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STUDIO KAMADA

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News and updates, November 2005

Nov 30, 2005

By Yousuke Koide / GMP-ECM
10⁴⁹⁷+1 = 1(0)₄₉₆1_<498> = 11 · 290249 · 909091 · 31321069464181068355415209323405389541706979493156189716729115659_<65> · C421
C421 = P45 · C376
P45 = 257206104226396960131527490253249591680919459_<45>
C376 = [4276725442844752084195044656852273452212189375274225952303705838930103356448606379274091472971879572677521453500151622763813191162899831949211457740137364703233755308405775264223457732676289894608533653739990364258897375954976343843923488590427317885165863553810505710052210760654344760310403003777839499733979012393924648170070669849341581368014258278534406166148949196622329_<376>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 28, 2005

Jason Papadopoulos's Msieve Version 1.03 was released.

Nov 25, 2005

By Robert Backstrom / GGNFS-0.77.1-20050930-athlon gnfs
(32·10¹⁶⁰-23)/9 = 3(5)₁₅₉3_<161> = 3² · 7 · 16878144188469281_<17> · 189434529856544291359630189822681_<33> · C111
C111 = P35(4118...) · P35(4759...) · P41
P35(4118...) = 41188122897353797743078248493349093_<35>
P35(4759...) = 47593069691496385363636147203850481_<35>
P41 = 90046609522723902890416032436182592043387_<41>

Number: n N=1765155955283971894965184413924047407319434606138080431576 95885317846927354528755225679405187762112269145483671 ( 111 digits) Divisors found: r1=41188122897353797743078248493349093 (pp35) r2=47593069691496385363636147203850481 (pp35) r3=90046609522723902890416032436182592043387 (pp41) Version: GGNFS-0.77.1-20050930-athlon Total time: 28.34 hours. Scaled time: 18.91 units (timescale=0.667). Factorization parameters were as follows: # 355555...555553 (159 5's) # (32*10^160-23)/9 name: n n: 176515595528397189496518441392404740731943460613808043157 695885317846927354528755225679405187762112269145483671 skew: 21821.03 # norm 2.65e+014 c5: 3900 c4: 640497854 c3: 131320705402 c2: -172149383147910141 c1: -1100165321270460367988 c0: 8860814731706342417727825 # alpha -4.35 Y1: 11634369223 Y0: -2143599354655530493828 # Murphy_E 9.26e-010 # M 100301042918189501491054762514367770434534098282913556488800 758058426232457447529369045821047415529707263817393 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [640000, 1840001) Primes: RFBsize:230209, AFBsize:230031, largePrimes:7309111 encountered Relations: rels:7052907, finalFF:531991 Max relations in full relation-set: 28 Initial matrix: 460320 x 531991 with sparse part having weight 41456589. Pruned matrix : 399066 x 401431 with weight 25779177. Total sieving time: 23.72 hours. Total relation processing time: 0.51 hours. Matrix solve time: 3.94 hours. Time per square root: 0.17 hours. Prototype def-par.txt line would be: gnfs,110,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,max Time,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 28.34 hours. --------- CPU info (if available) ---------- Athlon 64 3400+, using Win 2000 and Cygwin

Nov 23, 2005

(10¹⁶⁴+53)/9 = (1)₁₆₃7_<164> = 23 · 1181 · 1072846141_<10> · 4979637490110920135575357_<25> · C125
C125 = P45 · P81
P45 = 579666422697751975195269908990369569487929393_<45>
P81 = 132088935761780860187538433903244358628257819621586279422515597881892186313365999_<81>

