 2007 length 2 : 14946 Sat Jan 27 08:17:57 2007 length 3 : 14053 Sat Jan 27 08:17:57 2007 length 4 : 10885 Sat Jan 27 08:17:57 2007 length 5 : 8137 Sat Jan 27 08:17:57 2007 length 6 : 5231 Sat Jan 27 08:17:57 2007 length 7 : 3252 Sat Jan 27 08:17:57 2007 length 9+: 4441 Sat Jan 27 08:17:57 2007 largest cycle: 18 relations Sat Jan 27 08:17:58 2007 matrix is 81176 x 81535 with weight 5530736 (avg 67.83/col) Sat Jan 27 08:17:59 2007 filtering completed in 3 passes Sat Jan 27 08:17:59 2007 matrix is 79614 x 79678 with weight 5312625 (avg 66.68/col) Sat Jan 27 08:18:00 2007 saving the first 48 matrix rows for later Sat Jan 27 08:18:00 2007 matrix is 79566 x 79678 with weight 4464667 (avg 56.03/col) Sat Jan 27 08:18:00 2007 matrix includes 32 packed rows Sat Jan 27 08:21:49 2007 lanczos halted after 1260 iterations Sat Jan 27 08:21:49 2007 recovered 17 nontrivial dependencies Sat Jan 27 08:21:50 2007 prp45 factor: 224862363761607190215772027417022972537690791 Sat Jan 27 08:21:50 2007 prp51 factor: 390623396058772295453140324659480039189781576841383 Sat Jan 27 08:21:50 2007 elapsed time 06:42:43

Jan 27, 2007 (2nd)

By anonymous / GMP-ECM B1=1000000
3·10¹⁸⁷-1 = 2(9)_187<188> = 337638313967807182936900258849_<30> · 99433004049017708218656527004744377_<35> · C123
C123 = P38 · P86
P38 = 47527930809248160978423930812756482163_<38>
P86 = 18801394593718690635972065355070083787495002798358052698294076860191499763907183853901_<86>

Jan 27, 2007

By anonymous / GMP-ECM B1=250000, MSieve v1.16
(88·10¹⁹⁴-7)/9 = 9(7)_194<195> = 43 · 23003 · 634535111927_<12> · 1951393022626261924751_<22> · 547570844499373857530554471573_<30> · C127
C127 = P32 · P95
P32 = 48107124890599585578495748781261_<32>
P95 = 30306592044099494833296625144191873374602388878007797681916634756640525090115817870813053056673_<95>
(2·10¹⁹¹-17)/3 = (6)₁₉₀1_<191> = 7 · 173 · 971 · 2927 · 14214359 · 100193434669659501271_<21> · 1602281856559924955652817548643_<31> · C124
C124 = P31 · P94
P31 = 1644531636700037764624359507241_<31>
P94 = 5161488372639752825103822995595924817290232477476092481206743069772069525520002906576390320729_<94>
(37·10¹⁹⁵-1)/9 = 4(1)_195<196> = 71 · 113 · 46807 · 3384119 · 486904141 · 417295439123_<12> · 4293419064773_<13> · 97703178491495521151_<20> · C128
C128 = P27 · P31 · P35 · P37
P27 = 196191505225250176990551527_<27>
P31 = 1761861763144099356621413608877_<31>
P35 = 20971151211185507399381645857980401_<35>
P37 = 5235915257838810422327427243635140559_<37>

Jan 26, 2007 (2nd)

