Factorizations of near-repdigit-related numbers

Table of contents

1. Introduction
2. How to contribute your factors ▶
3. Graphs ▶
4. Wanted list ▶
5. Records ▶
6. Reserved numbers and submitted numbers
7. News and updates
8. Contributors
9. Factor tables
   • Last update
   • Repunit numbers
   • Near-repdigit numbers of the form AA...AAB
   • Near-repdigit numbers of the form ABB...BB
   • Near-repdigit palindrome numbers of the form AA...AABAA...AA
   • Plateau and depression numbers of the form ABB...BBA
   • Quasi-repdigit numbers of the form ABB...BBC
10. List of near-repdigit-related prime numbers
11. Expression generator of near-repdigit-related numbers
12. Implementations
13. Related links

1. Introduction

We are collecting prime factorizations of near-repdigit-related numbers such as repunit numbers, near-repdigit numbers, plateau and depression numbers, quasi-repdigit numbers, and so on.

2. How to contribute your factors ▶

3. Graphs ▶

4. Wanted list ▶

5. Records ▶

6. Reserved numbers and submitted numbers

7. News and updates

Nov 7, 2009 (6th)

By Dmitry Domanov / GGNFS/msieve / Nov 7, 2009
(65·10¹⁵⁵+7)/9 = 7(2)₁₅₄3_<156> = 3 · 9007 · 1081789 · 8911250809018619_<16> · 142782376236086436331_<21> · C110
C110 = P52 · P58
P52 = 7392507812931635296203627398671630725771305605141003_<52>
P58 = 2626768526217301127090637292882797495139799918052500317901_<58>

N=19418406852824315665554762157458974239206989197334760372678432542908053342430535858752210495531479837429994703 ( 110 digits) Divisors found: r1=7392507812931635296203627398671630725771305605141003 (pp52) r2=2626768526217301127090637292882797495139799918052500317901 (pp58) Version: Msieve-1.40 Total time: 15.75 hours. Scaled time: 31.01 units (timescale=1.969). Factorization parameters were as follows: name: g110 n: 19418406852824315665554762157458974239206989197334760372678432542908053342430535858752210495531479837429994703 skew: 29767.14 # norm 3.00e+015 c5: 16560 c4: 3825657986 c3: 19567041570883 c2: -2418931829640980736 c1: 30620557498708644779402 c0: -74115411399096749338291340 # alpha -6.43 Y1: 203416736417 Y0: -1032349374499642407141 # Murphy_E 1.04e-009 # M 4165853837495179387505368821618801681724638475605636957434987794044042429718757847059943296685210951731399213 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, 2300001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 391563 x 391788 Polynomial selection time: 1.42 hours. Total sieving time: 13.33 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.44 hours. Time per square root: 0.50 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: 15.75 hours. --------- CPU info (if available) ----------

Nov 7, 2009 (5th)

By Sinkiti Sibata / Msieve / Nov 7, 2009
(62·10¹⁵⁰-17)/9 = 6(8)₁₄₉7_<151> = 19 · 96457 · 54014052471186550121_<20> · C125
C125 = P61 · P64
P61 = 7152115416516333263116824921083071837423457619295848531485227_<61>
P64 = 9730172787565460411900025374086137070224048862984493336589028567_<64>

Number: 68887_150 N=69591318799314634387182087997398280009882822525775350033620638088104875270633081216732421635499310384553331373497069641479709 ( 125 digits) SNFS difficulty: 151 digits. Divisors found: r1=7152115416516333263116824921083071837423457619295848531485227 (pp61) r2=9730172787565460411900025374086137070224048862984493336589028567 (pp64) Version: Msieve-1.40 Total time: 17.64 hours. Scaled time: 36.65 units (timescale=2.078). Factorization parameters were as follows: name: 68887_150 n: 69591318799314634387182087997398280009882822525775350033620638088104875270633081216732421635499310384553331373497069641479709 m: 1000000000000000000000000000000 deg: 5 c5: 62 c0: -17 skew: 0.77 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 407535 x 407783 Total sieving time: 16.87 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.57 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 17.64 hours. --------- CPU info (if available) ----------

(83·10¹⁹⁰+7)/9 = 9(2)₁₈₉3_<191> = 3 · C191
C191 = P86 · P105
P86 = 31409756452905266401572874729021762403039657905422482493898473135389505774302363727127_<86>
P105 = 978700385239610967893947803706059231473265933390451927236545688516093764875631745635126600791366581119683_<105>

Number: 92223_190 N=30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741 ( 191 digits) SNFS difficulty: 191 digits. Divisors found: r1=31409756452905266401572874729021762403039657905422482493898473135389505774302363727127 (pp86) r2=978700385239610967893947803706059231473265933390451927236545688516093764875631745635126600791366581119683 (pp105) Version: Msieve v. 1.42 Total time: 12.72 hours. Scaled time: 13.02 units (timescale=1.024). Factorization parameters were as follows: name: 92223_190 n: 30740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740740741 m: 100000000000000000000000000000000000000 deg: 5 c5: 83 c0: 7 skew: 0.61 type: snfs lss: 1 rlim: 11100000 alim: 11100000 lpbr: 28 lpba: 28 mfbr: 54 mfba: 54 rlambda: 2.5 alambda: 2.5 Factor base limits: 11100000/11100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 54/54 Sieved rational special-q in [5550000, 10550001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2084496 x 2084721 Total sieving time: 0.00 hours. Total relation processing time: 0.21 hours. Matrix solve time: 11.53 hours. Time per square root: 0.98 hours. Prototype def-par.txt line would be: snfs,191.000,5,0,0,0,0,0,0,0,0,11100000,11100000,28,28,54,54,2.5,2.5,100000 total time: 12.72 hours. --------- CPU info (if available) ---------- CPU0: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU1: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU2: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b CPU3: Intel(R) Core(TM)2 Quad CPU Q6600 @ 2.40GHz stepping 0b Memory: 3057976k/3145344k available (3786k kernel code, 496k absent, 86872k reserved, 2294k data, 1304k init) Calibrating delay loop (skipped), value calculated using timer frequency.. 4787.88 BogoMIPS (lpj=2393941) Calibrating delay using timer specific routine.. 4787.76 BogoMIPS (lpj=2393880) Calibrating delay using timer specific routine.. 4787.77 BogoMIPS (lpj=2393886) Calibrating delay using timer specific routine.. 4787.78 BogoMIPS (lpj=2393891) Total of 4 processors activated (19151.19 BogoMIPS). total time: 9 days 1 hour.

Nov 7, 2009 (4th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 7, 2009
(67·10¹⁴⁹+41)/9 = 7(4)₁₄₈9_<150> = 29 · 967 · 10301 · 164117 · 63136961 · 75921228000284137_<17> · C112
C112 = P54 · P58
P54 = 658356174664422161569086775878853672793637262114046597_<54>
P58 = 4975847405368765597872979135265543799568390928601303262351_<58>

Number: 74449_149 N=3275879863512470866831524279102943957767823250262292240603618506109442210271627224143756567808563929798129769547 ( 112 digits) SNFS difficulty: 151 digits. Divisors found: r1=658356174664422161569086775878853672793637262114046597 r2=4975847405368765597872979135265543799568390928601303262351 Version: Total time: 9.16 hours. Scaled time: 21.88 units (timescale=2.390). Factorization parameters were as follows: n: 3275879863512470866831524279102943957767823250262292240603618506109442210271627224143756567808563929798129769547 m: 1000000000000000000000000000000 deg: 5 c5: 67 c0: 410 skew: 1.44 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7095270 Max relations in full relation-set: Initial matrix: Pruned matrix : 381891 x 382139 Total sieving time: 8.45 hours. Total relation processing time: 0.32 hours. Matrix solve time: 0.31 hours. Time per square root: 0.08 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000 total time: 9.16 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(26·10¹⁵⁵-11)/3 = 8(6)₁₅₄3_<156> = 7 · 1279 · 83773 · 865854809489_<12> · 1961948617039_<13> · 67938871020299_<14> · C110
C110 = P53 · P57
P53 = 50356743151076883375850389237566626845654858552124607_<53>
P57 = 198824902404933934450436748117874509387381569435016167809_<57>

Number: 86663_155 N=10012174542443186661944529159441458449529896878553572027502711511349648695308726206045539833575579812190176063 ( 110 digits) Divisors found: r1=50356743151076883375850389237566626845654858552124607 r2=198824902404933934450436748117874509387381569435016167809 Version: Total time: 9.20 hours. Scaled time: 21.96 units (timescale=2.387). Factorization parameters were as follows: name: 86663_155 n: 10012174542443186661944529159441458449529896878553572027502711511349648695308726206045539833575579812190176063 skew: 19361.44 # norm 7.28e+14 c5: 36960 c4: -373375372 c3: 24010419126067 c2: 188419687096119335 c1: -10703912390072075189035 c0: -9921381275227903704194995 # alpha -5.79 Y1: 308100795223 Y0: -770122196696138062932 # Murphy_E 1.05e-09 # M 6923705748279385336736257457255098262017080868569703732932894391890534226799406036569569582345272734642801167 type: gnfs rlim: 2100000 alim: 2100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1050000, 1700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7841955 Max relations in full relation-set: Initial matrix: Pruned matrix : 402815 x 403063 Polynomial selection time: 0.80 hours. Total sieving time: 7.42 hours. Total relation processing time: 0.49 hours. Matrix solve time: 0.34 hours. Time per square root: 0.15 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000 total time: 9.20 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(26·10¹⁵⁶-11)/3 = 8(6)₁₅₅3_<157> = 19 · 439 · 4201 · 22108555559_<11> · 18897188991137_<14> · 19562245823564779_<17> · C110
C110 = P54 · P56
P54 = 694703188931333880775047897831384327876136440996742187_<54>
P56 = 43561789316255219047093334112623127241673869427391777277_<56>

Number: 86663_156 N=30262513953557411191067054802305039488066876688632568417434093173819283820734068340557697961554591668893884799 ( 110 digits) Divisors found: r1=694703188931333880775047897831384327876136440996742187 r2=43561789316255219047093334112623127241673869427391777277 Version: Total time: 8.76 hours. Scaled time: 20.90 units (timescale=2.387). Factorization parameters were as follows: name: 86663_156 n: 30262513953557411191067054802305039488066876688632568417434093173819283820734068340557697961554591668893884799 skew: 46936.13 # norm 2.00e+15 c5: 4800 c4: -1514434876 c3: -32339594241746 c2: 4238527376382421943 c1: -26343690099191295496866 c0: -124555876330930538048212671 # alpha -6.41 Y1: 329728317391 Y0: -1445236780624805468530 # Murphy_E 1.08e-09 # M 26147608521632649352970030633720039196717174907616904289542536532064184713838448536232324936389216869986608630 type: gnfs rlim: 2100000 alim: 2100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1050000, 1650001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7866072 Max relations in full relation-set: Initial matrix: Pruned matrix : 385170 x 385418 Polynomial selection time: 0.66 hours. Total sieving time: 7.20 hours. Total relation processing time: 0.46 hours. Matrix solve time: 0.36 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,109,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000 total time: 8.76 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(64·10¹⁵¹+17)/9 = 7(1)₁₅₀3_<152> = 29 · 283 · 134839 · 172147 · 757057201 · C129
C129 = P56 · P74
P56 = 13630504369805610897121892199912194495690789284130587631_<56>
P74 = 36174074472493502044830834515488572039115437822520724375951219171660917333_<74>

Number: 71113_151 N=493070880170996278534516753255530271753988214548501769867880630567332323531819123807127232541599603419990823093435241101803308123 ( 129 digits) SNFS difficulty: 152 digits. Divisors found: r1=13630504369805610897121892199912194495690789284130587631 r2=36174074472493502044830834515488572039115437822520724375951219171660917333 Version: Total time: 8.48 hours. Scaled time: 20.14 units (timescale=2.374). Factorization parameters were as follows: n: 493070880170996278534516753255530271753988214548501769867880630567332323531819123807127232541599603419990823093435241101803308123 m: 2000000000000000000000000000000 deg: 5 c5: 20 c0: 17 skew: 0.97 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved rational special-q in [1000000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7995257 Max relations in full relation-set: Initial matrix: Pruned matrix : 358493 x 358741 Total sieving time: 7.81 hours. Total relation processing time: 0.33 hours. Matrix solve time: 0.31 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,152,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,50,50,2.4,2.4,100000 total time: 8.48 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 7, 2009 (3rd)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 7, 2009
(26·10¹⁶⁵-11)/3 = 8(6)₁₆₄3_<166> = 83 · 173 · 6255630651772921_<16> · 166231483601086409378491_<24> · C123
C123 = P41 · P83
P41 = 24162374121281115547743488148094071736559_<41>
P83 = 24021709649431187683343098336454103859214433857791311652928195887896967260267801493_<83>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=522846101 Step 1 took 34052ms Step 2 took 13550ms ********** Factor found in step 2: 24162374121281115547743488148094071736559 Found probable prime factor of 41 digits: 24162374121281115547743488148094071736559 Probable prime cofactor 24021709649431187683343098336454103859214433857791311652928195887896967260267801493 has 83 digits

Nov 7, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Nov 6, 2009
(67·10¹⁸⁴-31)/9 = 7(4)₁₈₃1_<185> = 317 · 809 · 3547 · 33564732315787_<14> · 114897340823411617_<18> · 60403131124295658838209997353451_<32> · C114
C114 = P48 · P67
P48 = 339804285505812771909306394351621065329986786223_<48>
P67 = 1033907895700441246559141545237427637530368994032326666507566286553_<67>

Number: 74441_184 N=351326333777306830594696036569012983844843250127802988338902578492097989153379793913822350569995529157766770559319 ( 114 digits) Divisors found: r1=339804285505812771909306394351621065329986786223 (pp48) r2=1033907895700441246559141545237427637530368994032326666507566286553 (pp67) Version: Msieve-1.40 Total time: 23.21 hours. Scaled time: 22.44 units (timescale=0.967). Factorization parameters were as follows: n: 351326333777306830594696036569012983844843250127802988338902578492097989153379793913822350569995529157766770559319 c5: 10800 c4: 1941725750 c3: 81144728246589 c2: -2951244695963751041 c1: 4701141700422248571895 c0: 240834821565109408055254255 Y1: 1235140464791 Y0:-7988311196055664378158 skew: 35675.38 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1750000, 2750001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 525895 x 526143 Total sieving time: 22.16 hours. Total relation processing time: 0.09 hours. Matrix solve time: 0.61 hours. Time per square root: 0.34 hours. Prototype def-par.txt line would be: gnfs,113,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 23.21 hours. --------- CPU info (if available) ----------

Nov 7, 2009

By Erik Branger / PFGW / Nov 7, 2009
7·10¹⁴⁴³⁶+3 = 7(0)₁₄₄₃₅3_<14437> is PRP.
7·10²⁸³³⁸+3 = 7(0)₂₈₃₃₇3_<28339> is PRP.
7·10³²⁷⁹⁶+3 = 7(0)₃₂₇₉₅3_<32797> is PRP.
7·10³⁸⁰⁷⁹+3 = 7(0)₃₈₀₇₈3_<38080> is PRP.
7·10⁵⁶⁷⁷⁹+3 = 7(0)₅₆₇₇₈3_<56780> is PRP.
7·10⁹¹²¹⁵+3 = 7(0)₉₁₂₁₄3_<91216> is PRP.
PRP91216 is the second largest unprovable quasi-repdigit PRP in our tables so far. Congratulations!