Number: 11117_164 N=76567520870984671402216372146068685131617912693435529484170929976066856392989540304421179373251166466237815528208010678908607 ( 125 digits) SNFS difficulty: 165 digits. Divisors found: r1=579666422697751975195269908990369569487929393 (pp45) r2=132088935761780860187538433903244358628257819621586279422515597881892186313365999 (pp81) Version: GGNFS-0.77.1 Total time: 129.67 hours. Scaled time: 86.23 units (timescale=0.665). Factorization parameters were as follows: name: 11117_164 n: 76567520870984671402216372146068685131617912693435529484170929976066856392989540304421179373251166466237815528208010678908607 m: 1000000000000000000000000000000000 c5: 1 c0: 530 skew: 3 type:snfs Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2500000, 5400001) Relations: rels:6106429, finalFF:833852 Initial matrix: 696993 x 833852 with sparse part having weight 50667968. Pruned matrix : 649687 x 653235 with weight 30381938. Total sieving time: 116.64 hours. Total relation processing time: 0.64 hours. Matrix solve time: 12.16 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: type:snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 129.67 hours. --------- CPU info (if available) ----------

Nov 20, 2005 (2nd)

Jason Papadopoulos's Msieve Version 1.02 was released.

Nov 20, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
10¹⁷⁵-3 = (9)₁₇₄7_<175> = 7 · 1597 · 29881 · 172999063 · C159
C159 = P49 · P110
P49 = 9268821528859618014021841051698997978389808253059_<49>
P110 = 18669541205894303564860318174560332272211175169567548259092720680541673892290464197693810037820913078505439459_<110>

Number: 99997_175 N=173044645463124875308654250148307327141282691858450047624533570449134406107713916877846274540355538407060169874982484056017148608411257699070904980141876055081 ( 159 digits) SNFS difficulty: 175 digits. Divisors found: r1=9268821528859618014021841051698997978389808253059 (pp49) r2=18669541205894303564860318174560332272211175169567548259092720680541673892290464197693810037820913078505439459 (pp110) Version: GGNFS-0.77.1 Total time: 291.77 hours. Scaled time: 228.75 units (timescale=0.784). Factorization parameters were as follows: name: 99997_175 n: 173044645463124875308654250148307327141282691858450047624533570449134406107713916877846274540355538407060169874982484056017148608411257699070904980141876055081 m: 100000000000000000000000000000000000 c5: 1 c0: -3 type: snfs skew: 1 qintsize: 10000 Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [3700000, 9880001) Relations: rels:6823811, finalFF:1152346 Initial matrix: 1003587 x 1152346 with sparse part having weight 62879673. Pruned matrix : 940067 x 945148 with weight 42644863. Total sieving time: 274.39 hours. Total relation processing time: 0.55 hours. Matrix solve time: 16.56 hours. Time per square root: 0.27 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: 291.77 hours. --------- CPU info (if available) ----------

Nov 19, 2005

By Bruce Dodson / GMP-ECM
10³³⁷+1 = 1(0)₃₃₆1_<338> = 11 · 121321 · 2251702571_<10> · 55027074590990508852961_<23> · C299
C299 = P50 · C249
P50 = 71489171229856447321502908314697600957469967193571_<50>
C249 = [845947911267668011260418402905221798709538045194622532077124717667915696516323339976849125310476270253990769838122404582089780235313355012026006342260665712122542154882083354742870813133191883569094583330071977149328116963184987608368374283219788971_<249>]
Reference: Factorizations of Repunit Numbers (Yousuke Koide)

Nov 17, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁶²+53)/9 = (1)₁₆₁7_<162> = 3 · 17 · 122719115923_<12> · 8289991952909_<13> · 2341170250453601111_<19> · C117
C117 = P53 · P65
P53 = 24506725673911022704067759597717156724027838359864899_<53>
P65 = 37325247945845446415539113922343529144726238473977360155829584229_<65>