By Yousuke Koide / GMP-ECM
10¹¹²²+1 = 1(0)₁₁₂₁1_<1123> = 89 · 101 · 409 · 3061 · 7481 · 9901 · 1867009 · 5969449 · 28559389 · 134703241 · 259377229 · 330669109 · 1052788969_<10> · 1056689261_<10> · 1491383821_<10> · 5419170769_<10> · 155623169021_<12> · 225974065503889_<15> · 789390798020221_<15> · 2324557465671829_<16> · 2361000305507449_<16> · 44398000479007997569751764249_<29> · [86753591722429179196277499864388589956480152295384249796160875422130713714757701234774165691602257489604032643162429671366217011869609438248577758376700876992475958101904038555335751011999472619586747569193118442466419043654128126430212767873933904801118916504403436000264521920016711367535910291073154001_<305>] · C617
C617 = P34 · C584
P34 = 1626069667027811730097890497028709_<34>
C584 = [38024895493148854800653422613283099215921829542069685361376149530438607273756761856080690798460858306013738403327210096775753858364955072111700913685550086323551314496528572109201746210331371495892159739537730861707388507713450420982812460820500955660272354154047565719880526386831017892454808856584932783761589855269118267078394398844310325020537409424027865400201612007047186241443549154632450444461827579970147399485860432046334343781990972197401352137429710056905803889915605437642224194276297147589246706218777067781645257302547483648186681711700509728333708023948604899809154361_<584>]
10¹¹³⁴+1 = 1(0)₁₁₃₃1_<1135> = 29 · 101 · 109 · 281 · 1009 · 2269 · 9901 · 138349 · 153469 · 226549 · 2925721 · 121499449 · 605070649 · 43266855241_<11> · 999999000001_<12> · 4458192223320340849_<19> · 59779577156334533866654838281_<29> · 165358820733883770736233015527320175869593121_<45> · 22906246896437231227899575633620139766044690040039603689929_<59> · 341796090604674881849636380229010216626944264336893367139245334739710314141368913850637159182300704681_<102> · [6047454835259897495291763612688187307633783265817592232229921776128879618476797113843402906053007327639026397234531321020396264462376520701053491628306270734047741866573281_<172>] · C631
C631 = P31 · C600
P31 = 9391041808951630899634282002781_<31>
C600 = [560621332357238934616966299475879185594948023213484989719849902347321607522840870868240982017830818609496576717751001846384992466019177575772113466002928362881638102389245311752023261289995871190888731510926552515187860263342389008022937210983038113151859183801393207845341298386085668783815342356365241094283815795715052041003342637144443511871673205339970315039695946256107631941004511626733919690430244484123521955214196537703861419349594802139614911527667460644786375501470464939842659073308365090467618293426438485316382071831630280526263470317231189296842007453423797425254132235918123995126309_<600>]
10¹¹⁷⁶+1 = 1(0)₁₁₇₅1_<1177> = 17 · 113 · 337 · 54881 · 5882353 · 90982417 · 9999999900000001_<16> · 243827582384762881_<18> · 73765755896403138401_<20> · 403539336813078648113_<21> · 119968369144846370226083377_<27> · 2070270028985341766616009080161_<31> · 5649333362757164788488040397332687608183771313_<46> · 1433319827159466789806966856379479179916136529424792832495021393_<64> · [7992725630817993387509447658266753245639852185667964923325577122343436495149387850592327530913518038942862729080180818453049855292323904941844008543186707256609661088744711417696766636212293916732420331335060909121431187023889518420170993615058113539941380716719809_<265>] · C647
C647 = P31 · P616
P31 = 6026493503971642113374043042529_<31>
P616 = 7479886445735310298212281574509336546511732856430925087547061188016676845865995264958848117161322132078362683907579847337705836608461661471467610052096672642482112477495893044762678819315272269257998380984735846571207890240541285222802753354488658169465262832949126119749586317994111722121309522760462519340189609610673636927758365329167905230525383356760951540829820516095240537115382434110142048426496301179744763138100240260075123226913663798333509484702964612409358454187157356940022441684271671949641382237872243785316464905028255039958968839518027891677204894071733245344036271799385225297918407032044365486097_<616>
10¹¹⁹⁷+1 = 1(0)₁₁₉₆1_<1198> = 7² · 11 · 13 · 19² · 127 · 2053 · 2689 · 52579 · 459691 · 909091 · 1458973 · 3014047 · 5274739 · 4410785971_<10> · 2911579215499_<13> · 425991366045253_<15> · 909090909090909091_<18> · 247025236977306025681323889_<27> · 307010852070382484317401373_<27> · 1512142910568778709935813681_<28> · 189772422673235585874485732659_<30> · 753201806271328462547977919407_<30> · 61828645758322140842666144519962696417487_<41> · 72021403933746126426491665754465510017877_<41> · 17499101101496101893247811440257935152097401_<44> · 9284668536078237580134472469990637899155265743957_<49> · 6508684267533856834852965580950145565983063793936631379_<55> · 13147963643704652632557279758698587212033283223333451187877069162714784603584406816150353817835190742091970171_<110> · C615
C615 = P30 · C585
P30 = 237496748126669166794404728277_<30>
C585 = [922922847813274238465132665036974822845258340644871405049259288157037278960832039185277361106989442033855182445021438441460557399754790305129137620361964345260321681895127537725577401157304125322364765852776880361958443014430688589178204497272072060536416186604376537044072702325440583554858414064745202261449782554748371997504328009626327185383358681482752898447663266556749331693716692867547107530177574318083085484173010253581739509297324615785328784094793245470981713427472307156882602024997235453435574170873703830526131287425439986638786476519308647363490124573515449894635706459_<585>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 26, 2007

By anonymous / GMP-ECM
2·10¹⁷⁹-9 = 1(9)₁₇₈1_<180> = 11 · 109 · 1531 · 197084090167072070444501_<24> · 30192185167289557139962813541_<29> · C122
C122 = P32 · C91
P32 = 11175180923359872868625684424731_<32>
C91 = [1638456613705646625512724389739829497429579295062517050049568260367385691018719269270812409_<91>]
(7·10¹⁸⁵-61)/9 = (7)₁₈₄1_<185> = 15869070719_<11> · 221773283827_<12> · 277298503527337722497_<21> · 6105120015064145026321_<22> · C122
C122 = P27 · C95
P27 = 148620272450318305620892247_<27>
C95 = [87836500178362012339391534087557870391705073829131196795608369383843280519245566419346506803953_<95>]
(46·10¹⁸⁵-1)/9 = 5(1)_185<186> = 408259642487330101945035612397_<30> · 3203645235931038405785927946751_<31> · C126
C126 = P29 · P97
P29 = 42225614244343951163609141599_<29>
P97 = 9254617593308380520522644377019828568736648765423288773779267862870153521377141934322650187063587_<97>

Jan 25, 2007

By Bruce Dodson / GMP-ECM
10³¹⁹+1 = 1(0)₃₁₈1_<320> = 11² · 23 · 59 · 1277 · 4093 · 8779 · 357281 · 49561573447_<11> · 154083204930662557781201849_<27> · C261
C261 = P48 · P213
P48 = 776277205967881079419436133930781972785940099183_<48>
P213 = 626657074575157591670286302317367581085608444623672462325497948095754924038193523465028605939320242167544103268138744951272220715162590347092606720139597682209974278152746342271155492839334102785932336774383913103_<213>
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 24, 2007

By suberi / GGNFS-0.77.1-20060513-pentium4
(65·10¹⁵²+43)/9 = 7(2)₁₅₁7_<153> = C153
C153 = P67 · P87
P67 = 6550213397685364775986550762989701971314721157128662740183066777671_<67>
P87 = 110259342463168051908664963775205452537386095869746869361395515038990560570276567780437_<87>