Nov 6, 2009 (8th)

By Jo Yeong Uk / GGNFS, Msieve v1.39 / Nov 6, 2009
(64·10¹⁷⁶+17)/9 = 7(1)₁₇₅3_<177> = 18122431 · 827630411 · 618217711189847_<15> · 51198705749027445793243239875789577253_<38> · C109
C109 = P53 · P56
P53 = 27199328739913350726751375837743051073898498013179701_<53>
P56 = 55071379802039998793236341692499167334341927807025765323_<56>

Number: 71113_176 N=1497904563396310154769792820729281585688689422098966010957032096218297475296578253879252017930370140253308423 ( 109 digits) Divisors found: r1=27199328739913350726751375837743051073898498013179701 r2=55071379802039998793236341692499167334341927807025765323 Version: Total time: 7.39 hours. Scaled time: 17.62 units (timescale=2.385). Factorization parameters were as follows: name: 71113_176 n: 1497904563396310154769792820729281585688689422098966010957032096218297475296578253879252017930370140253308423 skew: 37228.70 # norm 1.29e+15 c5: 6720 c4: 1929577034 c3: -28048451333417 c2: -2581066827369582849 c1: 23728062558893855083337 c0: 189889730972645309855811835 # alpha -6.65 Y1: 294450677543 Y0: -740650055075990989806 # Murphy_E 1.28e-09 # M 406037342834116125047075340806279652058520344301271931613697935723559786272925786257733844006528099117428762 type: gnfs rlim: 2100000 alim: 2100000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2100000/2100000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [1050000, 2200001) Primes: rational ideals reading, algebraic ideals reading, Relations: 8123905 Max relations in full relation-set: Initial matrix: Pruned matrix : 371166 x 371414 Polynomial selection time: 0.58 hours. Total sieving time: 5.59 hours. Total relation processing time: 0.85 hours. Matrix solve time: 0.30 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: gnfs,108,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2100000,2100000,27,27,51,51,2.6,2.6,50000 total time: 7.39 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁴⁷-31)/9 = 7(4)₁₄₆1_<148> = 7² · 173 · 1007857 · C138
C138 = P49 · P90
P49 = 3543243945117669927050599146096106098149924350703_<49>
P90 = 245917899090014024113532245535836223215750238360235398952104060053448988922276779413690323_<90>

Number: 74441_147 N=871347106946750342151715673907223653960159603609685187432378536350270402789209264962140023280103965088548237737624848609941132704889347069 ( 138 digits) SNFS difficulty: 148 digits. Divisors found: r1=3543243945117669927050599146096106098149924350703 r2=245917899090014024113532245535836223215750238360235398952104060053448988922276779413690323 Version: Total time: 8.99 hours. Scaled time: 21.45 units (timescale=2.385). Factorization parameters were as follows: n: 871347106946750342151715673907223653960159603609685187432378536350270402789209264962140023280103965088548237737624848609941132704889347069 m: 100000000000000000000000000000 deg: 5 c5: 6700 c0: -31 skew: 0.34 type: snfs lss: 1 rlim: 3300000 alim: 3300000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 3300000/3300000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1650000, 3375001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7066652 Max relations in full relation-set: Initial matrix: Pruned matrix : 456862 x 457110 Total sieving time: 7.75 hours. Total relation processing time: 0.74 hours. Matrix solve time: 0.44 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,3300000,3300000,27,27,49,49,2.3,2.3,75000 total time: 8.99 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁴⁷-13)/9 = 7(4)₁₄₆3_<148> = 3⁴ · 23 · 15032488729_<11> · 8212675315501962911_<19> · C116
C116 = P50 · P66
P50 = 35712120107599973268429717906238004919995676811669_<50>
P66 = 906333983462578850099373864796225485410057952884119428606963987551_<66>

Number: 74443_147 N=32367108075015143797053757675227277037681912296576239310580627885454876717201364888999929590596992736623682287532619 ( 116 digits) SNFS difficulty: 148 digits. Divisors found: r1=35712120107599973268429717906238004919995676811669 r2=906333983462578850099373864796225485410057952884119428606963987551 Version: Total time: 8.34 hours. Scaled time: 19.90 units (timescale=2.385). Factorization parameters were as follows: n: 32367108075015143797053757675227277037681912296576239310580627885454876717201364888999929590596992736623682287532619 m: 100000000000000000000000000000 deg: 5 c5: 6700 c0: -13 skew: 0.29 type: snfs lss: 1 rlim: 3150000 alim: 3150000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 3150000/3150000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1575000, 3150001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7259667 Max relations in full relation-set: Initial matrix: Pruned matrix : 442603 x 442851 Total sieving time: 7.15 hours. Total relation processing time: 0.71 hours. Matrix solve time: 0.43 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: snfs,148,5,0,0,0,0,0,0,0,0,3150000,3150000,27,27,49,49,2.4,2.4,75000 total time: 8.34 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁴⁹-31)/9 = 7(4)₁₄₈1_<150> = 3 · 127 · 1753489837597_<13> · C136
C136 = P44 · P92
P44 = 20881086487350036134625000283626100896654287_<44>
P92 = 53364319064384742665900100125286466593148958555660756921564191235935418790516441550676542399_<92>

Number: 74441_149 N=1114304961721960173022091383380176976662874322011077839586378960447874153953371814034523514291547521078222901018637342512063392400614513 ( 136 digits) SNFS difficulty: 151 digits. Divisors found: r1=20881086487350036134625000283626100896654287 r2=53364319064384742665900100125286466593148958555660756921564191235935418790516441550676542399 Version: Total time: 10.05 hours. Scaled time: 23.97 units (timescale=2.386). Factorization parameters were as follows: n: 1114304961721960173022091383380176976662874322011077839586378960447874153953371814034523514291547521078222901018637342512063392400614513 m: 1000000000000000000000000000000 deg: 5 c5: 67 c0: -310 skew: 1.36 type: snfs lss: 1 rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1000000, 2000001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7412479 Max relations in full relation-set: Initial matrix: Pruned matrix : 371929 x 372177 Total sieving time: 9.35 hours. Total relation processing time: 0.37 hours. Matrix solve time: 0.30 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2000000,2000000,27,27,49,49,2.4,2.4,100000 total time: 10.05 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 6, 2009 (7th)

By Ignacio Santos / GGNFS, Msieve / Nov 6, 2009
5·10¹⁷⁴-7 = 4(9)₁₇₃3_<175> = 876443 · 26652181993_<11> · C159
C159 = P68 · P91
P68 = 46574391450747667692326738358784174396260537130314435096266571242987_<68>
P91 = 4595855531487340412820083355763538183249547281424390205839848914976852602041592456013124361_<91>

Number: 49993_174 N=214049174574575365805581376060199503058514198958035247503679069080324429338324460035489376300752092001338476663839616038201832417706699020583274339297180106307 ( 159 digits) SNFS difficulty: 175 digits. Divisors found: r1=46574391450747667692326738358784174396260537130314435096266571242987 (pp68) r2=4595855531487340412820083355763538183249547281424390205839848914976852602041592456013124361 (pp91) Version: Msieve v. 1.43 Total time: 56.13 hours. Scaled time: 97.62 units (timescale=1.739). Factorization parameters were as follows: n: 214049174574575365805581376060199503058514198958035247503679069080324429338324460035489376300752092001338476663839616038201832417706699020583274339297180106307 m: 100000000000000000000000000000000000 deg: 5 c5: 1 c0: -14 skew: 1.70 type: snfs lss: 1 rlim: 5800000 alim: 5800000 lpbr: 28 lpba: 28 mfbr: 52 mfba: 52 rlambda: 2.5 alambda: 2.5 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 52/52 Sieved rational special-q in [2900000, 5500001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 995237 x 995463 Total sieving time: 54.41 hours. Total relation processing time: 0.30 hours. Matrix solve time: 1.30 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,175.000,5,0,0,0,0,0,0,0,0,5800000,5800000,28,28,52,52,2.5,2.5,100000 total time: 56.13 hours.

Nov 6, 2009 (6th)

By Wataru Sakai / GMP-ECM 6.2.1 / Nov 6, 2009
(22·10¹⁵⁷-7)/3 = 7(3)₁₅₆1_<158> = 367 · 316304551 · 8534437607_<10> · 2443395325355902608359_<22> · C116
C116 = P38 · P79
P38 = 23693488595112602719126859782566256591_<38>
P79 = 1278592829499304611645554337323796642663523431026589589200118777890584774879621_<79>

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=236403890 Step 1 took 31182ms Step 2 took 13038ms ********** Factor found in step 2: 23693488595112602719126859782566256591 Found probable prime factor of 38 digits: 23693488595112602719126859782566256591 Probable prime cofactor 1278592829499304611645554337323796642663523431026589589200118777890584774879621 has 79 digits

(59·10¹⁶⁴+31)/9 = 6(5)₁₆₃9_<165> = 41 · 257 · 5763713135701_<13> · C149
C149 = P33 · C116
P33 = 632793202179705926119343697193231_<33>
C116 = [17058009798902811382752770514092749096039916701396886379742470377517403076500372505435723966037254679924690425475197_<116>]

Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=3331270017 Step 1 took 47229ms Step 2 took 16627ms ********** Factor found in step 2: 632793202179705926119343697193231 Found probable prime factor of 33 digits: 632793202179705926119343697193231 Composite cofactor 17058009798902811382752770514092749096039916701396886379742470377517403076500372505435723966037254679924690425475197 has 116 digits

(35·10¹⁹⁸+1)/9 = 3(8)₁₉₇9_<199> = 47 · C197
C197 = P82 · P116
P82 = 6326374989656440646106970407770659705730121493408302755378873328843303115001775919_<82>
P116 = 13078945987260134036462322502917867367044969527869559453471699062092522781634351546825345197002805196515382338315673_<116>

Number: 38889_198 N=82742316784869976359338061465721040189125295508274231678486997635933806146572104018912529550827423167848699763593380614657210401891252955082742316784869976359338061465721040189125295508274231678487 ( 197 digits) SNFS difficulty: 200 digits. Divisors found: r1=6326374989656440646106970407770659705730121493408302755378873328843303115001775919 r2=13078945987260134036462322502917867367044969527869559453471699062092522781634351546825345197002805196515382338315673 Version: Total time: 569.79 hours. Scaled time: 1133.32 units (timescale=1.989). Factorization parameters were as follows: n: 82742316784869976359338061465721040189125295508274231678486997635933806146572104018912529550827423167848699763593380614657210401891252955082742316784869976359338061465721040189125295508274231678487 m: 10000000000000000000000000000000000000000 deg: 5 c5: 7 c0: 20 skew: 1.23 type: snfs lss: 1 rlim: 15600000 alim: 15600000 lpbr: 29 lpba: 29 mfbr: 56 mfba: 56 rlambda: 2.6 alambda: 2.6Factor base limits: 15600000/15600000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 56/56 Sieved rational special-q in [7800000, 13500001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2705232 x 2705480 Total sieving time: 569.79 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,200,5,0,0,0,0,0,0,0,0,15600000,15600000,29,29,56,56,2.6,2.6,100000 total time: 569.79 hours. --------- CPU info (if available) ----------

(44·10¹⁹³-71)/9 = 4(8)₁₉₂1_<194> = 6203 · C190
C190 = P43 · P71 · P78
P43 = 1618166115802996840565371152078318243943573_<43>
P71 = 18615892194719893987578001772834971645694757182039038565591672722464263_<71>
P78 = 261638365738076548906793103513491078188631394698342571980380378304781956600273_<78>

Number: 48881_193 N=7881491034803947910509251795726082361581313701255664821681265337560678524728178121697386569222777509090583409461371737689648378024969996596628871334658856825550360936464434771705447185053827 ( 190 digits) SNFS difficulty: 194 digits. Divisors found: r1=1618166115802996840565371152078318243943573 r2=18615892194719893987578001772834971645694757182039038565591672722464263 r3=261638365738076548906793103513491078188631394698342571980380378304781956600273 Version: Total time: 653.71 hours. Scaled time: 1316.58 units (timescale=2.014). Factorization parameters were as follows: n: 7881491034803947910509251795726082361581313701255664821681265337560678524728178121697386569222777509090583409461371737689648378024969996596628871334658856825550360936464434771705447185053827 m: 200000000000000000000000000000000000000 deg: 5 c5: 1375 c0: -71 skew: 0.55 type: snfs lss: 1 rlim: 12300000 alim: 12300000 lpbr: 28 lpba: 28 mfbr: 55 mfba: 55 rlambda: 2.5 alambda: 2.5Factor base limits: 12300000/12300000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 55/55 Sieved rational special-q in [6150000, 13250001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 2399210 x 2399457 Total sieving time: 653.71 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,194,5,0,0,0,0,0,0,0,0,12300000,12300000,28,28,55,55,2.5,2.5,100000 total time: 653.71 hours. --------- CPU info (if available) ----------

Nov 6, 2009 (5th)

By Sinkiti Sibata / Msieve / Nov 6, 2009
(67·10¹⁴⁰+41)/9 = 7(4)₁₃₉9_<141> = 7 · 3371 · C137
C137 = P30 · P108
P30 = 191509589725032360358047867623_<30>
P108 = 164734656570897235288033852810835623477513274568840397755400314955254385028426104714427625363827448134452979_<108>

Number: 74449_140 N=31548266493386635777617682097065069476816732823852372947596916745537332900133256110710871909329340358708498726297599035658958530509998917 ( 137 digits) SNFS difficulty: 141 digits. Divisors found: r1=191509589725032360358047867623 (pp30) r2=164734656570897235288033852810835623477513274568840397755400314955254385028426104714427625363827448134452979 (pp108) Version: Msieve-1.40 Total time: 7.22 hours. Scaled time: 14.81 units (timescale=2.051). Factorization parameters were as follows: name: 74449_140 n: 31548266493386635777617682097065069476816732823852372947596916745537332900133256110710871909329340358708498726297599035658958530509998917 m: 10000000000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 type: snfs lss: 1 rlim: 1620000 alim: 1620000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1620000/1620000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [810000, 1710001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 239634 x 239869 Total sieving time: 6.92 hours. Total relation processing time: 0.07 hours. Matrix solve time: 0.19 hours. Time per square root: 0.04 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1620000,1620000,26,26,48,48,2.3,2.3,100000 total time: 7.22 hours. --------- CPU info (if available) ----------