Number: 11117_162 N=914719612119545263675461937241443063013555037248436307849707742871314393654601415900660242680746530526004491781077871 ( 117 digits) SNFS difficulty: 162 digits. Divisors found: r1=24506725673911022704067759597717156724027838359864899 (pp53) r2=37325247945845446415539113922343529144726238473977360155829584229 (pp65) Version: GGNFS-0.77.1 Total time: 105.69 hours. Scaled time: 70.39 units (timescale=0.666). Factorization parameters were as follows: name: 11117_162 n: 914719612119545263675461937241443063013555037248436307849707742871314393654601415900660242680746530526004491781077871 m: 100000000000000000000000000000000 c5: 100 c0: 53 skew: 2 type: snfs Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2250000, 4750001) Relations: rels:5972203, finalFF:751230 Initial matrix: 631348 x 751230 with sparse part having weight 49104424. Pruned matrix : 595482 x 598702 with weight 29675461. Total sieving time: 94.57 hours. Total relation processing time: 0.69 hours. Matrix solve time: 10.23 hours. Time per square root: 0.20 hours. Prototype def-par.txt line would be: snfs,162,5,0,0,0,0,0,0,0,0,4500000,4500000,27,27,48,48,2.3,2.3,100000 total time: 105.69 hours. --------- CPU info (if available) ----------

Nov 13, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁶¹+53)/9 = (1)₁₆₀7_<161> = 281 · 4013 · C154
C154 = P35 · P58 · P62
P35 = 50739852137588998696251543347050693_<35>
P58 = 3262787785327459169159050401052035323713463022204671436907_<58>
P62 = 59517404782483971274142048942014964043816026944188184646684639_<62>

Number: 11117_161 N=9853306922529458185373613257900356857216813249387099676151361377224297821325453052588971173854998932394194943933205614769003506496334520558284428907750089 ( 154 digits) SNFS difficulty: 161 digits. Divisors found: r1=50739852137588998696251543347050693 (pp35) r2=3262787785327459169159050401052035323713463022204671436907 (pp58) r3=59517404782483971274142048942014964043816026944188184646684639 (pp62) Version: GGNFS-0.77.1 Total time: 83.06 hours. Scaled time: 49.51 units (timescale=0.596). Factorization parameters were as follows: name: 11117_161 n: 9853306922529458185373613257900356857216813249387099676151361377224297821325453052588971173854998932394194943933205614769003506496334520558284428907750089 m: 100000000000000000000000000000000 c5: 10 c0: 53 skew: 3 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2000000, 3900001) Relations: rels:5837083, finalFF:702561 Initial matrix: 566664 x 702561 with sparse part having weight 45920716. Pruned matrix : 526237 x 529134 with weight 25119688. Total sieving time: 74.33 hours. Total relation processing time: 0.54 hours. Matrix solve time: 7.98 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,161,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 83.06 hours. --------- CPU info (if available) ----------

Nov 9, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁵⁸+53)/9 = (1)₁₅₇7_<158> = 29² · 97 · 463247 · 626147 · C141
C141 = P60 · P81
P60 = 985983236774903257591498125826627448246288079036449469432979_<60>
P81 = 476245965444136338163665893620237334994768974375044142478647515154052568234133411_<81>

Number: 11117_158 N=469570538509598273965270891402290886093146419388365280422511467051739803132582009457307720315293338569836222653663259799014426447555609161369 ( 141 digits) SNFS difficulty: 158 digits. Divisors found: r1=985983236774903257591498125826627448246288079036449469432979 (pp60) r2=476245965444136338163665893620237334994768974375044142478647515154052568234133411 (pp81) Version: GGNFS-0.77.1 Total time: 67.58 hours. Scaled time: 45.08 units (timescale=0.667). Factorization parameters were as follows: name: 11117_158 n: 469570538509598273965270891402290886093146419388365280422511467051739803132582009457307720315293338569836222653663259799014426447555609161369 m: 10000000000000000000000000000000 c5: 1000 c0: 53 skew: 2 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 3200001) Relations: rels:5754223, finalFF:563571 Initial matrix: 433663 x 563571 with sparse part having weight 51133785. Pruned matrix : 408428 x 410660 with weight 26962081. Total sieving time: 61.35 hours. Total relation processing time: 0.33 hours. Matrix solve time: 5.74 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,158,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 67.58 hours. --------- CPU info (if available) ----------

Nov 8, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
10¹⁷⁰-3 = (9)₁₆₉7_<170> = 38817280012777264790994290797_<29> · C142
C142 = P69 · P73
P69 = 785177523560258358188968099569100871126763206274307022292736906310723_<69>
P73 = 3281006120624321591156094138451344572368459459917701683211206237910480987_<73>