Number: 72227_152 N=722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227 ( 153 digits) SNFS difficulty: 153 digits. Divisors found: r1=6550213397685364775986550762989701971314721157128662740183066777671 (pp67) r2=110259342463168051908664963775205452537386095869746869361395515038990560570276567780437 (pp87) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 43.65 hours. Scaled time: 28.11 units (timescale=0.644). Factorization parameters were as follows: n: 722222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222222227 m: 1000000000000000000000000000000 c5: 6500 c0: 43 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 100000 ) Primes: RFBsize:176302, AFBsize:176528, largePrimes:5513675 encountered Relations: rels:5400593, finalFF:452520 Max relations in full relation-set: 28 Initial matrix: 352897 x 452520 with sparse part having weight 40973848. Pruned matrix : 314268 x 316096 with weight 25151271. Total sieving time: 38.70 hours. Total relation processing time: 0.26 hours. Matrix solve time: 4.53 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 43.65 hours. --------- CPU info (if available) ----------

Jan 22, 2007

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(64·10¹⁹⁹-1)/9 = 7(1)_199<200> = 213858623010582669308138843_<27> · C174
C174 = P37 · P138
P37 = 1077191248228337884969877852893668437_<37>
P138 = 308686674498773596485102045607380792674577494444212073502216332070219814475881776793364497854287456457170773816915942831194015229438823921_<138>

Jan 22, 2007 (2nd)

By anonymous / GGNFS-0.77.1-20060513-athlon-xp
(88·10¹⁹⁹-7)/9 = 9(7)_199<200> = 4519 · 896656869650457347_<18> · 8483312795598774487816778893_<28> · 1543835570469777214012062083587_<31> · C121
C121 = P48 · P73
P48 = 914873563129692842500063828197206474139300829067_<48>
P73 = 2013927998159455384275057837246928675939493887607041425750660883017786337_<73>

Jan 22, 2007

By suberi / GGNFS-0.77.1-20060513-pentium4
(46·10¹⁵⁶-1)/9 = 5(1)_156<157> = C157
C157 = P71 · P86
P71 = 67019244981090782189600282925830264926764069416668648055858406658449659_<71>
P86 = 76263334696670950528282975338822886018690472664746650628843107889406583521316114469029_<86>

Number: 51111_156 N=5111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 ( 157 digits) SNFS difficulty: 157 digits. Divisors found: r1=67019244981090782189600282925830264926764069416668648055858406658449659 (pp71) r2=76263334696670950528282975338822886018690472664746650628843107889406583521316114469029 (pp86) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 51.94 hours. Scaled time: 32.88 units (timescale=0.633). Factorization parameters were as follows: n: 5111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111111 m: 10000000000000000000000000000000 c5: 460 c0: -1 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 2800001) Primes: RFBsize:216816, AFBsize:216621, largePrimes:5675467 encountered Relations: rels:5682667, finalFF:589446 Max relations in full relation-set: 28 Initial matrix: 433504 x 589446 with sparse part having weight 47631889. Pruned matrix : 344252 x 346483 with weight 29516259. Total sieving time: 45.09 hours. Total relation processing time: 0.38 hours. Matrix solve time: 6.28 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 51.94 hours. --------- CPU info (if available) ----------

Jan 20, 2007 (3rd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(32·10¹⁵²-23)/9 = 3(5)₁₅₁3_<153> = 166436508169_<12> · C142
C142 = P56 · P86
P56 = 24983431076103788248780535505480205082016621953205041909_<56>
P86 = 85508008469422781728401987797180068200107544091935710529435160405484716934720561999893_<86>

Number: trial N=2136283436050723047271475802452405123406573092123782739942106166426777071226645962304450583198389424242352782711578731736541539865039918515737 ( 142 digits) SNFS difficulty: 153 digits. Divisors found: r1=24983431076103788248780535505480205082016621953205041909 (pp56) r2=85508008469422781728401987797180068200107544091935710529435160405484716934720561999893 (pp86) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 48.45 hours. Scaled time: 26.60 units (timescale=0.549). Factorization parameters were as follows: n: 2136283436050723047271475802452405123406573092123782739942106166426777071226645962304450583198389424242352782711578731736541539865039918515737 m: 2000000000000000000000000000000 c5: 100 c0: -23 skew: 1 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176568, largePrimes:5365061 encountered Relations: rels:5173821, finalFF:395912 Max relations in full relation-set: 0 Initial matrix: 352934 x 395912 with sparse part having weight 33592138. Pruned matrix : 332328 x 334156 with weight 25008927. Total sieving time: 38.94 hours. Total relation processing time: 0.36 hours. Matrix solve time: 8.79 hours. Time per square root: 0.36 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 48.45 hours. --------- CPU info (if available) ----------

Jan 20, 2007 (2nd)

By anonymous / GMP-ECM 6.0.1 B1=250000
(14·10¹⁵²-41)/9 = 1(5)₁₅₁1_<153> = 151 · 973057 · C145
C145 = P33 · C112
P33 = 847196941648551132106333324010269_<33>
C112 = [1249642878021033284825168208794036075612473963907528490275936932677995158635356633750195668907903252864903462797_<112>]