(67·10¹³¹-31)/9 = 7(4)₁₃₀1_<132> = 3 · 143834439524998271722493_<24> · C109
C109 = P42 · P67
P42 = 323849544307374500128746883591241254838333_<42>
P67 = 5327271893239009943943442287524260619878365564348217121263894689563_<67>

Number: 74441_131 N=1725234575026937588591813062917426515403728981243743236270453675510075150479189227318557947230693458787418479 ( 109 digits) SNFS difficulty: 134 digits. Divisors found: r1=323849544307374500128746883591241254838333 (pp42) r2=5327271893239009943943442287524260619878365564348217121263894689563 (pp67) Version: Msieve-1.40 Total time: 4.53 hours. Scaled time: 9.44 units (timescale=2.085). Factorization parameters were as follows: name: 74441_131 n: 1725234575026937588591813062917426515403728981243743236270453675510075150479189227318557947230693458787418479 m: 200000000000000000000000000 deg: 5 c5: 335 c0: -496 skew: 1.08 type: snfs lss: 1 rlim: 1200000 alim: 1200000 lpbr: 26 lpba: 26 mfbr: 47 mfba: 47 rlambda: 2.3 alambda: 2.3 Factor base limits: 1200000/1200000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 47/47 Sieved rational special-q in [600000, 1200001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 166901 x 167149 Total sieving time: 4.35 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.09 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,134.000,5,0,0,0,0,0,0,0,0,1200000,1200000,26,26,47,47,2.3,2.3,75000 total time: 4.53 hours. --------- CPU info (if available) ----------

(67·10¹⁴⁴+41)/9 = 7(4)₁₄₃9_<145> = 3 · 79 · 25803630551_<11> · 2084763626306649558391910071_<28> · C105
C105 = P42 · P64
P42 = 423626916383930124653960797887297047400541_<42>
P64 = 1378360327126022364048330167071772464929240931307881983759154457_<64>

Number: 74449_144 N=583910535046342049640391332785757616154332420151820936864626808268428880468476996626812295569863964361237 ( 105 digits) SNFS difficulty: 146 digits. Divisors found: r1=423626916383930124653960797887297047400541 (pp42) r2=1378360327126022364048330167071772464929240931307881983759154457 (pp64) Version: Msieve-1.40 Total time: 15.07 hours. Scaled time: 29.55 units (timescale=1.961). Factorization parameters were as follows: name: 74449_144 n: 583910535046342049640391332785757616154332420151820936864626808268428880468476996626812295569863964361237 m: 100000000000000000000000000000 deg: 5 c5: 67 c0: 410 skew: 1.44 type: snfs lss: 1 rlim: 1960000 alim: 1960000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1960000/1960000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [980000, 2480001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 353335 x 353583 Total sieving time: 15.07 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,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000 total time: 15.07 hours. --------- CPU info (if available) ----------

(67·10¹³⁵+41)/9 = 7(4)₁₃₄9_<136> = 3 · 13 · 163 · 251 · 189043 · C125
C125 = P56 · P69
P56 = 71240130359442359976794234666514935013351341284492389997_<56>
P69 = 346434435442088830363099162339575704342482076530326806769161585968817_<69>

Number: 74449_135 N=24680034341894226799147907831007002424011323440141068996191301321234332937934131467895911287545293909501468601748729044723549 ( 125 digits) SNFS difficulty: 136 digits. Divisors found: r1=71240130359442359976794234666514935013351341284492389997 (pp56) r2=346434435442088830363099162339575704342482076530326806769161585968817 (pp69) Version: Msieve-1.40 Total time: 4.73 hours. Scaled time: 9.85 units (timescale=2.085). Factorization parameters were as follows: name: 74449_135 n: 24680034341894226799147907831007002424011323440141068996191301321234332937934131467895911287545293909501468601748729044723549 m: 1000000000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 type: snfs lss: 1 rlim: 1340000 alim: 1340000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3 Factor base limits: 1340000/1340000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [670000, 1270001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 189985 x 190228 Total sieving time: 4.52 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.12 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,136.000,5,0,0,0,0,0,0,0,0,1340000,1340000,26,26,48,48,2.3,2.3,75000 total time: 4.73 hours. --------- CPU info (if available) ----------

Nov 6, 2009 (4th)

By Lionel Debroux / ggnfs-lasieve4I14e on the RSALS grid + msieve 1.44 SVN. / Nov 6, 2009
(49·10²⁰¹+41)/9 = 5(4)₂₀₀9_<202> = 1653191 · C196
C196 = P44 · P152
P44 = 37275012028726822642622072954781884705885423_<44>
P152 = 88351259701921852832633429667747775669808345171415609203853358189987067824413888270327700386840290722262317778160874561417235000119736451519483267715993_<152>

Msieve v. 1.44 Thu Nov 5 21:18:46 2009 random seeds: 0f697e6c 28abe295 factoring 3293294268142304455107996864515016380106378781667964829499098679126879135226628045062212681078256804231600852197020455860480999741980475604116187690620408920956165648400241983197612643937962670039 (196 digits) searching for 15-digit factors commencing number field sieve (196-digit input) R0: -10000000000000000000000000000000000000000 R1: 1 A0: 41 A1: 0 A2: 0 A3: 0 A4: 0 A5: 490 skew 0.61, size 2.833956e-14, alpha 1.214899, combined = 9.459428e-12 commencing relation filtering estimated available RAM is 1148.0 MB commencing duplicate removal, pass 1 error -9 reading relation 8945276 error -9 reading relation 11307712 error -9 reading relation 11518069 error -15 reading relation 11544804 error -9 reading relation 12509643 error -15 reading relation 12756522 error -15 reading relation 12795024 error -1 reading relation 23489632 error -9 reading relation 23643833 error -15 reading relation 24407655 error -15 reading relation 25776837 error -1 reading relation 26227026 error -15 reading relation 26416665 error -9 reading relation 31485538 found 8862011 hash collisions in 44999986 relations added 730520 free relations commencing duplicate removal, pass 2 found 9014662 duplicates and 36715844 unique relations memory use: 213.2 MB reading ideals above 19202048 commencing singleton removal, initial pass memory use: 753.0 MB removing singletons from LP file start with 36715844 relations and 36580329 ideals pass 1: found 14595173 singletons pruned dataset has 22120671 relations and 19124588 large ideals reading all ideals from disk memory use: 382.0 MB commencing in-memory singleton removal begin with 22120671 relations and 19124588 unique ideals reduce to 15684674 relations and 12316705 ideals in 18 passes max relations containing the same ideal: 30 reading ideals above 720000 commencing singleton removal, initial pass memory use: 376.5 MB reading all ideals from disk memory use: 531.7 MB keeping 14648359 ideals with weight <= 200, target excess is 116482 commencing in-memory singleton removal begin with 15684983 relations and 14648359 unique ideals reduce to 15682203 relations and 14644226 ideals in 9 passes max relations containing the same ideal: 200 removing 2846610 relations and 2446610 ideals in 400000 cliques commencing in-memory singleton removal begin with 12835593 relations and 14644226 unique ideals reduce to 12465195 relations and 11815179 ideals in 11 passes max relations containing the same ideal: 175 removing 2135745 relations and 1735745 ideals in 400000 cliques commencing in-memory singleton removal begin with 10329450 relations and 11815179 unique ideals reduce to 10053854 relations and 9795074 ideals in 9 passes max relations containing the same ideal: 147 removing 792609 relations and 668949 ideals in 123660 cliques commencing in-memory singleton removal begin with 9261245 relations and 9795074 unique ideals reduce to 9216708 relations and 9081049 ideals in 7 passes max relations containing the same ideal: 139 relations with 0 large ideals: 2906 relations with 1 large ideals: 272 relations with 2 large ideals: 7222 relations with 3 large ideals: 70678 relations with 4 large ideals: 374670 relations with 5 large ideals: 1150194 relations with 6 large ideals: 2257720 relations with 7+ large ideals: 5353046 commencing 2-way merge reduce to 5570453 relation sets and 5434794 unique ideals commencing full merge memory use: 661.0 MB found 2928967 cycles, need 2910994 weight of 2910994 cycles is about 203790381 (70.01/cycle) distribution of cycle lengths: 1 relations: 364884 2 relations: 359563 3 relations: 360513 4 relations: 323963 5 relations: 286525 6 relations: 247293 7 relations: 211854 8 relations: 175678 9 relations: 142574 10+ relations: 438147 heaviest cycle: 23 relations commencing cycle optimization start with 15939067 relations pruned 326649 relations memory use: 540.6 MB distribution of cycle lengths: 1 relations: 364884 2 relations: 366593 3 relations: 371489 4 relations: 329960 5 relations: 291790 6 relations: 249668 7 relations: 212738 8 relations: 175029 9 relations: 140569 10+ relations: 408274 heaviest cycle: 23 relations RelProcTime: 1858 elapsed time 00:31:01 Msieve v. 1.44 Thu Nov 5 21:54:39 2009 random seeds: 239a98bf cd32137d factoring 3293294268142304455107996864515016380106378781667964829499098679126879135226628045062212681078256804231600852197020455860480999741980475604116187690620408920956165648400241983197612643937962670039 (196 digits) searching for 15-digit factors commencing number field sieve (196-digit input) R0: -10000000000000000000000000000000000000000 R1: 1 A0: 41 A1: 0 A2: 0 A3: 0 A4: 0 A5: 490 skew 0.61, size 2.833956e-14, alpha 1.214899, combined = 9.459428e-12 commencing linear algebra read 2910994 cycles cycles contain 9097602 unique relations read 9097602 relations using 20 quadratic characters above 536868404 building initial matrix memory use: 1163.2 MB read 2910994 cycles matrix is 2910816 x 2910994 (876.2 MB) with weight 256607789 (88.15/col) sparse part has weight 197667834 (67.90/col) filtering completed in 2 passes matrix is 2908807 x 2908984 (876.0 MB) with weight 256551143 (88.19/col) sparse part has weight 197651271 (67.95/col) read 2908984 cycles matrix is 2908807 x 2908984 (876.0 MB) with weight 256551143 (88.19/col) sparse part has weight 197651271 (67.95/col) saving the first 48 matrix rows for later matrix is 2908759 x 2908984 (831.7 MB) with weight 204497989 (70.30/col) sparse part has weight 188932378 (64.95/col) matrix includes 64 packed rows using block size 65536 for processor cache size 4096 kB commencing Lanczos iteration (2 threads) memory use: 849.9 MB restarting at iteration 45547 (dim = 2880023) linear algebra completed 2908597 of 2908984 dimensions (100.0%, ETA 0h 0m) lanczos halted after 46003 iterations (dim = 2908755) recovered 35 nontrivial dependencies BLanczosTime: 102677 commencing square root phase reading relations for dependency 1 read 1454148 cycles cycles contain 4549318 unique relations read 4549318 relations multiplying 4549318 relations multiply complete, coefficients have about 146.17 million bits initial square root is modulo 176051 reading relations for dependency 2 read 1453033 cycles cycles contain 4546544 unique relations read 4546544 relations multiplying 4546544 relations multiply complete, coefficients have about 146.07 million bits initial square root is modulo 174721 sqrtTime: 6024 prp44 factor: 37275012028726822642622072954781884705885423 prp152 factor: 88351259701921852832633429667747775669808345171415609203853358189987067824413888270327700386840290722262317778160874561417235000119736451519483267715993 elapsed time 01:57:43

Nov 6, 2009 (3rd)

By Dmitry Domanov / GGNFS/msieve / Nov 6, 2009
(67·10¹⁷³-31)/9 = 7(4)₁₇₂1_<174> = 3 · C174
C174 = P84 · P90
P84 = 430710479242399035363062350740645865987466720557004828022753286974516590870289028663_<84>
P90 = 576136778897578548828836762015811405604962956451806450404338507568484460587741229848480869_<90>

N=248148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147 ( 174 digits) SNFS difficulty: 176 digits. Divisors found: r1=430710479242399035363062350740645865987466720557004828022753286974516590870289028663 (pp84) r2=576136778897578548828836762015811405604962956451806450404338507568484460587741229848480869 (pp90) Version: Msieve-1.40 Total time: 104.00 hours. Scaled time: 197.49 units (timescale=1.899). Factorization parameters were as follows: n: 248148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148148147 m: 50000000000000000000000000000000000 deg: 5 c5: 536 c0: -775 skew: 1.08 type: snfs lss: 1 rlim: 6100000 alim: 6100000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5Factor base limits: 6100000/6100000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3050000, 8350001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1467553 x 1467786 Total sieving time: 100.25 hours. Total relation processing time: 0.17 hours. Matrix solve time: 2.82 hours. Time per square root: 0.75 hours. Prototype def-par.txt line would be: snfs,176.000,5,0,0,0,0,0,0,0,0,6100000,6100000,28,28,53,53,2.5,2.5,100000 total time: 104.00 hours. --------- CPU info (if available) ----------

Nov 6, 2009 (2nd)

By Erik Branger / GGNFS, Msieve / Nov 6, 2009
(22·10¹⁵⁶+17)/3 = 7(3)₁₅₅9_<157> = 13 · 19 · 6971 · 470900400663529_<15> · C136
C136 = P32 · P51 · P54
P32 = 22374456972596767383679482063529_<32>
P51 = 828191017353098997423669770686587010084194267524507_<51>
P54 = 488087078674160901172508648961369204695734529976060181_<54>

Number: 73339_156 N=9044411846105054274209815905986355691082748507066852603612928749817550676873652715990888627685568833319637972505812247201723505291521743 ( 136 digits) SNFS difficulty: 158 digits. Divisors found: r1=22374456972596767383679482063529 (pp32) r2=828191017353098997423669770686587010084194267524507 (pp51) r3=488087078674160901172508648961369204695734529976060181 (pp54) Version: Msieve-1.40 Total time: 26.33 hours. Scaled time: 23.30 units (timescale=0.885). Factorization parameters were as follows: n: 9044411846105054274209815905986355691082748507066852603612928749817550676873652715990888627685568833319637972505812247201723505291521743 m: 20000000000000000000000000000000 deg: 5 c5: 55 c0: 136 skew: 1.20 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, 2700001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 560422 x 560649 Total sieving time: 24.67 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.80 hours. Time per square root: 0.74 hours. Prototype def-par.txt line would be: snfs,158.000,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,50,50,2.4,2.4,100000 total time: 26.33 hours. --------- CPU info (if available) ----------

Nov 6, 2009

By Markus Tervooren / Msieve / Nov 6, 2009
(67·10¹⁴⁶+41)/9 = 7(4)₁₄₅9_<147> = 7³ · 2579 · 137933 · C136
C136 = P42 · P95
P42 = 552752232810877924907944618081429138807679_<42>
P95 = 11037942908547355150244790836990039717387364320115120207780436833145912926736258397877527823631_<95>