Number: 99997_170 N=2576172260577855142848298542798072596718901873646661264007524216056015115292366099141617460574776708224208202201460542857840458968464605723601 ( 142 digits) SNFS difficulty: 170 digits. Divisors found: r1=785177523560258358188968099569100871126763206274307022292736906310723 (pp69) r2=3281006120624321591156094138451344572368459459917701683211206237910480987 (pp73) Version: GGNFS-0.77.1 Total time: 117.10 hours. Scaled time: 131.62 units (timescale=1.124). Factorization parameters were as follows: name: 99997_170 n: 2576172260577855142848298542798072596718901873646661264007524216056015115292366099141617460574776708224208202201460542857840458968464605723601 m: 10000000000000000000000000000000000 c5: 1 c0: -3 type: snfs skew: 1 qintsize: 10000 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [3000000, 6770001) Relations: rels:6238207, finalFF:927778 Initial matrix: 825609 x 927778 with sparse part having weight 50425277. Pruned matrix : 785050 x 789242 with weight 35183083. Total sieving time: 110.15 hours. Total relation processing time: 0.28 hours. Matrix solve time: 6.51 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,6000000,27,27,48,48,2.6,2.6,100000 total time: 117.10 hours. --------- CPU info (if available) ----------

Nov 6, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁵⁶+53)/9 = (1)₁₅₅7_<156> = 3³ · 243871 · 773779 · 7628621820151_<13> · C130
C130 = P44 · P86
P44 = 80973023481624511633767692358155083219925491_<44>
P86 = 35304509873348597125490432448515136345367528972449377872256910472199043353418974134759_<86>

Number: 11117_156 N=2858712906981900368281118448301739997723969786176745172377611548740090357833579081883869141630888902748695880468417245300173241669 ( 130 digits) SNFS difficulty: 156 digits. Divisors found: r1=80973023481624511633767692358155083219925491 (pp44) r2=35304509873348597125490432448515136345367528972449377872256910472199043353418974134759 (pp86) Version: GGNFS-0.77.1 Total time: 52.52 hours. Scaled time: 35.03 units (timescale=0.667). Factorization parameters were as follows: name: 11117_156 n: 2858712906981900368281118448301739997723969786176745172377611548740090357833579081883869141630888902748695880468417245300173241669 m: 10000000000000000000000000000000 c5: 10 c0: 53 skew: 2 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2700001) Relations: rels:5615157, finalFF:560696 Initial matrix: 433643 x 560696 with sparse part having weight 45021990. Pruned matrix : 400970 x 403202 with weight 22657062. Total sieving time: 47.23 hours. Total relation processing time: 0.29 hours. Matrix solve time: 4.85 hours. Time per square root: 0.16 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: 52.52 hours. --------- CPU info (if available) ----------

Nov 4, 2005

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁵⁵+53)/9 = (1)₁₅₄7_<155> = 233 · 3037 · 107857 · 169803233 · C135
C135 = P50 · P86
P50 = 15565457897782952939101666553930106105882725052823_<50>
P86 = 55080843875587155475209767290120086884583549324550097061432527306270679817057702993679_<86>

Number: 11117_155 N=857358556319807883303961653311890561571369091658335896770480362432033819097213029290292821918924367560869953150832995161829340510105817 ( 135 digits) SNFS difficulty: 155 digits. Divisors found: r1=15565457897782952939101666553930106105882725052823 (pp50) r2=55080843875587155475209767290120086884583549324550097061432527306270679817057702993679 (pp86) Version: GGNFS-0.77.1 Total time: 48.39 hours. Scaled time: 32.23 units (timescale=0.666). Factorization parameters were as follows: name: 11117_155 n: 857358556319807883303961653311890561571369091658335896770480362432033819097213029290292821918924367560869953150832995161829340510105817 m: 10000000000000000000000000000000 c5: 1 c0: 53 skew: 2 type: snfsFactor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [1500000, 2700001) Relations: rels:5706648, finalFF:592979 Initial matrix: 433781 x 592979 with sparse part having weight 47303127. Pruned matrix : 394227 x 396459 with weight 21255170. Total sieving time: 43.27 hours. Total relation processing time: 0.26 hours. Matrix solve time: 4.71 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,155,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 48.39 hours. --------- CPU info (if available) ----------