Jan 20, 2007

By Philippe STROHL / GMP-ECM 6.1.1, Msieve v. 1.15
(7·10¹⁶⁶-43)/9 = (7)₁₆₅3_<166> = 3 · 7481 · 13757 · 148473482141539_<15> · 853488537369761_<15> · C129
C129 = P32 · P98
P32 = 14538253415215247868020585242079_<32>
P98 = 13673889379613398816674163054944244938766219062696794576223016527492008237104180821858195847688303_<98>
(7·10¹⁶⁷-43)/9 = (7)₁₆₆3_<167> = 53 · 229 · 3067 · 2967427 · 50588827 · C146
C146 = P38 · P108
P38 = 47278220151991681544364704654234008633_<38>
P108 = 294397847651944968902502340312163444716371421074662099661707779901800819546932063167621491168426789665148391_<108>
(7·10¹⁶⁹-43)/9 = (7)₁₆₈3_<169> = 3² · 113 · 49991 · C162
C162 = P31 · C131
P31 = 5632442647674936588605121832519_<31>
C131 = [27161013734198267779787441623856865261526769714349621384721227945530504045181223735394220143911476359430775105460879711466662180261_<131>]
(7·10¹⁷⁴-43)/9 = (7)₁₇₃3_<174> = 2763763 · 684763151954031346584259_<24> · C144
C144 = P40 · P41 · P64
P40 = 2473302413612770799643152842693818608929_<40>
P41 = 48717161252159813125322496014384853177479_<41>
P64 = 3410791362646423058561965131274823744860566964407906465017976259_<64>

Msieve v. 1.15 Thu Jan 18 12:37:58 2007 random seeds: 1cc05034 008c3284 Thu Jan 18 12:37:58 2007 factoring 166164072811519690832461794293729536181397138309018877229323442903299839132241567459806526348130335471061 (105 digits) Thu Jan 18 12:37:59 2007 using multiplier of 5 Thu Jan 18 12:37:59 2007 sieve interval: 9 blocks of size 65536 Thu Jan 18 12:37:59 2007 processing polynomials in batches of 6 Thu Jan 18 12:37:59 2007 using a sieve bound of 3877483 (137335 primes) Thu Jan 18 12:37:59 2007 using large prime bound of 581622450 (29 bits) Thu Jan 18 12:37:59 2007 using double large prime bound of 5975222047534050 (44-53 bits) Thu Jan 18 12:37:59 2007 using trial factoring cutoff of 60 bits Thu Jan 18 12:37:59 2007 polynomial 'A' values have 14 factors Thu Jan 18 12:38:05 2007 restarting with 28567 full and 1880708 partial relations Thu Jan 18 17:57:13 2007 137489 relations (31331 full + 106158 combined from 2063696 partial), need 137431 Thu Jan 18 17:58:20 2007 begin with 2095027 relations Thu Jan 18 17:58:39 2007 reduce to 368362 relations in 12 passes Thu Jan 18 17:58:39 2007 attempting to read 368362 relations Thu Jan 18 17:59:35 2007 recovered 368362 relations Thu Jan 18 17:59:36 2007 recovered 362031 polynomials Thu Jan 18 17:59:36 2007 attempting to build 137489 cycles Thu Jan 18 17:59:36 2007 found 137489 cycles in 6 passes Thu Jan 18 17:59:36 2007 distribution of cycle lengths: Thu Jan 18 17:59:36 2007 length 1 : 31331 Thu Jan 18 17:59:36 2007 length 2 : 22747 Thu Jan 18 17:59:36 2007 length 3 : 22468 Thu Jan 18 17:59:36 2007 length 4 : 19018 Thu Jan 18 17:59:36 2007 length 5 : 14682 Thu Jan 18 17:59:36 2007 length 6 : 10283 Thu Jan 18 17:59:36 2007 length 7 : 6972 Thu Jan 18 17:59:36 2007 length 9+: 9988 Thu Jan 18 17:59:36 2007 largest cycle: 25 relations Thu Jan 18 17:59:38 2007 matrix is 137335 x 137489 with weight 9928481 (avg 72.21/col) Thu Jan 18 17:59:39 2007 filtering completed in 3 passes Thu Jan 18 17:59:39 2007 matrix is 135618 x 135682 with weight 9726461 (avg 71.69/col) Thu Jan 18 17:59:40 2007 saving the first 48 matrix rows for later Thu Jan 18 17:59:41 2007 matrix is 135570 x 135682 with weight 7744943 (avg 57.08/col) Thu Jan 18 17:59:41 2007 matrix includes 32 packed rows Thu Jan 18 18:14:22 2007 lanczos halted after 2145 iterations Thu Jan 18 18:14:24 2007 recovered 16 nontrivial dependencies Thu Jan 18 18:14:25 2007 prp41 factor: 48717161252159813125322496014384853177479 Thu Jan 18 18:14:25 2007 prp64 factor: 3410791362646423058561965131274823744860566964407906465017976259

Jan 19, 2007

By suberi / GGNFS-0.77.1-20060513-pentium4
(82·10¹⁵²-1)/9 = 9(1)_152<153> = 62011 · 1325918057_<10> · C140
C140 = P50 · P90
P50 = 22550069509713664559026749569442993274151819905367_<50>
P90 = 491403265370574320319518339345132528573678706318350804575322001861825388135684665475793579_<90>