Sieving time: ~5 hours Msieve v. 1.43 Thu Nov 5 15:55:15 2009 random seeds: 22e75df5 c52ae233 factoring 6101247588338546677929745539946244193317898526731142823774618663407511729661540242208206561765864438885995914092862234746612155140462449 (136 digits) searching for 15-digit factors commencing number field sieve (136-digit input) R0: 100000000000000000000000000000 R1: -1 A0: 41 A1: 0 A2: 0 A3: 0 A4: 0 A5: 670 skew 0.57, size 1.339951e-10, alpha 0.971714, combined = 1.477459e-09 commencing relation filtering estimated available RAM is 8010.2 MB commencing duplicate removal, pass 1 found 2463214 hash collisions in 18330753 relations added 379270 free relations commencing duplicate removal, pass 2 found 2223391 duplicates and 16486632 unique relations memory use: 98.6 MB reading ideals above 720000 commencing singleton removal, initial pass memory use: 344.5 MB reading all ideals from disk memory use: 435.9 MB keeping 12885881 ideals with weight <= 200, target excess is 116169 commencing in-memory singleton removal begin with 16486632 relations and 12885881 unique ideals reduce to 11845160 relations and 7680342 ideals in 12 passes max relations containing the same ideal: 166 removing 1545647 relations and 1145647 ideals in 400000 cliques commencing in-memory singleton removal begin with 10299513 relations and 7680342 unique ideals reduce to 10195507 relations and 6426531 ideals in 7 passes max relations containing the same ideal: 147 removing 1178313 relations and 778313 ideals in 400000 cliques commencing in-memory singleton removal begin with 9017194 relations and 6426531 unique ideals reduce to 8952428 relations and 5581283 ideals in 6 passes max relations containing the same ideal: 136 removing 1045750 relations and 645750 ideals in 400000 cliques commencing in-memory singleton removal begin with 7906678 relations and 5581283 unique ideals reduce to 7837859 relations and 4863952 ideals in 5 passes max relations containing the same ideal: 122 removing 954446 relations and 554446 ideals in 400000 cliques commencing in-memory singleton removal begin with 6883413 relations and 4863952 unique ideals reduce to 6814170 relations and 4236837 ideals in 5 passes max relations containing the same ideal: 110 removing 927971 relations and 527971 ideals in 400000 cliques commencing in-memory singleton removal begin with 5886199 relations and 4236837 unique ideals reduce to 5819767 relations and 3638595 ideals in 5 passes max relations containing the same ideal: 98 removing 899906 relations and 499906 ideals in 400000 cliques commencing in-memory singleton removal begin with 4919861 relations and 3638595 unique ideals reduce to 4851525 relations and 3065913 ideals in 7 passes max relations containing the same ideal: 92 removing 875905 relations and 475905 ideals in 400000 cliques commencing in-memory singleton removal begin with 3975620 relations and 3065913 unique ideals reduce to 3901513 relations and 2509651 ideals in 5 passes max relations containing the same ideal: 77 removing 854371 relations and 454371 ideals in 400000 cliques commencing in-memory singleton removal begin with 3047142 relations and 2509651 unique ideals reduce to 2976954 relations and 1979149 ideals in 8 passes max relations containing the same ideal: 60 removing 853727 relations and 453727 ideals in 400000 cliques commencing in-memory singleton removal begin with 2123227 relations and 1979149 unique ideals reduce to 2056703 relations and 1453401 ideals in 6 passes max relations containing the same ideal: 45 removing 649792 relations and 350445 ideals in 299347 cliques commencing in-memory singleton removal begin with 1406911 relations and 1453401 unique ideals reduce to 1352520 relations and 1044337 ideals in 6 passes max relations containing the same ideal: 35 removing 361208 relations and 202857 ideals in 158351 cliques commencing in-memory singleton removal begin with 991312 relations and 1044337 unique ideals reduce to 943024 relations and 789269 ideals in 7 passes max relations containing the same ideal: 28 removing 67885 relations and 48887 ideals in 18998 cliques commencing in-memory singleton removal begin with 875139 relations and 789269 unique ideals reduce to 870935 relations and 736093 ideals in 5 passes max relations containing the same ideal: 27 relations with 0 large ideals: 2892 relations with 1 large ideals: 12725 relations with 2 large ideals: 78477 relations with 3 large ideals: 199963 relations with 4 large ideals: 264046 relations with 5 large ideals: 196441 relations with 6 large ideals: 93686 relations with 7+ large ideals: 22705 commencing 2-way merge reduce to 716617 relation sets and 581775 unique ideals commencing full merge memory use: 59.6 MB found 334086 cycles, need 315975 weight of 315975 cycles is about 22212740 (70.30/cycle) distribution of cycle lengths: 1 relations: 17641 2 relations: 28997 3 relations: 35315 4 relations: 35873 5 relations: 34500 6 relations: 30819 7 relations: 27240 8 relations: 23611 9 relations: 20033 10+ relations: 61946 heaviest cycle: 18 relations commencing cycle optimization start with 1977808 relations pruned 109779 relations memory use: 55.2 MB distribution of cycle lengths: 1 relations: 17641 2 relations: 30199 3 relations: 38011 4 relations: 38567 5 relations: 37162 6 relations: 32764 7 relations: 28595 8 relations: 23952 9 relations: 19883 10+ relations: 49201 heaviest cycle: 17 relations RelProcTime: 483 commencing linear algebra read 315975 cycles cycles contain 820073 unique relations read 820073 relations using 20 quadratic characters above 134195000 building initial matrix memory use: 99.5 MB read 315975 cycles matrix is 315792 x 315975 (91.9 MB) with weight 27669770 (87.57/col) sparse part has weight 20606850 (65.22/col) filtering completed in 2 passes matrix is 315546 x 315729 (91.8 MB) with weight 27657347 (87.60/col) sparse part has weight 20599994 (65.25/col) read 315729 cycles matrix is 315546 x 315729 (91.8 MB) with weight 27657347 (87.60/col) sparse part has weight 20599994 (65.25/col) saving the first 48 matrix rows for later matrix is 315498 x 315729 (86.7 MB) with weight 21774880 (68.97/col) sparse part has weight 19583486 (62.03/col) matrix includes 64 packed rows using block size 65536 for processor cache size 4096 kB commencing Lanczos iteration (4 threads) memory use: 90.9 MB linear algebra at 1.9%, ETA 0h 6m315729 dimensions (1.9%, ETA 0h 6m) linear algebra completed 313716 of 315729 dimensions (99.4%, ETA 0h 0m) lanczos halted after 4990 iterations (dim = 315494) recovered 34 nontrivial dependencies BLanczosTime: 435 commencing square root phase reading relations for dependency 1 read 157809 cycles cycles contain 410208 unique relations read 410208 relations multiplying 410208 relations multiply complete, coefficients have about 12.09 million bits initial square root is modulo 8837471 sqrtTime: 48 prp42 factor: 552752232810877924907944618081429138807679 prp95 factor: 11037942908547355150244790836990039717387364320115120207780436833145912926736258397877527823631 elapsed time 00:16:07

Nov 5, 2009 (7th)

By Ignacio Santos / GGNFS, Msieve / Nov 5, 2009
(65·10¹⁷⁴+7)/9 = 7(2)₁₇₃3_<175> = 17 · 3919 · C171
C171 = P35 · P136
P35 = 28045218294644002661656500892213117_<35>
P136 = 3865341215601827188809187731591195001845176710932875113565226610209954285454175288779980587070108534688701518416552656964627055137706053_<136>

Number: 72223_174 N=108404338174837852126476175228107743905591495763058136412683641118265797430650409351458538676166222208880149831472948114348231424916653741534038128307374663738081776897201 ( 171 digits) SNFS difficulty: 176 digits. Divisors found: r1=28045218294644002661656500892213117 (pp35) r2=3865341215601827188809187731591195001845176710932875113565226610209954285454175288779980587070108534688701518416552656964627055137706053 (pp136) Version: Msieve-1.40 Total time: 77.49 hours. Scaled time: 134.75 units (timescale=1.739). Factorization parameters were as follows: n: 108404338174837852126476175228107743905591495763058136412683641118265797430650409351458538676166222208880149831472948114348231424916653741534038128307374663738081776897201 m: 100000000000000000000000000000000000 deg: 5 c5: 13 c0: 14 skew: 1.01 type: snfs lss: 1 rlim: 6000000 alim: 6000000 lpbr: 28 lpba: 28 mfbr: 53 mfba: 53 rlambda: 2.5 alambda: 2.5 Factor base limits: 6000000/6000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 53/53 Sieved rational special-q in [3000000, 6700001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1284651 x 1284877 Total sieving time: 74.58 hours. Total relation processing time: 0.35 hours. Matrix solve time: 2.34 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,176.000,5,0,0,0,0,0,0,0,0,6000000,6000000,28,28,53,53,2.5,2.5,100000 total time: 77.49 hours.

Nov 5, 2009 (6th)

By Jo Yeong Uk / GGNFS, Msieve v1.39, GMP-ECM v6.2.3, YAFU v1.10 / Nov 5, 2009
(67·10¹⁶⁸-31)/9 = 7(4)₁₆₇1_<169> = 7606561 · 163572667 · 590259537485086986353_<21> · 151964056301483322443154779593_<30> · C104
C104 = P47 · P57
P47 = 97126863769841467874236485364535089605312141371_<47>
P57 = 686767840130450661304870889966446488159378580482101462377_<57>

Number: 74441_168 N=66703606449858545643662707449559166574748186359301268429300565428305734048800989227920948282512461698867 ( 104 digits) Divisors found: r1=97126863769841467874236485364535089605312141371 r2=686767840130450661304870889966446488159378580482101462377 Version: Total time: 4.22 hours. Scaled time: 10.06 units (timescale=2.384). Factorization parameters were as follows: name: 74441_168 n: 66703606449858545643662707449559166574748186359301268429300565428305734048800989227920948282512461698867 skew: 22384.96 # norm 2.87e+14 c5: 15660 c4: -501824996 c3: -18525148742447 c2: 266426610854246285 c1: 4333073707957086227643 c0: 14764715322523703194493871 # alpha -6.14 Y1: 7300412317 Y0: -84308575724840796752 # Murphy_E 2.08e-09 # M 5388142146302891828223044752647144935689243276179164408869092559758099099626333652594346077847048977290 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: 4950394 Max relations in full relation-set: Initial matrix: Pruned matrix : 255278 x 255526 Polynomial selection time: 0.29 hours. Total sieving time: 3.36 hours. Total relation processing time: 0.35 hours. Matrix solve time: 0.14 hours. Time per square root: 0.08 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: 4.22 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁴⁴-31)/9 = 7(4)₁₄₃1_<145> = 1086632116511402147705630873_<28> · C118
C118 = P47 · P72
P47 = 34655482245468834228541408388489501901665410519_<47>
P72 = 197686862953873716181311104410965221646157892429803380406605260036919143_<72>

Number: 74441_144 N=6850933569260401192979346688968304304118740526220941882187274314238921954387217432618656883866956371791087169104665217 ( 118 digits) SNFS difficulty: 146 digits. Divisors found: r1=34655482245468834228541408388489501901665410519 r2=197686862953873716181311104410965221646157892429803380406605260036919143 Version: Total time: 7.05 hours. Scaled time: 16.85 units (timescale=2.389). Factorization parameters were as follows: n: 6850933569260401192979346688968304304118740526220941882187274314238921954387217432618656883866956371791087169104665217 m: 100000000000000000000000000000 deg: 5 c5: 67 c0: -310 skew: 1.36 type: snfs lss: 1 rlim: 2550000 alim: 2550000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2550000/2550000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1275000, 2775001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4934852 Max relations in full relation-set: Initial matrix: Pruned matrix : 407050 x 407298 Total sieving time: 6.06 hours. Total relation processing time: 0.44 hours. Matrix solve time: 0.33 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2550000,2550000,26,26,49,49,2.3,2.3,75000 total time: 7.05 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁵⁵+41)/9 = 7(4)₁₅₄9_<156> = 47 · 53 · 241 · 302983 · 14851037 · 252442321 · 79435952371_<11> · 96107273394271_<14> · C105
C105 = P36 · P69
P36 = 513981777262743485425131597124856197_<36>
P69 = 278216723864481525034470316274854133774845275372355082172887637024697_<69>

Number: 74449_155 N=142998326196084153152602303181725148518916237710184541230536160066661148293488886572640010918329062497309 ( 105 digits) Divisors found: r1=513981777262743485425131597124856197 r2=278216723864481525034470316274854133774845275372355082172887637024697 Version: Total time: 4.48 hours. Scaled time: 10.70 units (timescale=2.388). Factorization parameters were as follows: name: 74449_155 n: 142998326196084153152602303181725148518916237710184541230536160066661148293488886572640010918329062497309 skew: 16634.07 # norm 6.75e+14 c5: 36000 c4: 2507890170 c3: -33754989641093 c2: -411802020026744711 c1: 5598836560479622272525 c0: 714646846507642901515845 # alpha -6.87 Y1: 30603097547 Y0: -83138744797431074138 # Murphy_E 2.01e-09 # M 23638809882836740827105361457170598519475955087418326994978122984763654287971205979734490448061304881821 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 1700001) Primes: rational ideals reading, algebraic ideals reading, Relations: 6901969 Max relations in full relation-set: Initial matrix: Pruned matrix : 284502 x 284750 Polynomial selection time: 0.34 hours. Total sieving time: 3.45 hours. Total relation processing time: 0.46 hours. Matrix solve time: 0.17 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,104,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000 total time: 4.48 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(67·10¹⁵⁷+41)/9 = 7(4)₁₅₆9_<158> = 19 · 79 · 569 · 13280256271_<11> · 679103402368889_<15> · 396291799469414089_<18> · C110
C110 = P33 · P38 · P40
P33 = 896016956955767255596724244933401_<33>
P38 = 13950563607253532674032704293646041067_<38>
P40 = 1951074733192853860565440794148429905793_<40>