Nov 3, 2005

By Makoto Kamada / GGNFS-0.77.1-20050930-pentium4
(5·10¹⁷⁰+31)/9 = (5)₁₆₉9_<170> = C170
C170 = P77 · P94
P77 = 10324769197737224566684914222305982001893528968121934066755022389561971195587_<77>
P94 = 5380803627816794763419223827948916327062256097990336526388743980119926827911302731685260313357_<94>

Number: 55559_170 N=55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559 ( 170 digits) SNFS difficulty: 170 digits. Divisors found: r1=10324769197737224566684914222305982001893528968121934066755022389561971195587 (pp77) r2=5380803627816794763419223827948916327062256097990336526388743980119926827911302731685260313357 (pp94) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 188.51 hours. Scaled time: 115.75 units (timescale=0.614). Factorization parameters were as follows: type: snfs n: 55555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555555559 m: 10000000000000000000000000000000000 c5: 5 c0: 31 skew: 3 rlim: 6000000 alim: 3000000 lpbr: 27 lpba: 27 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 q0: 3000000 qintsize: 25000 Factor base limits: 6000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3000000, 8925001) Primes: RFBsize:412849, AFBsize:217137, largePrimes:6461696 encountered Relations: rels:6759240, finalFF:709598 Max relations in full relation-set: 28 Initial matrix: 630051 x 709598 with sparse part having weight 95754203. Pruned matrix : 572543 x 575757 with weight 81682473. Total sieving time: 161.54 hours. Total relation processing time: 0.47 hours. Matrix solve time: 26.36 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: snfs,170,5,0,0,0,0,0,0,0,0,6000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 188.51 hours. --------- CPU info (if available) ----------

Note: P77 is the largest factor found by GGNFS in our tables so far. The changes of qintsize were 1000000(3000000-), 500000(7000000-), 100000(8500000-) and 25000(8900000-).

Nov 2, 2005 (2nd)

By Sinkiti Sibata / GGNFS-0.77.1
(10¹⁶⁰+17)/9 = (1)₁₅₉3_<160> = 3³ · 7 · 23² · 53 · 107881 · 301787558315959860024628403_<27> · C121
C121 = P49 · P73
P49 = 2658405350165222545211816611457772806715036944933_<49>
P73 = 2422683311177048724550239437910491994873142257019128245981528735469849839_<73>

Number: 11113_160 N=6440474276189063029469896370990258701549175964742824120735650981327705765751244667703443710331099759156990377210821915787 ( 121 digits) SNFS difficulty: 160 digits. Divisors found: r1=2658405350165222545211816611457772806715036944933 (pp49) r2=2422683311177048724550239437910491994873142257019128245981528735469849839 (pp73) Version: GGNFS-0.77.1 Total time: 59.99 hours. Scaled time: 39.96 units (timescale=0.666). Factorization parameters were as follows: name: 11113_160 n: 6440474276189063029469896370990258701549175964742824120735650981327705765751244667703443710331099759156990377210821915787 m: 100000000000000000000000000000000 c5: 1 c0: 17 skew: 2 type: snfs Factor base limits: 4000000/4000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2000000, 3400001) Relations: rels:5785461, finalFF:720044 Initial matrix: 566192 x 720044 with sparse part having weight 43544586. Pruned matrix : 506039 x 508933 with weight 21456343. Total sieving time: 52.98 hours. Total relation processing time: 0.26 hours. Matrix solve time: 6.59 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,160,5,0,0,0,0,0,0,0,0,4000000,4000000,27,27,48,48,2.3,2.3,100000 total time: 59.99 hours. --------- CPU info (if available) ----------