Number: 91111_152 N=11081177791406720661140565361292085684700961206642439012506081693013377229211683049809107096356752560306216353598571706777675679193006238493 ( 140 digits) SNFS difficulty: 153 digits. Divisors found: r1=22550069509713664559026749569442993274151819905367 (pp50) r2=491403265370574320319518339345132528573678706318350804575322001861825388135684665475793579 (pp90) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 50.37 hours. Scaled time: 31.94 units (timescale=0.634). Factorization parameters were as follows: n: 11081177791406720661140565361292085684700961206642439012506081693013377229211683049809107096356752560306216353598571706777675679193006238493 m: 1000000000000000000000000000000 c5: 8200 c0: -1 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2700001) Primes: RFBsize:176302, AFBsize:176209, largePrimes:5716740 encountered Relations: rels:5645464, finalFF:433017 Max relations in full relation-set: 28 Initial matrix: 352578 x 433017 with sparse part having weight 45882923. Pruned matrix : 324886 x 326712 with weight 31719937. Total sieving time: 43.89 hours. Total relation processing time: 0.40 hours. Matrix solve time: 5.88 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 50.37 hours. --------- CPU info (if available) ----------

Jan 18, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
5·10¹⁵²-1 = 4(9)_152<153> = 6855481 · 2245341102733892629_<19> · C128
C128 = P54 · P74
P54 = 744672514925099317753393598897750509322858911004792161_<54>
P74 = 43619875480449736340301463870436173570992711432762799275899219166322466491_<74>

Number: trial N=32482522374746180058621483531208610399036688675149812231189223879705895716746882551984274642698225023160685803137554338341977051 ( 128 digits) SNFS difficulty: 152 digits. Divisors found: r1=744672514925099317753393598897750509322858911004792161 (pp54) r2=43619875480449736340301463870436173570992711432762799275899219166322466491 (pp74) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 47.42 hours. Scaled time: 24.85 units (timescale=0.524). Factorization parameters were as follows: n: 32482522374746180058621483531208610399036688675149812231189223879705895716746882551984274642698225023160685803137554338341977051 m: 1000000000000000000000000000000 c5: 500 c0: -1 skew: 1 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:175758, largePrimes:5321331 encountered Relations: rels:5123801, finalFF:397027 Max relations in full relation-set: 0 Initial matrix: 352126 x 397027 with sparse part having weight 34163740. Pruned matrix : 330330 x 332154 with weight 25010739. Total sieving time: 37.60 hours. Total relation processing time: 0.37 hours. Matrix solve time: 9.06 hours. Time per square root: 0.40 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 47.42 hours. --------- CPU info (if available) ----------

Jan 15, 2007 (2nd)

By Yousuke Koide / GMP-ECM
(10¹⁰⁸³-1)/9 = (1)_1083<1083> = 3 · 37 · 21319 · 10749631 · 81671197 · 14830831597_<11> · 100110048074161_<15> · 1111111111111111111_<19> · 88231338953639484307_<20> · 103143975536225777711_<21> · 1290118416840734700343441_<25> · 2747268108721464854672161_<25> · 3931123022305129377976519_<25> · 4604283618329785428488803_<25> · 11614395396735967816534625117_<29> · 220706363362058009698248377980921202870796191_<45> · [191052108988079642161639478453077817431939492714409561224107609992762821015057864360563144173296784309543301342314616278756836677316469309622645791578584595972760708661277734651667182128879712026387_<198>] · C612
C612 = P33 · C579
P33 = 281997552115245416778864294482683_<33>
C579 = [402086827149525774203662574494762629781977575683448426528585129955793038573903462046000944607841346127321128768455654455924188986573902734362553095147618565475236745929228030480592036362734811733853089917782754468236923798842212827701672228437829439017037811329791783886407486347321166723616477001381322703982864461430430770579143530473025432640645589916634282025494866497100131324334144862038619504404398219865858608567272827886724898522016094545757984781148617753287717459033960492246352633577245622244313202654308552812851000246392034695534030715521754959243493574827942501717_<579>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 15, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(7·10¹⁵²-1)/3 = 2(3)_152<153> = 83 · 113 · 727 · 2451016031350978753621_<22> · C125
C125 = P44 · P81
P44 = 26409294675329952520047051769456344988144483_<44>
P81 = 528667830402888076655586260487501175538292363907075027865455219436299973499985007_<81>

Number: trial N=13961744518477230470350606331141294339438120672030969453053758445119353748825714158062698843568975300693893288090793249766381 ( 125 digits) SNFS difficulty: 152 digits. Divisors found: r1=26409294675329952520047051769456344988144483 (pp44) r2=528667830402888076655586260487501175538292363907075027865455219436299973499985007 (pp81) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 43.19 hours. Scaled time: 22.16 units (timescale=0.513). Factorization parameters were as follows: n: 13961744518477230470350606331141294339438120672030969453053758445119353748825714158062698843568975300693893288090793249766381 m: 1000000000000000000000000000000 c5: 700 c0: -1 skew: 1 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2000001) Primes: RFBsize:176302, AFBsize:176098, largePrimes:5270546 encountered Relations: rels:5044165, finalFF:395396 Max relations in full relation-set: 0 Initial matrix: 352467 x 395396 with sparse part having weight 33232459. Pruned matrix : 329623 x 331449 with weight 23770136. Total sieving time: 33.68 hours. Total relation processing time: 0.32 hours. Matrix solve time: 8.80 hours. Time per square root: 0.39 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 43.19 hours. --------- CPU info (if available) ----------

Jan 14, 2007

By suberi / GGNFS-0.77.1-20060513-pentium4
(89·10¹⁵²+1)/9 = 9(8)₁₅₁9_<153> = C153
C153 = P44 · P110
P44 = 10190419905946011268576405253557768498330481_<44>
P110 = 97041034424094909444203541070911753967506741360316917336324363078053621728588507016698294822884773453384829769_<110>