GMP-ECM 6.2.3 [powered by GMP 4.2.4] [ECM] Input number is 24388320126912700619412278763299846909289095649545527020097226863181940482234364839456257636794737384518876531 (110 digits) Using B1=1000000, B2=1045563762, polynomial Dickson(6), sigma=5977138773 Step 1 took 3494ms Step 2 took 3760ms ********** Factor found in step 2: 896016956955767255596724244933401 Found probable prime factor of 33 digits: 896016956955767255596724244933401 Composite cofactor 27218592167912123174017720102720354477066164208529016911587995682062219201131 has 77 digits 11/05/09 08:01:26 v1.10 @ 조영욱-PC, starting SIQS on c77: 27218592167912123174017720102720354477066164208529016911587995682062219201131 11/05/09 08:01:26 v1.10 @ 조영욱-PC, random seeds: 1415046673, 1328948052 11/05/09 08:01:27 v1.10 @ 조영욱-PC, ==== sieve params ==== 11/05/09 08:01:27 v1.10 @ 조영욱-PC, n = 77 digits, 258 bits 11/05/09 08:01:27 v1.10 @ 조영욱-PC, factor base: 32200 primes (max prime = 805451) 11/05/09 08:01:27 v1.10 @ 조영욱-PC, single large prime cutoff: 68463335 (85 * pmax) 11/05/09 08:01:27 v1.10 @ 조영욱-PC, using 12 large prime slices of factor base 11/05/09 08:01:27 v1.10 @ 조영욱-PC, buckets hold 1024 elements 11/05/09 08:01:27 v1.10 @ 조영욱-PC, sieve interval: 5 blocks of size 65536 11/05/09 08:01:27 v1.10 @ 조영욱-PC, polynomial A has ~ 10 factors 11/05/09 08:01:27 v1.10 @ 조영욱-PC, using multiplier of 11 11/05/09 08:01:27 v1.10 @ 조영욱-PC, using small prime variation correction of 18 bits 11/05/09 08:01:27 v1.10 @ 조영욱-PC, using SSE2 for trial division and x64 sieve scanning 11/05/09 08:01:27 v1.10 @ 조영욱-PC, trial factoring cutoff at 94 bits 11/05/09 08:01:27 v1.10 @ 조영욱-PC, ==== sieving started ==== 11/05/09 08:04:45 v1.10 @ 조영욱-PC, sieve time = 101.5450, relation time = 27.2180, poly_time = 69.2010 11/05/09 08:04:45 v1.10 @ 조영욱-PC, 32279 relations found: 16966 full + 15313 from 161385 partial, using 73331 polys (143 A polys) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, on average, sieving found 2.43 rels/poly and 899.51 rels/sec 11/05/09 08:04:45 v1.10 @ 조영욱-PC, trial division touched 1264882 sieve locations out of 48058204160 11/05/09 08:04:45 v1.10 @ 조영욱-PC, ==== post processing stage (msieve-1.38) ==== 11/05/09 08:04:45 v1.10 @ 조영욱-PC, begin with 178351 relations 11/05/09 08:04:45 v1.10 @ 조영욱-PC, reduce to 45610 relations in 2 passes 11/05/09 08:04:45 v1.10 @ 조영욱-PC, recovered 45610 relations 11/05/09 08:04:45 v1.10 @ 조영욱-PC, recovered 33913 polynomials 11/05/09 08:04:45 v1.10 @ 조영욱-PC, attempting to build 32279 cycles 11/05/09 08:04:45 v1.10 @ 조영욱-PC, found 32279 cycles in 1 passes 11/05/09 08:04:45 v1.10 @ 조영욱-PC, distribution of cycle lengths: 11/05/09 08:04:45 v1.10 @ 조영욱-PC, length 1 : 16966 11/05/09 08:04:45 v1.10 @ 조영욱-PC, length 2 : 15313 11/05/09 08:04:45 v1.10 @ 조영욱-PC, largest cycle: 2 relations 11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix is 32200 x 32279 (4.7 MB) with weight 967198 (29.96/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, sparse part has weight 967198 (29.96/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, filtering completed in 4 passes 11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix is 27821 x 27885 (4.0 MB) with weight 819515 (29.39/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, sparse part has weight 819515 (29.39/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, saving the first 48 matrix rows for later 11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix is 27773 x 27885 (2.8 MB) with weight 596633 (21.40/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, sparse part has weight 452964 (16.24/col) 11/05/09 08:04:45 v1.10 @ 조영욱-PC, matrix includes 64 packed rows 11/05/09 08:04:45 v1.10 @ 조영욱-PC, commencing Lanczos iteration 11/05/09 08:04:45 v1.10 @ 조영욱-PC, memory use: 3.9 MB 11/05/09 08:04:52 v1.10 @ 조영욱-PC, lanczos halted after 441 iterations (dim = 27773) 11/05/09 08:04:52 v1.10 @ 조영욱-PC, recovered 18 nontrivial dependencies 11/05/09 08:04:52 v1.10 @ 조영욱-PC, prp38 = 13950563607253532674032704293646041067 11/05/09 08:04:52 v1.10 @ 조영욱-PC, prp40 = 1951074733192853860565440794148429905793 11/05/09 08:04:52 v1.10 @ 조영욱-PC, Lanczos elapsed time = 7.2070 seconds. 11/05/09 08:04:52 v1.10 @ 조영욱-PC, Sqrt elapsed time = 0.2030 seconds. 11/05/09 08:04:52 v1.10 @ 조영욱-PC, SIQS elapsed time = 205.6860 seconds. 11/05/09 08:04:52 v1.10 @ 조영욱-PC, 11/05/09 08:04:52 v1.10 @ 조영욱-PC,

(67·10¹⁴⁵-31)/9 = 7(4)₁₄₄1_<146> = 709 · 322066412869815736192367293_<27> · C117
C117 = P55 · P62
P55 = 9260894445086141962651210313544909342955325247050444087_<55>
P62 = 35203649447637528618873300517503888994181400098044701486542239_<62>

Number: 74441_145 N=326017281616386218615956963496149396800689269848098363793483088850308834552548967331260168013696545100284199033290793 ( 117 digits) SNFS difficulty: 146 digits. Divisors found: r1=9260894445086141962651210313544909342955325247050444087 r2=35203649447637528618873300517503888994181400098044701486542239 Version: Total time: 6.29 hours. Scaled time: 15.05 units (timescale=2.391). Factorization parameters were as follows: n: 326017281616386218615956963496149396800689269848098363793483088850308834552548967331260168013696545100284199033290793 m: 100000000000000000000000000000 deg: 5 c5: 67 c0: -31 skew: 0.86 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 1800001) Primes: rational ideals reading, algebraic ideals reading, Relations: 4800623 Max relations in full relation-set: Initial matrix: Pruned matrix : 307282 x 307530 Total sieving time: 5.82 hours. Total relation processing time: 0.19 hours. Matrix solve time: 0.20 hours. Time per square root: 0.09 hours. Prototype def-par.txt line would be: snfs,146,5,0,0,0,0,0,0,0,0,2400000,2400000,26,26,49,49,2.3,2.3,75000 total time: 6.29 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

(64·10¹⁹⁹+17)/9 = 7(1)₁₉₈3_<200> = 89 · 179 · 16258282818944805107865067621_<29> · 490563121353478979588912991233_<30> · 5075327543140798696604465814559_<31> · C108
C108 = P52 · P56
P52 = 1407294183161809776961599301547364443542425110383681_<52>
P56 = 78356655111566972388515530318074663443442995516794711409_<56>

Number: 71113_199 N=110270864950524289144339133459841021143400357504267999886887205650991511373184710031303560333324391658116529 ( 108 digits) Divisors found: r1=1407294183161809776961599301547364443542425110383681 r2=78356655111566972388515530318074663443442995516794711409 Version: Total time: 7.36 hours. Scaled time: 17.58 units (timescale=2.389). Factorization parameters were as follows: name: 71113_199 n: 110270864950524289144339133459841021143400357504267999886887205650991511373184710031303560333324391658116529 skew: 16176.26 # norm 1.23e+15 c5: 35700 c4: -1151299406 c3: -81809870864120 c2: 211043661978170827 c1: 3912276685296992122992 c0: -12446168675693330275146900 # alpha -5.86 Y1: 307474834733 Y0: -314746746576521188279 # Murphy_E 1.37e-09 # M 20791178240142767970955924393944064521478715602414181529369486113938951120512110021307848257334770395712637 type: gnfs rlim: 2000000 alim: 2000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 50000 Factor base limits: 2000000/2000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [1000000, 1550001) Primes: rational ideals reading, algebraic ideals reading, Relations: 7458099 Max relations in full relation-set: Initial matrix: Pruned matrix : 288207 x 288455 Polynomial selection time: 0.50 hours. Total sieving time: 6.22 hours. Total relation processing time: 0.41 hours. Matrix solve time: 0.17 hours. Time per square root: 0.06 hours. Prototype def-par.txt line would be: gnfs,107,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2000000,2000000,27,27,50,50,2.6,2.6,50000 total time: 7.36 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: 8046820k/8912896k available (2494k kernel code, 339408k reserved, 1262k data, 200k init) Calibrating delay using timer specific routine.. 5347.57 BogoMIPS (lpj=2673786) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672344) Calibrating delay using timer specific routine.. 5344.68 BogoMIPS (lpj=2672341) Calibrating delay using timer specific routine.. 5284.81 BogoMIPS (lpj=2642406)

Nov 5, 2009 (5th)

By Dmitry Domanov / GGNFS, msieve 1.43 / Nov 5, 2009
(67·10¹³⁸-31)/9 = 7(4)₁₃₇1_<139> = 43 · 1487 · 128826294607_<12> · C123
C123 = P52 · P72
P52 = 2155169564333464472349918628266493657340772283669081_<52>
P72 = 419340596308113045083191970050775890985316605601219929324602580966516003_<72>

Number: 123-1 N=903750090252691191717440333954198932390180191786769441344692739715470950187355528108887414276522629304579395374002342803243 ( 123 digits) SNFS difficulty: 141 digits. Divisors found: r1=2155169564333464472349918628266493657340772283669081 (pp52) r2=419340596308113045083191970050775890985316605601219929324602580966516003 (pp72) Version: Msieve-1.40 Total time: 6.21 hours. Scaled time: 12.23 units (timescale=1.969). Factorization parameters were as follows: n: 903750090252691191717440333954198932390180191786769441344692739715470950187355528108887414276522629304579395374002342803243 m: 5000000000000000000000000000 deg: 5 c5: 536 c0: -775 skew: 1.08 type: snfs lss: 1 rlim: 1580000 alim: 1580000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1580000/1580000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [790000, 1990001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 264792 x 265017 Total sieving time: 5.97 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.18 hours. Time per square root: 0.02 hours. Prototype def-par.txt line would be: snfs,141.000,5,0,0,0,0,0,0,0,0,1580000,1580000,26,26,48,48,2.3,2.3,100000 total time: 6.21 hours. --------- CPU info (if available) ----------

(67·10¹⁴¹+41)/9 = 7(4)₁₄₀9_<142> = 3² · 13 · C140
C140 = P30 · P45 · P67
P30 = 104293407448198211674022417719_<30>
P45 = 266908416852904564619693685732080119715284043_<45>
P67 = 2285742510120211041888511644779295382229835659384985236947755209441_<67>

Number: 140-1 N=63627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294397 ( 140 digits) SNFS difficulty: 142 digits. Divisors found: r1=104293407448198211674022417719 (pp30) r2=266908416852904564619693685732080119715284043 (pp45) r3=2285742510120211041888511644779295382229835659384985236947755209441 (pp67) Version: Msieve-1.40 Total time: 6.69 hours. Scaled time: 12.74 units (timescale=1.905). Factorization parameters were as follows: n: 63627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294396961063627730294397 m: 10000000000000000000000000000 deg: 5 c5: 670 c0: 41 skew: 0.57 type: snfs lss: 1 rlim: 1680000 alim: 1680000 lpbr: 26 lpba: 26 mfbr: 48 mfba: 48 rlambda: 2.3 alambda: 2.3Factor base limits: 1680000/1680000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 48/48 Sieved rational special-q in [840000, 2040001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 294207 x 294432 Total sieving time: 6.17 hours. Total relation processing time: 0.04 hours. Matrix solve time: 0.32 hours. Time per square root: 0.16 hours. Prototype def-par.txt line would be: snfs,142.000,5,0,0,0,0,0,0,0,0,1680000,1680000,26,26,48,48,2.3,2.3,100000 total time: 6.69 hours. --------- CPU info (if available) ----------

(67·10¹³³+41)/9 = 7(4)₁₃₂9_<134> = 353081 · 7404732168439_<13> · 949521322502583250865947_<24> · C92
C92 = P36 · P57
P36 = 206990362108995995540706786083800799_<36>
P57 = 144875098665335013194730379024627109574296907971431258387_<57>

Thu Nov 05 13:28:38 2009 Msieve v. 1.43 Thu Nov 05 13:28:38 2009 random seeds: b092c728 739803fc Thu Nov 05 13:28:38 2009 factoring 29987749133314216840538328401109372365462907275873647359634749454350166358605722808406051213 (92 digits) Thu Nov 05 13:28:39 2009 searching for 15-digit factors Thu Nov 05 13:28:40 2009 commencing quadratic sieve (92-digit input) Thu Nov 05 13:28:40 2009 using multiplier of 53 Thu Nov 05 13:28:40 2009 using VC8 32kb sieve core Thu Nov 05 13:28:40 2009 sieve interval: 36 blocks of size 32768 Thu Nov 05 13:28:40 2009 processing polynomials in batches of 6 Thu Nov 05 13:28:40 2009 using a sieve bound of 1787717 (66930 primes) Thu Nov 05 13:28:40 2009 using large prime bound of 187710285 (27 bits) Thu Nov 05 13:28:40 2009 using double large prime bound of 780330238063215 (42-50 bits) Thu Nov 05 13:28:40 2009 using trial factoring cutoff of 50 bits Thu Nov 05 13:28:40 2009 polynomial 'A' values have 12 factors Thu Nov 05 15:11:33 2009 67077 relations (17712 full + 49365 combined from 818509 partial), need 67026 Thu Nov 05 15:11:37 2009 begin with 836221 relations Thu Nov 05 15:11:37 2009 reduce to 166378 relations in 11 passes Thu Nov 05 15:11:37 2009 attempting to read 166378 relations Thu Nov 05 15:11:39 2009 recovered 166378 relations Thu Nov 05 15:11:39 2009 recovered 145981 polynomials Thu Nov 05 15:11:40 2009 attempting to build 67077 cycles Thu Nov 05 15:11:40 2009 found 67077 cycles in 6 passes Thu Nov 05 15:11:40 2009 distribution of cycle lengths: Thu Nov 05 15:11:40 2009 length 1 : 17712 Thu Nov 05 15:11:40 2009 length 2 : 12595 Thu Nov 05 15:11:40 2009 length 3 : 11833 Thu Nov 05 15:11:40 2009 length 4 : 8937 Thu Nov 05 15:11:40 2009 length 5 : 6400 Thu Nov 05 15:11:40 2009 length 6 : 4055 Thu Nov 05 15:11:40 2009 length 7 : 2510 Thu Nov 05 15:11:40 2009 length 9+: 3035 Thu Nov 05 15:11:40 2009 largest cycle: 23 relations Thu Nov 05 15:11:40 2009 matrix is 66930 x 67077 (16.4 MB) with weight 4018873 (59.91/col) Thu Nov 05 15:11:40 2009 sparse part has weight 4018873 (59.91/col) Thu Nov 05 15:11:40 2009 filtering completed in 3 passes Thu Nov 05 15:11:40 2009 matrix is 62762 x 62826 (15.4 MB) with weight 3798024 (60.45/col) Thu Nov 05 15:11:40 2009 sparse part has weight 3798024 (60.45/col) Thu Nov 05 15:11:40 2009 saving the first 48 matrix rows for later Thu Nov 05 15:11:41 2009 matrix is 62714 x 62826 (9.0 MB) with weight 2879392 (45.83/col) Thu Nov 05 15:11:41 2009 sparse part has weight 1970064 (31.36/col) Thu Nov 05 15:11:41 2009 matrix includes 64 packed rows Thu Nov 05 15:11:41 2009 using block size 25130 for processor cache size 6144 kB Thu Nov 05 15:11:41 2009 commencing Lanczos iteration Thu Nov 05 15:11:41 2009 memory use: 9.6 MB Thu Nov 05 15:11:48 2009 linear algebra at 38.3%, ETA 0h 0m Thu Nov 05 15:11:59 2009 lanczos halted after 993 iterations (dim = 62714) Thu Nov 05 15:11:59 2009 recovered 18 nontrivial dependencies Thu Nov 05 15:12:00 2009 prp36 factor: 206990362108995995540706786083800799 Thu Nov 05 15:12:00 2009 prp57 factor: 144875098665335013194730379024627109574296907971431258387 Thu Nov 05 15:12:00 2009 elapsed time 01:43:22