Nov 2, 2005

By Tyler Cadigan / GGNFS-0.77.1-20050930-pentium4 gnfs
(7·10¹⁹⁴-43)/9 = (7)₁₉₃3_<194> = 73 · 109 · 3137 · 9001482062398106549_<19> · 54197355242387283113232438971_<29> · 494427323393845610326557724357_<30> · C110
C110 = P43 · P68
P43 = 1081275244876495547140212463963289256888791_<43>
P68 = 11947053709410444515749918449698943779961647139818245895249015990389_<68>

Number: (7*10^194-43)/9 N=12918053425195422867659167365721895242221179503016675627829364459926836953922196214827503153705191131697829699 ( 110 digits) Divisors found: r1=1081275244876495547140212463963289256888791 (pp43) r2=11947053709410444515749918449698943779961647139818245895249015990389 (pp68) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 49.83 hours. Scaled time: 20.13 units (timescale=0.404). Factorization parameters were as follows: name: try n: 12918053425195422867659167365721895242221179503016675627829364459926836953922196214827503153705191131697829699 skew: 40217.58 # norm 2.28e+015 c5: 22980 c4: -2308719653 c3: -119209020031866 c2: 3825072400142755084 c1: 101184301382580690814260 c0: 20189302016292719852953675 # alpha -6.27 Y1: 249823805609 Y0: -891193184845354492152 # Murphy_E 1.01e-009 # M 3247585310473453904553525590428175069451308527492470094601002246311000322146842698721636642813183484508254259 type: gnfs rlim: 3200000 alim: 3200000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3200000/3200000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1600000, 2400001) Primes: RFBsize:230209, AFBsize:230488, largePrimes:7738317 encountered Relations: rels:7912072, finalFF:822785 Max relations in full relation-set: 28 Initial matrix: 460777 x 822785 with sparse part having weight 72672320. Pruned matrix : 236281 x 238648 with weight 44311067. Polynomial selection time: 1.54 hours. Total sieving time: 40.36 hours. Total relation processing time: 0.59 hours. Matrix solve time: 6.97 hours. Time per square root: 0.37 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3200000,3200000,27,27,50,50,2.6,2.6,100000 total time: 49.83 hours. --------- CPU info (if available) ----------

Nov 1, 2005

By Kenichiro Yamaguchi / GGNFS-0.77.1
10¹⁶⁴-3 = (9)₁₆₃7_<164> = 78059 · C160
C160 = P41 · P119
P41 = 36841398161094229698993656374635785098993_<41>
P119 = 34772900113347798545372640730250755934955225972025356975366115874254163597722740653619367252030365507420285880379259431_<119>

Number: 99997_164 N=1281082258291804916793707323947270654248709309624771006546330339871123124815844425370553043210904572182579843451748036741439167808965013643526050807722363852983 ( 160 digits) SNFS difficulty: 165 digits. Divisors found: r1=36841398161094229698993656374635785098993 (pp41) r2=34772900113347798545372640730250755934955225972025356975366115874254163597722740653619367252030365507420285880379259431 (pp119) Version: GGNFS-0.77.1 Total time: 77.00 hours. Scaled time: 88.24 units (timescale=1.146). Factorization parameters were as follows: name: 99997_164 n: 1281082258291804916793707323947270654248709309624771006546330339871123124815844425370553043210904572182579843451748036741439167808965013643526050807722363852983 m: 1000000000000000000000000000000000 c5: 1 c0: -30 type: snfs skew: 1 qintsize: 50000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Sieved special-q in [2500000, 2500000) Relations: rels:5962757, finalFF:812872 Initial matrix: 695898 x 812872 with sparse part having weight 43782554. Pruned matrix : 654120 x 657663 with weight 27274461. Total sieving time: 69.67 hours. Total relation processing time: 0.28 hours. Matrix solve time: 6.92 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,165,5,0,0,0,0,0,0,0,0,5000000,5000000,27,27,48,48,2.5,2.5,100000 total time: 77.00 hours. --------- CPU info (if available) ----------