Number: 98889_152 N=988888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889 ( 153 digits) SNFS difficulty: 153 digits. Divisors found: r1=10190419905946011268576405253557768498330481 (pp44) r2=97041034424094909444203541070911753967506741360316917336324363078053621728588507016698294822884773453384829769 (pp110) Version: GGNFS-0.77.1-20060513-pentium4 Total time: 43.91 hours. Scaled time: 25.77 units (timescale=0.587). Factorization parameters were as follows: n: 988888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888888889 m: 1000000000000000000000000000000 c5: 8900 c0: 1 skew: 1 type: snfs Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2300001) Primes: RFBsize:176302, AFBsize:176708, largePrimes:5432566 encountered Relations: rels:5283059, finalFF:427140 Max relations in full relation-set: 28 Initial matrix: 353077 x 427140 with sparse part having weight 38289802. Pruned matrix : 323868 x 325697 with weight 25340331. Total sieving time: 38.58 hours. Total relation processing time: 0.32 hours. Matrix solve time: 4.83 hours. Time per square root: 0.18 hours. Prototype def-par.txt line would be: snfs,153,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 43.91 hours. --------- CPU info (if available) ----------

Jan 13, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(82·10¹⁵¹+71)/9 = 9(1)₁₅₀9_<152> = 3 · 11 · C151
C151 = P44 · P107
P44 = 35069973450053660193547829746422455292614743_<44>
P107 = 78726685233305657195869491293886236269349095897975770932964245045062337031935266807921069259133902472143401_<107>

Number: trial N=2760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760943 ( 151 digits) SNFS difficulty: 152 digits. Divisors found: r1=35069973450053660193547829746422455292614743 (pp44) r2=78726685233305657195869491293886236269349095897975770932964245045062337031935266807921069259133902472143401 (pp107) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 48.94 hours. Scaled time: 26.53 units (timescale=0.542). Factorization parameters were as follows: n: 2760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760942760943 m: 1000000000000000000000000000000 c5: 820 c0: 71 skew: 1 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:177415, largePrimes:5450553 encountered Relations: rels:5305620, finalFF:400263 Max relations in full relation-set: 0 Initial matrix: 353784 x 400263 with sparse part having weight 29574952. Pruned matrix : 328941 x 330773 with weight 22211379. Total sieving time: 39.83 hours. Total relation processing time: 0.37 hours. Matrix solve time: 8.35 hours. Time per square root: 0.39 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 48.94 hours. --------- CPU info (if available) ----------

Jan 12, 2007

By Sinkiti Sibata / GGNFS-0.77.1-20060722-pentium4
10¹⁷⁴+9 = 1(0)₁₇₃9_<175> = 17 · 61 · 1549 · 2389 · 100193 · 322986173 · 6165013601203081_<16> · C136
C136 = P60 · P76
P60 = 208421712381864306682687832510484289595729702062678553885057_<60>
P76 = 6266937537962105847323092604694692272408337913842644374735743827566692617849_<76>

Number: 10009_174 N=1306165853052246849781899785761522612064909196147670902104619894369304705937455838360831479554162941730696135578839680075251560772582393 ( 136 digits) SNFS difficulty: 175 digits. Divisors found: r1=208421712381864306682687832510484289595729702062678553885057 (pp60) r2=6266937537962105847323092604694692272408337913842644374735743827566692617849 (pp76) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 377.97 hours. Scaled time: 255.13 units (timescale=0.675). Factorization parameters were as follows: name: 10009_174 n: 1306165853052246849781899785761522612064909196147670902104619894369304705937455838360831479554162941730696135578839680075251560772582393 m: 100000000000000000000000000000000000 c5: 1 c0: 90 skew: 4 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 11100001) Primes: RFBsize:501962, AFBsize:502106, largePrimes:6479175 encountered Relations: rels:6943230, finalFF:1125572 Max relations in full relation-set: 0 Initial matrix: 1004132 x 1125572 with sparse part having weight 67043105. Pruned matrix : 899940 x 905024 with weight 52364715. Total sieving time: 323.38 hours. Total relation processing time: 1.57 hours. Matrix solve time: 52.66 hours. Time per square root: 0.36 hours. Prototype def-par.txt line would be: snfs,175,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 377.97 hours. --------- CPU info (if available) ----------

Jan 11, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(71·10¹⁵¹-17)/9 = 7(8)₁₅₀7_<152> = 7 · 11 · C151
C151 = P31 · P120
P31 = 2205331001349523573387368105769_<31>
P120 = 464570181938256034584375771245098460597040578279992603056301171490975801434203173520421749936099623719003021600191268699_<120>

Number: trial N=1024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531 ( 151 digits) SNFS difficulty: 152 digits. Divisors found: r1=2205331001349523573387368105769 (pp31) r2=464570181938256034584375771245098460597040578279992603056301171490975801434203173520421749936099623719003021600191268699 (pp120) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 56.86 hours. Scaled time: 27.41 units (timescale=0.482). Factorization parameters were as follows: n: 1024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531024531 m: 1000000000000000000000000000000 c5: 710 c0: -17 skew: 1 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2300001) Primes: RFBsize:176302, AFBsize:176394, largePrimes:5541572 encountered Relations: rels:5380892, finalFF:396083 Max relations in full relation-set: 0 Initial matrix: 352763 x 396083 with sparse part having weight 35361529. Pruned matrix : 336068 x 337895 with weight 27207539. Total sieving time: 46.19 hours. Total relation processing time: 0.48 hours. Matrix solve time: 9.73 hours. Time per square root: 0.47 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 56.86 hours. --------- CPU info (if available) ----------