Nov 5, 2009 (4th)

By Sinkiti Sibata / Msieve, GGNFS / Nov 5, 2009
(67·10¹⁵⁰+41)/9 = 7(4)₁₄₉9_<151> = 3² · 23 · 198148463 · C141
C141 = P35 · P106
P35 = 20717939788962621561499247182422137_<35>
P106 = 8760414861837486390460724581872136579955758254687113253234500957057212238208046927618976198274194583616297_<106>

Number: 74449_150 N=181497747633882346312517962380201339855560835063081505846794519711730643938420467789908245811486286339700685380221257507780590325469086766689 ( 141 digits) SNFS difficulty: 151 digits. Divisors found: r1=20717939788962621561499247182422137 (pp35) r2=8760414861837486390460724581872136579955758254687113253234500957057212238208046927618976198274194583616297 (pp106) Version: Msieve-1.40 Total time: 17.61 hours. Scaled time: 36.48 units (timescale=2.071). Factorization parameters were as follows: name: 74449_150 n: 181497747633882346312517962380201339855560835063081505846794519711730643938420467789908245811486286339700685380221257507780590325469086766689 m: 1000000000000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 1900001) Primes: rational ideals reading, algebraic ideals reading, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 448148 x 448396 Total sieving time: 16.69 hours. Total relation processing time: 0.12 hours. Matrix solve time: 0.69 hours. Time per square root: 0.11 hours. Prototype def-par.txt line would be: snfs,151.000,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 17.61 hours. --------- CPU info (if available) ----------

(62·10¹⁵⁰-71)/9 = 6(8)₁₄₉1_<151> = 985483 · 41851752012515441_<17> · C129
C129 = P42 · P87
P42 = 487000537391850390878280007869998072687387_<42>
P87 = 342970652274908800371221025897560617960050601182101051487751425298682261487633167922521_<87>

Number: 68881_150 N=167026891967514041560512106776883305292659958797087512558130233271448139287140102811153939235403213386239930950692215778269942627 ( 129 digits) SNFS difficulty: 151 digits. Divisors found: r1=487000537391850390878280007869998072687387 (pp42) r2=342970652274908800371221025897560617960050601182101051487751425298682261487633167922521 (pp87) Version: GGNFS-0.77.1-20060513-k8 Total time: 28.87 hours. Scaled time: 56.06 units (timescale=1.942). Factorization parameters were as follows: name: 68881_150 n: 167026891967514041560512106776883305292659958797087512558130233271448139287140102811153939235403213386239930950692215778269942627 m: 1000000000000000000000000000000 deg: 5 c5: 62 c0: -71 skew: 1.03 type: snfs lss: 1 rlim: 2400000 alim: 2400000 lpbr: 27 lpba: 27 mfbr: 49 mfba: 49 rlambda: 2.4 alambda: 2.4 Factor base limits: 2400000/2400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 49/49 Sieved rational special-q in [1200000, 2100001) Primes: RFBsize:176302, AFBsize:176285, largePrimes:6922539 encountered Relations: rels:6824198, finalFF:406801 Max relations in full relation-set: 28 Initial matrix: 352653 x 406801 with sparse part having weight 42278766. Pruned matrix : 332656 x 334483 with weight 31669257. Total sieving time: 26.80 hours. Total relation processing time: 0.17 hours. Matrix solve time: 1.72 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,151,5,0,0,0,0,0,0,0,0,2400000,2400000,27,27,49,49,2.4,2.4,100000 total time: 28.87 hours. --------- CPU info (if available) ----------

Nov 5, 2009 (3rd)

By Serge Batalov / Msieve / Nov 5, 2009
(67·10¹²⁰-31)/9 = 7(4)₁₁₉1_<121> = 72126317 · 10506700696103_<14> · C100
C100 = P48 · P53
P48 = 248173394390078679300038958119545859112216157363_<48>
P53 = 39583751858057050006460477944893403895270269829507257_<53>

SNFS difficulty: 121 digits. Divisors found: r1=248173394390078679300038958119545859112216157363 (pp48) r2=39583751858057050006460477944893403895270269829507257 (pp53) Version: Msieve v. 1.44 SVN130 Total time: 0.86 hours. Scaled time: 2.06 units (timescale=2.400). Factorization parameters were as follows: n: 9823634061308601992262375977557460526603204910482843794627402711296077541420800355402220532262483291 m: 1000000000000000000000000 deg: 5 c5: 67 c0: -31 skew: 0.86 type: snfs lss: 1 rlim: 750000 alim: 750000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 750000/750000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [375000, 675001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 80715 x 80940 Total sieving time: 0.79 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.04 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000 total time: 0.86 hours.

(67·10¹²⁰+41)/9 = 7(4)₁₁₉9_<121> = 3 · 10878293325400967777_<20> · C102
C102 = P44 · P58
P44 = 38149372465301295430054963118277813058918169_<44>
P58 = 5979472529270312373079165688301574540864076057469555901091_<58>

SNFS difficulty: 121 digits. Divisors found: r1=38149372465301295430054963118277813058918169 (pp44) r2=5979472529270312373079165688301574540864076057469555901091 (pp58) Version: Msieve v. 1.44 SVN130 Total time: 0.92 hours. Scaled time: 2.20 units (timescale=2.400). Factorization parameters were as follows: n: 228113124665170349134703467583011286242415225834237151834456021181025487623010089878132800918426822379 m: 1000000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 type: snfs lss: 1 rlim: 750000 alim: 750000 lpbr: 25 lpba: 25 mfbr: 46 mfba: 46 rlambda: 2.2 alambda: 2.2 Factor base limits: 750000/750000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [375000, 675001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 78053 x 78278 Total sieving time: 0.86 hours. Total relation processing time: 0.03 hours. Matrix solve time: 0.03 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,121.000,5,0,0,0,0,0,0,0,0,750000,750000,25,25,46,46,2.2,2.2,50000 total time: 0.92 hours.

Nov 5, 2009 (2nd)

By Robert Backstrom / Msieve / Nov 5, 2009
(8·10²²⁰+7)/3 = 2(6)₂₁₉9_<221> = 23432840917_<11> · C211
C211 = P63 · P72 · P76
P63 = 609079768500831052828490055657690521244152789163817285070668259_<63>
P72 = 796566640808664328548424906689815506613506880016762451255084828876058099_<72>
P76 = 2345565144724188907165081244897249978800113689094388155072548075040871134977_<76>

Sieving ~ 220 CPU days + 117 hrs Lanczos with Msieve 1.42 Sat Oct 31 15:34:27 2009 Sat Oct 31 15:34:27 2009 Sat Oct 31 15:34:27 2009 Msieve v. 1.42 Sat Oct 31 15:34:27 2009 random seeds: b45cd8a4 5e8cbb4f Sat Oct 31 15:34:27 2009 factoring 1138003998794725682926321155405412538979627242039312593634276438708887713594111225991671194456334842477805341329483266540910587391526508465762511226229679040784257745433430779376748272005804726927838540861403257 (211 digits) Sat Oct 31 15:34:29 2009 no P-1/P+1/ECM available, skipping Sat Oct 31 15:34:29 2009 commencing number field sieve (211-digit input) Sat Oct 31 15:34:29 2009 R0: -10000000000000000000000000000000000000 Sat Oct 31 15:34:29 2009 R1: 1 Sat Oct 31 15:34:29 2009 A0: 175 Sat Oct 31 15:34:29 2009 A1: 0 Sat Oct 31 15:34:29 2009 A2: 0 Sat Oct 31 15:34:29 2009 A3: 0 Sat Oct 31 15:34:29 2009 A4: 0 Sat Oct 31 15:34:29 2009 A5: 0 Sat Oct 31 15:34:29 2009 A6: 2 Sat Oct 31 15:34:29 2009 skew 1.00, size 3.489374e-11, alpha 1.918928, combined = 1.519785e-12 Sat Oct 31 15:34:29 2009 Sat Oct 31 15:34:29 2009 commencing relation filtering Sat Oct 31 15:34:29 2009 estimated available RAM is 7923.2 MB Sat Oct 31 15:34:29 2009 commencing duplicate removal, pass 1 Sat Oct 31 15:36:03 2009 error -11 reading relation 17254458 Sat Oct 31 15:36:54 2009 error -11 reading relation 26696095 Sat Oct 31 15:36:58 2009 error -11 reading relation 27363947 Sat Oct 31 15:36:58 2009 error -15 reading relation 27363955 Sat Oct 31 15:38:59 2009 error -11 reading relation 45804540 Sat Oct 31 15:39:03 2009 error -9 reading relation 46551733 Sat Oct 31 15:39:43 2009 found 10149236 hash collisions in 53207787 relations Sat Oct 31 15:39:58 2009 added 11 free relations Sat Oct 31 15:39:58 2009 commencing duplicate removal, pass 2 Sat Oct 31 15:40:36 2009 found 10095437 duplicates and 43112361 unique relations Sat Oct 31 15:40:36 2009 memory use: 330.4 MB Sat Oct 31 15:40:36 2009 reading ideals above 42532864 Sat Oct 31 15:40:36 2009 commencing singleton removal, initial pass Sat Oct 31 15:45:48 2009 memory use: 596.8 MB Sat Oct 31 15:45:52 2009 reading all ideals from disk Sat Oct 31 15:45:55 2009 memory use: 817.8 MB Sat Oct 31 15:46:00 2009 commencing in-memory singleton removal Sat Oct 31 15:46:04 2009 begin with 43112361 relations and 40663350 unique ideals Sat Oct 31 15:46:48 2009 reduce to 22314083 relations and 17056552 ideals in 16 passes Sat Oct 31 15:46:48 2009 max relations containing the same ideal: 27 Sat Oct 31 15:46:51 2009 reading ideals above 720000 Sat Oct 31 15:46:51 2009 commencing singleton removal, initial pass Sat Oct 31 15:50:17 2009 memory use: 532.8 MB Sat Oct 31 15:50:17 2009 reading all ideals from disk Sat Oct 31 15:50:18 2009 memory use: 816.4 MB Sat Oct 31 15:50:24 2009 keeping 22080764 ideals with weight <= 200, target excess is 125696 Sat Oct 31 15:50:29 2009 commencing in-memory singleton removal Sat Oct 31 15:50:34 2009 begin with 22314094 relations and 22080764 unique ideals Sat Oct 31 15:51:34 2009 reduce to 22292479 relations and 22059060 ideals in 11 passes Sat Oct 31 15:51:34 2009 max relations containing the same ideal: 200 Sat Oct 31 15:51:56 2009 removing 650811 relations and 607005 ideals in 43806 cliques Sat Oct 31 15:51:57 2009 commencing in-memory singleton removal Sat Oct 31 15:52:02 2009 begin with 21641668 relations and 22059060 unique ideals Sat Oct 31 15:52:44 2009 reduce to 21625957 relations and 21436291 ideals in 8 passes Sat Oct 31 15:52:44 2009 max relations containing the same ideal: 200 Sat Oct 31 15:53:06 2009 removing 467462 relations and 423656 ideals in 43806 cliques Sat Oct 31 15:53:06 2009 commencing in-memory singleton removal Sat Oct 31 15:53:12 2009 begin with 21158495 relations and 21436291 unique ideals Sat Oct 31 15:53:52 2009 reduce to 21150366 relations and 21004483 ideals in 8 passes Sat Oct 31 15:53:52 2009 max relations containing the same ideal: 198 Sat Oct 31 15:54:03 2009 relations with 0 large ideals: 4811 Sat Oct 31 15:54:03 2009 relations with 1 large ideals: 417 Sat Oct 31 15:54:03 2009 relations with 2 large ideals: 3897 Sat Oct 31 15:54:03 2009 relations with 3 large ideals: 44781 Sat Oct 31 15:54:03 2009 relations with 4 large ideals: 304685 Sat Oct 31 15:54:03 2009 relations with 5 large ideals: 1255957 Sat Oct 31 15:54:03 2009 relations with 6 large ideals: 3252807 Sat Oct 31 15:54:03 2009 relations with 7+ large ideals: 16283011 Sat Oct 31 15:54:03 2009 commencing 2-way merge Sat Oct 31 15:54:34 2009 reduce to 13461304 relation sets and 13315421 unique ideals Sat Oct 31 15:54:34 2009 commencing full merge Sat Oct 31 16:00:41 2009 memory use: 1639.9 MB Sat Oct 31 16:00:43 2009 found 7160180 cycles, need 7153621 Sat Oct 31 16:00:47 2009 weight of 7153621 cycles is about 500859937 (70.01/cycle) Sat Oct 31 16:00:47 2009 distribution of cycle lengths: Sat Oct 31 16:00:47 2009 1 relations: 1050682 Sat Oct 31 16:00:47 2009 2 relations: 1061471 Sat Oct 31 16:00:47 2009 3 relations: 984923 Sat Oct 31 16:00:47 2009 4 relations: 812616 Sat Oct 31 16:00:47 2009 5 relations: 657769 Sat Oct 31 16:00:47 2009 6 relations: 527246 Sat Oct 31 16:00:47 2009 7 relations: 421690 Sat Oct 31 16:00:47 2009 8 relations: 331726 Sat Oct 31 16:00:47 2009 9 relations: 261587 Sat Oct 31 16:00:47 2009 10+ relations: 1043911 Sat Oct 31 16:00:47 2009 heaviest cycle: 28 relations Sat Oct 31 16:00:50 2009 commencing cycle optimization Sat Oct 31 16:01:06 2009 start with 38264635 relations Sat Oct 31 16:02:27 2009 pruned 895565 relations Sat Oct 31 16:02:27 2009 memory use: 1259.8 MB Sat Oct 31 16:02:27 2009 distribution of cycle lengths: Sat Oct 31 16:02:27 2009 1 relations: 1050682 Sat Oct 31 16:02:27 2009 2 relations: 1084140 Sat Oct 31 16:02:27 2009 3 relations: 1019860 Sat Oct 31 16:02:27 2009 4 relations: 826893 Sat Oct 31 16:02:27 2009 5 relations: 666675 Sat Oct 31 16:02:27 2009 6 relations: 526965 Sat Oct 31 16:02:27 2009 7 relations: 417613 Sat Oct 31 16:02:27 2009 8 relations: 325306 Sat Oct 31 16:02:27 2009 9 relations: 253971 Sat Oct 31 16:02:27 2009 10+ relations: 981516 Sat Oct 31 16:02:27 2009 heaviest cycle: 28 relations Sat Oct 31 16:02:43 2009 RelProcTime: 1694 Sat Oct 31 16:02:43 2009 Sat Oct 31 16:02:43 2009 commencing linear algebra Sat Oct 31 16:02:48 2009 read 7153621 cycles Sat Oct 31 16:03:02 2009 cycles contain 20976846 unique relations Sat Oct 31 16:05:09 2009 read 20976846 relations Sat Oct 31 16:05:47 2009 using 20 quadratic characters above 536870702 Sat Oct 31 16:07:28 2009 building initial matrix Sat Oct 31 16:11:42 2009 memory use: 2662.3 MB Sat Oct 31 16:11:46 2009 read 7153621 cycles Sat Oct 31 16:11:50 2009 matrix is 7153443 x 7153621 (2122.1 MB) with weight 619248046 (86.56/col) Sat Oct 31 16:11:50 2009 sparse part has weight 484755663 (67.76/col) Sat Oct 31 16:13:28 2009 filtering completed in 2 passes Sat Oct 31 16:13:29 2009 matrix is 7151802 x 7151980 (2122.0 MB) with weight 619201053 (86.58/col) Sat Oct 31 16:13:29 2009 sparse part has weight 484741960 (67.78/col) Sat Oct 31 16:14:11 2009 read 7151980 cycles Sat Oct 31 16:14:15 2009 matrix is 7151802 x 7151980 (2122.0 MB) with weight 619201053 (86.58/col) Sat Oct 31 16:14:15 2009 sparse part has weight 484741960 (67.78/col) Sat Oct 31 16:14:15 2009 saving the first 48 matrix rows for later Sat Oct 31 16:14:18 2009 matrix is 7151754 x 7151980 (2042.1 MB) with weight 494163750 (69.09/col) Sat Oct 31 16:14:18 2009 sparse part has weight 463811895 (64.85/col) Sat Oct 31 16:14:18 2009 matrix includes 64 packed rows Sat Oct 31 16:14:18 2009 using block size 65536 for processor cache size 6144 kB Sat Oct 31 16:14:46 2009 commencing Lanczos iteration (4 threads) Sat Oct 31 16:14:46 2009 memory use: 2218.4 MB Thu Nov 5 10:26:49 2009 lanczos halted after 113099 iterations (dim = 7151754) Thu Nov 5 10:27:00 2009 recovered 40 nontrivial dependencies Thu Nov 5 10:27:00 2009 BLanczosTime: 411857 Thu Nov 5 10:27:00 2009 Thu Nov 5 10:27:00 2009 commencing square root phase Thu Nov 5 10:27:00 2009 reading relations for dependency 1 Thu Nov 5 10:27:02 2009 read 3576106 cycles Thu Nov 5 10:27:10 2009 cycles contain 12847903 unique relations Thu Nov 5 10:28:35 2009 read 12847903 relations Thu Nov 5 10:29:52 2009 multiplying 10490752 relations Thu Nov 5 10:49:26 2009 multiply complete, coefficients have about 272.47 million bits Thu Nov 5 10:49:29 2009 initial square root is modulo 77557 Thu Nov 5 11:21:08 2009 reading relations for dependency 2 Thu Nov 5 11:21:09 2009 read 3577523 cycles Thu Nov 5 11:21:17 2009 cycles contain 12847085 unique relations Thu Nov 5 11:22:42 2009 read 12847085 relations Thu Nov 5 11:24:00 2009 multiplying 10490164 relations Thu Nov 5 11:43:34 2009 multiply complete, coefficients have about 272.46 million bits Thu Nov 5 11:43:36 2009 initial square root is modulo 77557 Thu Nov 5 12:15:13 2009 reading relations for dependency 3 Thu Nov 5 12:15:14 2009 read 3574396 cycles Thu Nov 5 12:15:22 2009 cycles contain 12841056 unique relations Thu Nov 5 12:16:47 2009 read 12841056 relations Thu Nov 5 12:18:05 2009 multiplying 10485418 relations Thu Nov 5 12:37:39 2009 multiply complete, coefficients have about 272.32 million bits Thu Nov 5 12:37:41 2009 initial square root is modulo 77017 Thu Nov 5 13:09:16 2009 sqrtTime: 9736 Thu Nov 5 13:09:16 2009 prp63 factor: 609079768500831052828490055657690521244152789163817285070668259 Thu Nov 5 13:09:16 2009 prp72 factor: 796566640808664328548424906689815506613506880016762451255084828876058099 Thu Nov 5 13:09:16 2009 prp76 factor: 2345565144724188907165081244897249978800113689094388155072548075040871134977 Thu Nov 5 13:09:16 2009 elapsed time 117:34:49

Nov 5, 2009

By Erik Branger / GGNFS, Msieve / Nov 5, 2009
(67·10¹⁴⁵+41)/9 = 7(4)₁₄₄9_<146> = 563 · C144
C144 = P37 · P38 · P69
P37 = 6082655084179705302299740326973200613_<37>
P38 = 75145263081390269628363377895509391047_<38>
P69 = 289287120475685604509159180322914778804255865863282240870880979061193_<69>

Number: 74449_145 N=132228142885336491020327610025656206828498125123347148213933293862245904874679297414643773435958160647325833826721926189066508782316952832050523 ( 144 digits) SNFS difficulty: 146 digits. Divisors found: r1=6082655084179705302299740326973200613 (pp37) r2=75145263081390269628363377895509391047 (pp38) r3=289287120475685604509159180322914778804255865863282240870880979061193 (pp69) Version: Msieve-1.40 Total time: 9.60 hours. Scaled time: 9.62 units (timescale=1.002). Factorization parameters were as follows: n: 132228142885336491020327610025656206828498125123347148213933293862245904874679297414643773435958160647325833826721926189066508782316952832050523 m: 100000000000000000000000000000 deg: 5 c5: 67 c0: 41 skew: 0.91 type: snfs lss: 1 rlim: 1960000 alim: 1960000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.3 alambda: 2.3 Factor base limits: 1960000/1960000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved rational special-q in [980000, 2280001) Primes: , , Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 317816 x 318042 Total sieving time: 9.11 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.24 hours. Time per square root: 0.19 hours. Prototype def-par.txt line would be: snfs,146.000,5,0,0,0,0,0,0,0,0,1960000,1960000,26,26,49,49,2.3,2.3,100000 total time: 9.60 hours. --------- CPU info (if available) ----------

2009: November October September August July June May April March February January
2008: December November October September August July June May April March February January
2007: December November October September August July June May April March February January
2006: December November October September August July June May April March February January
2005: December November October September August July June May April March February January
2004: December November October September August

8. Contributors

I am thankful to contributors 10metreh, Alexander Mkrtychyan, Andreas Tete, Anton Korobeynikov, Bryan Koen, Cedric Vonck, Chris Monico, Dmitry Domanov, Erik Branger, Greg Childers, honeycrack7, Hugo Platzer, Ignacio Santos, Jeff Gilchrist, JMB, Jo Yeong Uk, JPascoa, Julien Peter Benney, Justin Card, Kenichiro Yamaguchi, Kenji Ibusuki, Lionel Debroux, Luigi Morelli, Maksym Voznyy, Markus Tervooren, matsui, Max Dettweiler, Michael Peterson, Nechaev Sergey, Naoki Yamamoto, Norbert Schneider, 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, Yang Hae Hun and Yoichi Hanatani.

9. Factor tables

Last update

Nov 8, 2009

Repunit numbers

• Factorizations of 11...11 (Repunit)
• Factorizations of 100...001
• Factorizations of Phi_n(10)

Recent changes
2009: August July June May April March February January
2008: December November October September

Near-repdigit numbers of the form AA...AAB

form	general term	range	terms which have not been factored yet	last update
11...113	(10n+17)/9	n≤250	n=184, 189, 192, 193, 201, 202, 203, 206, 208, 209, 210, 211, 214, 216, 217, 218, 219, 220, 223, 224, 225, 226, 227, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 243, 244, 246, 250 (37/250)	Oct 22, 2009
11...117	(10n+53)/9	n≤250	n=201, 202, 203, 205, 208, 209, 210, 212, 216, 217, 218, 219, 221, 222, 227, 228, 229, 231, 232, 233, 234, 235, 237, 238, 240, 243, 245, 246, 247, 248, 249 (31/250)	Oct 22, 2009
11...119	(10n+71)/9	n≤200	n=176, 177, 178, 179, 183, 188, 189, 190, 191, 193, 195, 199, 200 (13/200)	Oct 22, 2009
22...221	(2·10n-11)/9	n≤200	n=175, 176, 179, 183, 185, 186, 187, 188, 189, 191, 196, 199, 200 (13/200)	Nov 6, 2009
22...223	(2·10n+7)/9	n≤200	n=173, 174, 176, 179, 182, 184, 193, 195, 196, 198, 199, 200 (12/200)	Nov 6, 2009
22...227	(2·10n+43)/9	n≤200	n=179, 183, 184, 185, 186, 189, 190, 192, 194, 197, 199, 200 (12/200)	Nov 7, 2009
22...229	(2·10n+61)/9	n≤200	n=180, 181, 182, 183, 184, 186, 189, 191, 194, 195, 196, 199 (12/200)	Nov 6, 2009
33...331	(10n-7)/3	n≤250	n=182, 183, 189, 190, 196, 199, 200, 205, 206, 207, 208, 209, 211, 215, 217, 218, 219, 221, 226, 227, 229, 230, 231, 232, 233, 235, 237, 242, 243, 247, 248, 250 (32/250)	Oct 22, 2009
33...337	(10n+11)/3	n≤200	n=173, 178, 179, 180, 184, 185, 186, 187, 191, 192, 193, 194, 196, 197, 198, 199 (16/200)	Nov 5, 2009
44...441	(4·10n-31)/9	n≤200	n=174, 175, 176, 180, 181, 185, 195, 196, 197, 198 (10/200)	Nov 5, 2009
44...443	(4·10n-13)/9	n≤200	n=172, 175, 176, 178, 179, 180, 184, 185, 188, 189, 191, 193, 195, 196, 197, 198, 200 (17/200)	Nov 5, 2009
44...447	(4·10n+23)/9	n≤200	n=178, 181, 183, 184, 185, 188, 192, 193, 195, 196, 197, 200 (12/200)	Nov 5, 2009
44...449	(4·10n+41)/9	n≤200	n=178, 179, 180, 183, 184, 186, 188, 189, 193, 199, 200 (11/200)	Nov 5, 2009
55...551	(5·10n-41)/9	n≤200	n=180, 181, 183, 184, 187, 189, 190, 192, 196, 198, 199, 200 (12/200)	Nov 4, 2009
55...553	(5·10n-23)/9	n≤200	n=176, 178, 179, 182, 187, 188, 193, 196, 200 (9/200)	Nov 4, 2009
55...557	(5·10n+13)/9	n≤200	n=174, 175, 176, 179, 180, 181, 182, 183, 185, 187, 188, 191, 192, 193, 194, 198 (16/200)	Nov 4, 2009
55...559	(5·10n+31)/9	n≤200	n=173, 174, 179, 180, 181, 182, 183, 184, 191, 194, 196 (11/200)	Nov 4, 2009
66...661	(2·10n-17)/3	n≤200	n=172, 175, 176, 183, 186, 190, 193, 194, 195, 197, 200 (11/200)	Nov 4, 2009
66...667	(2·10n+1)/3	n≤250	n=198, 200, 201, 203, 207, 208, 210, 211, 212, 214, 215, 217, 218, 219, 220, 221, 222, 224, 225, 226, 227, 228, 230, 231, 232, 236, 237, 239, 241, 242, 243, 244, 246, 247, 248, 249 (36/250)	Nov 4, 2009
77...771	(7·10n-61)/9	n≤200	n=178, 179, 181, 182, 187, 189, 190, 191, 193, 194, 195, 197, 198 (13/200)	Oct 21, 2009
77...773	(7·10n-43)/9	n≤250	n=186, 195, 197, 199, 200, 203, 206, 208, 209, 210, 211, 212, 213, 215, 217, 218, 220, 225, 226, 227, 230, 232, 235, 236, 237, 238, 239, 240, 242, 245, 248, 249, 250 (33/250)	Oct 21, 2009
77...779	(7·10n+11)/9	n≤200	n=177, 178, 180, 181, 183, 185, 187, 191, 192, 193, 194, 196, 199 (13/200)	Oct 24, 2009
88...881	(8·10n-71)/9	n≤200	n=171, 176, 179, 180, 182, 184, 187, 188, 191, 193, 196, 197, 198, 199 (14/200)	Oct 22, 2009
88...883	(8·10n-53)/9	n≤200	n=172, 174, 176, 179, 184, 185, 186, 194, 195, 196, 197, 199 (12/200)	Oct 22, 2009
88...887	(8·10n-17)/9	n≤200	n=180, 181, 182, 183, 184, 187, 188, 189, 196, 198, 200 (11/200)	Oct 22, 2009
88...889	(8·10n+1)/9	n≤250	n=202, 203, 205, 206, 208, 214, 218, 220, 221, 224, 227, 229, 232, 235, 236, 238, 239, 242, 244, 248 (20/250)	Oct 22, 2009
99...991	10n-9	n≤250	n=201, 211, 215, 221, 229, 231, 235, 241, 243, 245, 247 (11/250)	Oct 23, 2009
99...997	10n-3	n≤200	n=181, 183, 186, 189, 192, 193, 195, 196, 198, 199 (10/200)	Oct 23, 2009