Jan 9, 2007

By Alexander Mkrtychyan / ECM 6.1.1 B1=250000, GGNFS gnfs
(13·10¹⁵²-31)/9 = 1(4)₁₅₁1_<153>= 3 · 19 · 13897843 · 1472439017099_<13> · C132
C132 = P29 · P36 · P67
P29 = 69203916985256093273443311767_<29>
P36 = 348036351261652831474816398956189791_<36>
P67 = 5141454366009327072515341569204717595183088932017476504080654912297_<67>

Jan 8, 2007 (2nd)

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(32·10¹⁵¹-23)/9 = 3(5)₁₅₀3_<152> = 3³ · 11 · 751 · C147
C147 = P35 · P49 · P63
P35 = 29704376250087176089384555018418717_<35>
P49 = 7329957724845526430867535194461391003844188206139_<49>
P63 = 732131639319491982759033718127556933102481696860560835703262873_<63>

Number: trial N=159408355887124935800775422021168433359585896943494221198023535647444509702240135736215037886882834360271851024921005687391247385329350117040603799 ( 147 digits) SNFS difficulty: 152 digits. Divisors found: r1=29704376250087176089384555018418717 (pp35) r2=7329957724845526430867535194461391003844188206139 (pp49) r3=732131639319491982759033718127556933102481696860560835703262873 (pp63) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 42.66 hours. Scaled time: 23.16 units (timescale=0.543). Factorization parameters were as follows: n: 159408355887124935800775422021168433359585896943494221198023535647444509702240135736215037886882834360271851024921005687391247385329350117040603799 m: 2000000000000000000000000000000 c5: 10 c0: -23 skew: 1.18 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2000001) Primes: RFBsize:176302, AFBsize:176848, largePrimes:5314675 encountered Relations: rels:5109303, finalFF:397925 Max relations in full relation-set: 0 Initial matrix: 353216 x 397925 with sparse part having weight 34108941. Pruned matrix : 329641 x 331471 with weight 24727169. Total sieving time: 33.39 hours. Total relation processing time: 0.31 hours. Matrix solve time: 8.56 hours. Time per square root: 0.40 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 42.66 hours. --------- CPU info (if available) ----------

Jan 8, 2007

By Wataru Sakai / GMP-ECM 6.1 B1=11000000
(22·10¹⁹⁹-1)/3 = 7(3)_199<200> = C200
C200 = P37 · C164
P37 = 3916191119470963292419684811737586897_<37>
C164 = [18725677857938635102800293854827076679431418635663009851050014378555511187283752984298513248021481688538630054612852943075905187223262519297988713024848150252683589_<164>]

Jan 6, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(68·10¹⁵¹+13)/9 = 7(5)₁₅₀7_<152> = 7 · 11² · 47419 · 12673998341_<11> · C135
C135 = P65 · P70
P65 = 49485565672041586998733670851755250709829332943434100817742227397_<65>
P70 = 2999427830798455535060535857115593476513217672800509841431136058898137_<70>

Number: trial N=148428382899526212777811198132944467792004330764376905321699883663179315020730966778383238234201544317147463027711347263226731913659389 ( 135 digits) SNFS difficulty: 152 digits. Divisors found: r1=49485565672041586998733670851755250709829332943434100817742227397 (pp65) r2=2999427830798455535060535857115593476513217672800509841431136058898137 (pp70) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 49.49 hours. Scaled time: 26.87 units (timescale=0.543). Factorization parameters were as follows: n: 148428382899526212777811198132944467792004330764376905321699883663179315020730966778383238234201544317147463027711347263226731913659389 m: 1000000000000000000000000000000 c5: 680 c0: 13 skew: 1 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 1 ) Primes: RFBsize:176302, AFBsize:176093, largePrimes:5609088 encountered Relations: rels:5535765, finalFF:399520 Max relations in full relation-set: 0 Initial matrix: 352462 x 399520 with sparse part having weight 27003417. Pruned matrix : 328388 x 330214 with weight 20757565. Total sieving time: 44.17 hours. Total relation processing time: 0.46 hours. Matrix solve time: 4.47 hours. Time per square root: 0.39 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 49.49 hours. --------- CPU info (if available) ----------

Jan 5, 2007

By Alexander Mkrtychyan / GMP-ECM 6.1.1
2·10¹⁵⁴-1 = 1(9)_154<155> = 7 · 47 · 6473 · 60889 · 820757286744157311721_<21> · C123
C123 = P30 · P93
P30 = 709409658839905576587856324121_<30>
P93 = 264897466561486457459040040838987171311953866242931984277806029435709662518462889628767297703_<93>
(8·10¹⁵⁷-17)/9 = (8)₁₅₆7_<157> = 7 · C157
C157 = P28 · C129
P28 = 8739994595235952825155053837_<28>
C129 = [145290852986733231960131889761460491703794538807068334652232282714626655166495302127159129035785015114582751752183571455452299093_<129>]

Jan 4, 2007 (3rd)

By Yousuke Koide / GMP-ECM
(10⁷⁶⁷-1)/9 = (1)_767<767> = 53 · 79 · 305267 · 52306333 · 265371653 · 22214840363_<11> · 2559647034361_<13> · 4340876285657460212144534289928559826755746751_<46> · C673
C673 = P40 · C633
P40 = 2853501516303948010794020280793592455507_<40>
C633 = [889174648697326939177684178268996371003045246228078861746645062156730400269719384944790989153058757148303931075688667206199979737929977594118405280407892375436810251127379517901088006159225027254825092728128056986443222555451048911731324918821013872861811819723206169438781888017389966772691574054134710717924112989922189761624097116462890343930462811061144042405510972749980054180919764197806156130640326602991234046425531622069602350611573632172807373054802126586780509133235592708043145380986200739118832686526332661035841701755113675284212097858014641864160740582669607631627484363510546376918980352636496474171658410323177124641_<633>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Jan 4, 2007 (2nd)

By Alexander Mkrtychyan / GMP-ECM 6.1.1 B1=250000
(71·10¹⁹⁸-17)/9 = 7(8)₁₉₇7_<199> = 3 · 214174957 · C191
C191 = P31 · C160
P31 = 7028572982139370167790480255649_<31>
C160 = [1746862562467380248119030911967387426321458529683450495371415590591659222234729701631478386438280766700113951265045633708921823699119520795223624506675796515953_<160>]

Jan 4, 2007

By Alexander Mkrtychyan / ggnfs-0.77.1-20060513-win32-athlon-xp gnfs
(71·10¹⁸²-17)/9 = 7(8)₁₈₁7_<183> = 379 · 1021 · 2254085732632417_<16> · 70354500661406300509_<20> · 12897936240962970721879_<23> · C120
C120 = P44 · P77
P44 = 13855196374270107186027526900439874151942013_<44>
P77 = 71937552978293304611770250967086159641208638041183449177873097949335842345303_<77>

r1=13855196374270107186027526900439874151942013 (pp44) r2=71937552978293304611770250967086159641208638041183449177873097949335842345303 (pp77) skew: 44899.59 # norm 2.44e+016 c5: 36540 c4: -12653216212 c3: 487308661251077 c2: 24468059663304010833 c1: 43344197537957658137219 c0: -2793341395855198500654392085 # alpha -5.46 Y1: 1416246269647 Y0: -122225074088335592900342 # Murphy_E 2.94e-010 # M 892389320392560569094612128195562317644209955514499986657591571589603307854782580578088218581614492481306060370855465122 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 52 mfba: 52 rlambda: 2.4 alambda: 2.4 special-q: [2000000;2708819)U[3000000;3256093) maxrelsinff=14 rels:9724854, initialFF:0, finalFF:772267 Pruning matrix with wt=0.700 Initial matrix is 664491 x 772267 with sparse part having weight 50696051. (total weight is 89193220) Matrix pruned to 610266 x 613652 with weight 33681497. factors found on 0 dependency

Jan 3, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(64·10¹⁵¹+53)/9 = 7(1)₁₅₀7_<152> = 7 · 11 · 16094242777874151616807_<23> · C128
C128 = P55 · P74
P55 = 1203829898530831982368976018578666612940790262374639019_<55>
P74 = 47666258705407778643846255032921079760125039476078784971539438996875578437_<74>

Number: trial N=57382067380675432813932087137355619458933771524799307680083423847570082150658194677901984048504274751332116408746591264695233303 ( 128 digits) SNFS difficulty: 152 digits. Divisors found: r1=1203829898530831982368976018578666612940790262374639019 (pp55) r2=47666258705407778643846255032921079760125039476078784971539438996875578437 (pp74) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 54.26 hours. Scaled time: 27.83 units (timescale=0.513). Factorization parameters were as follows: n: 57382067380675432813932087137355619458933771524799307680083423847570082150658194677901984048504274751332116408746591264695233303 m: 2000000000000000000000000000000 c5: 20 c0: 53 skew: 1.22 type: snfsFactor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1200000, 2200001) Primes: RFBsize:176302, AFBsize:175293, largePrimes:5554678 encountered Relations: rels:5471328, finalFF:394558 Max relations in full relation-set: 0 Initial matrix: 351661 x 394558 with sparse part having weight 26795082. Pruned matrix : 329629 x 331451 with weight 20952925. Total sieving time: 45.59 hours. Total relation processing time: 0.51 hours. Matrix solve time: 7.79 hours. Time per square root: 0.37 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,48,48,2.3,2.3,100000 total time: 54.26 hours. --------- CPU info (if available) ----------

Jan 1, 2007

By Tyler Cadigan / GGNFS-0.77.1-20060722-pentium4
(2·10¹⁵⁷+7)/9 = (2)₁₅₆3_<157> = 3² · 109 · 2617 · 532529 · 1600321 · 10276598863_<11> · C128
C128 = P57 · P72
P57 = 275644563889396195991601548242531083466591268839139865547_<57>
P72 = 358563065522327430052239803536935822255232574805406605801612939291916351_<72>

Number: trial N=98835959822746937698308102564263258552782657865133587909723978877125659006562567345781266447367330423891517396177228162110858997 ( 128 digits) SNFS difficulty: 157 digits. Divisors found: r1=275644563889396195991601548242531083466591268839139865547 (pp57) r2=358563065522327430052239803536935822255232574805406605801612939291916351 (pp72) Version: GGNFS-0.77.1-20060722-pentium4 Total time: 71.01 hours. Scaled time: 31.96 units (timescale=0.450). Factorization parameters were as follows: n: 98835959822746937698308102564263258552782657865133587909723978877125659006562567345781266447367330423891517396177228162110858997 m: 10000000000000000000000000000000 c5: 200 c0: 7 skew: 1 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 1 ) Primes: RFBsize:216816, AFBsize:216921, largePrimes:5627776 encountered Relations: rels:5564900, finalFF:499188 Max relations in full relation-set: 0 Initial matrix: 433802 x 499188 with sparse part having weight 36071355. Pruned matrix : 403610 x 405843 with weight 26335382. Total sieving time: 59.98 hours. Total relation processing time: 0.55 hours. Matrix solve time: 10.00 hours. Time per square root: 0.48 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 71.01 hours. --------- CPU info (if available) ----------