Near-repdigit numbers of the form ABB...BB

form	general term	range	terms which have not been factored yet	last update
133...33	(4·10n-1)/3	n≤250	n=209, 211, 213, 215, 219, 221, 229, 231, 237, 239, 247, 249 (12/250)	Oct 22, 2009
177...77	(16·10n-7)/9	n≤250	n=194, 205, 206, 209, 212, 213, 215, 218, 220, 221, 223, 227, 228, 231, 234, 235, 237, 238, 240, 241, 242, 245, 246, 248 (24/250)	Nov 4, 2009
199...99	2·10n-1	n≤250	n=195, 196, 197, 200, 202, 203, 205, 206, 208, 209, 214, 215, 218, 221, 223, 224, 226, 227, 228, 229, 230, 233, 234, 235, 237, 238, 239, 240, 241, 244, 246 (31/250)	Nov 4, 2009
211...11	(19·10n-1)/9	n≤200	n=176, 178, 179, 183, 184, 185, 188, 189, 192, 194, 195, 196, 197, 200 (14/200)	Nov 7, 2009
233...33	(7·10n-1)/3	n≤200	n=173, 175, 177, 179, 182, 183, 185, 186, 187, 189, 191, 193, 194, 197, 199, 200 (16/200)	Nov 7, 2009
277...77	(25·10n-7)/9	n≤200	n=175, 177, 179, 181, 183, 184, 187, 192, 193, 195, 196, 197, 198, 199 (14/200)	Nov 7, 2009
299...99	3·10n-1	n≤200	n=171, 172, 174, 176, 177, 178, 180, 182, 191, 192, 195, 197, 198, 199 (14/200)	Nov 7, 2009
311...11	(28·10n-1)/9	n≤200	n=175, 176, 177, 178, 180, 181, 182, 184, 187, 188, 194, 196, 197, 198, 199, 200 (16/200)	Nov 6, 2009
377...77	(34·10n-7)/9	n≤200	n=173, 174, 175, 177, 178, 179, 180, 184, 185, 186, 189, 191, 192, 197, 198 (15/200)	Nov 6, 2009
411...11	(37·10n-1)/9	n≤200	n=173, 174, 177, 178, 183, 184, 185, 187, 189, 190, 191, 198, 199 (13/200)	Nov 6, 2009
433...33	(13·10n-1)/3	n≤200	n=173, 176, 177, 179, 180, 181, 182, 184, 187, 189, 190, 192, 193, 194, 196, 198, 200 (17/200)	Nov 6, 2009
477...77	(43·10n-7)/9	n≤250	n=207, 210, 215, 218, 221, 223, 225, 226, 227, 230, 232, 233, 235, 239, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250 (24/250)	Nov 5, 2009
499...99	5·10n-1	n≤200	n=177, 182, 185, 186, 187, 189, 191, 193, 197, 198, 199 (11/200)	Nov 5, 2009
511...11	(46·10n-1)/9	n≤200	n=175, 176, 179, 180, 183, 184, 187, 188, 190, 192, 196, 197 (12/200)	Nov 4, 2009
533...33	(16·10n-1)/3	n≤250	n=181, 183, 185, 187, 189, 191, 193, 195, 197, 199, 213, 215, 217, 219, 221, 223, 225, 227, 229, 231, 235, 237 (22/250)	Nov 4, 2009
577...77	(52·10n-7)/9	n≤200	n=173, 176, 178, 182, 185, 188, 190, 191, 192, 195, 198, 200 (12/200)	Nov 4, 2009
599...99	6·10n-1	n≤200	n=172, 180, 190, 191, 193, 195, 196, 199 (8/200)	Nov 4, 2009
611...11	(55·10n-1)/9	n≤200	n=177, 179, 183, 185, 186, 188, 194, 196, 197, 198 (10/200)	Nov 4, 2009
677...77	(61·10n-7)/9	n≤200	n=176, 183, 184, 185, 189, 190, 191, 194, 196, 197, 200 (11/200)	Nov 4, 2009
711...11	(64·10n-1)/9	n≤350	n=205, 233, 245, 259, 263, 265, 271, 275, 277, 281, 283, 289, 293, 295, 299, 303, 305, 307, 311, 313, 315, 325, 329, 335, 337, 339, 341, 345, 347, 349 (30/350)	Oct 29, 2009
733...33	(22·10n-1)/3	n≤200	n=172, 173, 179, 180, 183, 185, 186, 188, 190, 192, 194, 197, 199 (13/200)	Oct 21, 2009
799...99	8·10n-1	n≤250	n=205, 217, 220, 223, 224, 226, 227, 235, 236, 239, 241, 244, 245, 248 (14/250)	Oct 22, 2009
811...11	(73·10n-1)/9	n≤250	n=188, 195, 199, 200, 201, 203, 204, 205, 206, 207, 210, 211, 212, 213, 214, 215, 218, 219, 220, 221, 222, 224, 225, 227, 229, 231, 233, 234, 235, 237, 239, 240, 241, 242, 243, 244, 246, 248, 249 (39/250)	Oct 28, 2009
833...33	(25·10n-1)/3	n≤250	n=203, 205, 207, 211, 213, 217, 221, 225, 227, 229, 233, 235, 239, 243, 245, 247, 249 (17/250)	Oct 22, 2009
877...77	(79·10n-7)/9	n≤200	n=177, 184, 185, 186, 188, 189, 190, 192, 193, 194, 195, 197, 198, 199 (14/200)	Oct 22, 2009
899...99	9·10n-1	n≤250	n=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 (25/250)	Oct 22, 2009
911...11	(82·10n-1)/9	n≤200	n=172, 176, 177, 178, 180, 181, 182, 183, 188, 189, 191, 194 (12/200)	Oct 23, 2009
977...77	(88·10n-7)/9	n≤200	n=173, 175, 177, 179, 181, 182, 185, 187, 188, 189, 191, 193, 197, 198, 200 (15/200)	Oct 23, 2009

Near-repdigit palindrome numbers of the form AA...AABAA...AA

form	general term	range	terms which have not been factored yet	last update
11...11311...11	(102n+1+18·10n-1)/9	n≤75	Completed / Jun 29, 2005	Jan 18, 2009
11...11411...11	(102n+1+27·10n-1)/9	n≤75	Completed / Oct 13, 2005	Jan 18, 2009
11...11511...11	(102n+1+36·10n-1)/9	n≤75	Completed / Oct 9, 2005	Jan 18, 2009
11...11611...11	(102n+1+45·10n-1)/9	n≤75	Completed / Oct 14, 2005	Jan 18, 2009
11...11711...11	(102n+1+54·10n-1)/9	n≤75	Completed / Oct 15, 2005	Jan 18, 2009
11...11811...11	(102n+1+63·10n-1)/9	n≤75	Completed / Sep 29, 2005	Jan 18, 2009
11...11911...11	(102n+1+72·10n-1)/9	n≤75	Completed / Oct 15, 2005	Jan 18, 2009
33...33133...33	(102n+1-6·10n-1)/3	n≤75	Completed / Aug 19, 2005	Jan 18, 2009
33...33533...33	(102n+1+6·10n-1)/3	n≤75	Completed / Oct 11, 2005	Jan 18, 2009
33...33733...33	(102n+1+12·10n-1)/3	n≤75	Completed / Oct 18, 2005	Jan 18, 2009
33...33833...33	(102n+1+15·10n-1)/3	n≤75	Completed / Jul 11, 2005	Jan 18, 2009
77...77177...77	(7·102n+1-54·10n-7)/9	n≤75	Completed / Sep 26, 2005	Jan 18, 2009
77...77277...77	(7·102n+1-45·10n-7)/9	n≤75	Completed / Oct 11, 2005	Jan 18, 2009
77...77377...77	(7·102n+1-36·10n-7)/9	n≤75	Completed / Oct 3, 2005	Jan 18, 2009
77...77477...77	(7·102n+1-27·10n-7)/9	n≤75	Completed / Jun 6, 2005	Jan 18, 2009
77...77577...77	(7·102n+1-18·10n-7)/9	n≤75	Completed / Oct 17, 2005	Jan 18, 2009
77...77677...77	(7·102n+1-9·10n-7)/9	n≤75	Completed / Oct 20, 2005	Jan 18, 2009
77...77877...77	(7·102n+1+9·10n-7)/9	n≤75	Completed / Oct 13, 2005	Jan 18, 2009
77...77977...77	(7·102n+1+18·10n-7)/9	n≤75	Completed / Sep 28, 2005	Jan 18, 2009
99...99199...99	102n+1-8·10n-1	n≤75	Completed / Sep 6, 2005	Jan 18, 2009
99...99299...99	102n+1-7·10n-1	n≤75	Completed / Sep 20, 2005	Jan 18, 2009
99...99499...99	102n+1-5·10n-1	n≤75	Completed / Sep 26, 2005	Jan 18, 2009
99...99599...99	102n+1-4·10n-1	n≤75	Completed / Aug 13, 2005	Jan 18, 2009
99...99799...99	102n+1-2·10n-1	n≤75	Completed / Jul 26, 2005	Jan 18, 2009
99...99899...99	102n+1-10n-1	n≤75	Completed / Jun 3, 2005	Jan 18, 2009

Plateau and depression numbers of the form ABB...BBA

form	general term	range	terms which have not been factored yet	last update
133...331	(4·10n-7)/3	n≤200	n=175, 176, 181, 184, 186, 188, 192, 194, 198, 200 (10/200)	Oct 22, 2009
144...441	(13·10n-31)/9	n≤200	n=172, 180, 184, 188, 190, 195, 197, 199 (8/200)	Oct 22, 2009
155...551	(14·10n-41)/9	n≤200	n=173, 174, 180, 181, 187, 188, 189, 191, 192, 193, 194, 195, 196, 197, 199, 200 (16/200)	Oct 22, 2009
166...661	(5·10n-17)/3	n≤200	n=172, 175, 176, 180, 181, 184, 186, 187, 190, 194, 195, 196, 197, 200 (14/200)	Oct 22, 2009
177...771	(16·10n-61)/9	n≤250	n=173, 176, 177, 179, 182, 183, 184, 185, 188, 193, 194, 198, 202, 203, 204, 207, 208, 209, 212, 213, 216, 217, 218, 219, 222, 223, 230, 231, 232, 233, 234, 239, 242, 244, 248 (35/250)	Oct 22, 2009
188...881	(17·10n-71)/9	n≤200	n=174, 180, 181, 182, 183, 184, 185, 186, 189, 191, 192, 193, 195, 197, 198, 199, 200 (17/200)	Oct 22, 2009
199...991	2·10n-9	n≤200	n=174, 176, 178, 182, 185, 186, 188, 189, 190, 193, 195, 196, 197, 198, 199 (15/200)	Oct 22, 2009
311...113	(28·10n+17)/9	n≤200	n=172, 177, 178, 180, 182, 186, 187, 189, 194, 195, 198, 199, 200 (13/200)	Nov 5, 2009
322...223	(29·10n+7)/9	n≤200	n=172, 175, 177, 180, 182, 188, 190, 192, 193, 196, 198 (11/200)	Nov 5, 2009
344...443	(31·10n-13)/9	n≤200	n=171, 173, 180, 190, 193, 195, 197, 199, 200 (9/200)	Nov 5, 2009
355...553	(32·10n-23)/9	n≤200	n=174, 175, 180, 181, 184, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200 (15/200)	Nov 6, 2009
377...773	(34·10n-43)/9	n≤200	n=178, 181, 183, 187, 188, 189, 190, 192, 194, 195, 197, 198, 199, 200 (14/200)	Nov 6, 2009
388...883	(35·10n-53)/9	n≤200	n=173, 176, 179, 183, 184, 185, 187, 189, 190, 191, 195, 197, 200 (13/200)	Nov 6, 2009
711...117	(64·10n+53)/9	n≤250	n=179, 182, 187, 188, 189, 191, 195, 197, 200, 204, 207, 209, 210, 211, 212, 213, 216, 217, 222, 224, 227, 230, 231, 233, 235, 236, 237, 239, 240, 241, 243, 247, 249, 250 (34/250)	Oct 21, 2009
722...227	(65·10n+43)/9	n≤200	n=172, 176, 177, 179, 182, 184, 185, 191, 192, 194, 196, 197, 199 (13/200)	Oct 28, 2009
744...447	(67·10n+23)/9	n≤200	n=178, 180, 182, 192, 193, 194, 195, 196, 198 (9/200)	Oct 21, 2009
755...557	(68·10n+13)/9	n≤200	n=174, 175, 178, 181, 182, 186, 189, 190, 191, 193, 197, 199, 200 (13/200)	Oct 21, 2009
766...667	(23·10n+1)/3	n≤200	n=172, 176, 180, 181, 184, 186, 189, 190, 191, 192, 194, 197, 198, 199 (14/200)	Oct 21, 2009
788...887	(71·10n-17)/9	n≤200	n=173, 179, 180, 181, 185, 186, 189, 191, 193, 194, 195, 196, 198 (13/200)	Oct 21, 2009
799...997	8·10n-3	n≤200	n=174, 176, 177, 181, 186, 188, 190, 191, 193, 195, 199, 200 (12/200)	Oct 21, 2009
911...119	(82·10n+71)/9	n≤200	n=173, 174, 177, 179, 180, 181, 187, 189, 190, 192, 196, 198, 200 (13/200)	Oct 23, 2009
922...229	(83·10n+61)/9	n≤200	n=171, 173, 175, 177, 179, 181, 184, 187, 191, 192, 193, 195, 196, 197, 199, 200 (16/200)	Oct 23, 2009
944...449	(85·10n+41)/9	n≤200	n=172, 173, 175, 176, 178, 181, 182, 187, 188, 190, 191, 193, 194, 197, 198, 199 (16/200)	Oct 23, 2009
955...559	(86·10n+31)/9	n≤200	n=175, 179, 180, 183, 185, 186, 188, 191, 196, 198, 200 (11/200)	Oct 23, 2009
988...889	(89·10n+1)/9	n≤200	n=176, 182, 184, 188, 192, 195, 196, 198, 200 (9/200)	Oct 23, 2009

Quasi-repdigit numbers of the form ABB...BBC

form	general term	range	terms which have not been factored yet	last update
100...003	10n+3	n≤250	n=201, 203, 205, 216, 218, 219, 220, 221, 222, 223, 224, 226, 227, 228, 229, 230, 231, 233, 234, 236, 239, 240, 241, 242, 243, 244, 245, 247, 248, 250 (30/250)	Oct 24, 2009
100...007	10n+7	n≤200	n=180, 181, 182, 183, 189, 191, 192, 194, 196, 198, 199, 200 (12/200)	Oct 22, 2009
100...009	10n+9	n≤200	n=176, 179, 182, 183, 186, 190, 195, 196, 198 (9/200)	Oct 22, 2009
122...223	(11·10n+7)/9	n≤200	n=178, 180, 181, 182, 183, 188, 189, 190, 192, 194, 196, 197, 199, 200 (14/200)	Oct 23, 2009
122...227	(11·10n+43)/9	n≤200	n=172, 178, 182, 183, 185, 186, 187, 190, 191, 192, 194, 199 (12/200)	Oct 22, 2009
122...229	(11·10n+61)/9	n≤200	n=174, 176, 181, 183, 188, 189, 190, 191, 193, 194, 195, 196, 197, 199 (14/200)	Oct 22, 2009
133...337	(4·10n+11)/3	n≤200	n=179, 182, 183, 185, 189, 191, 193, 194, 195, 197, 200 (11/200)	Oct 22, 2009
133...339	(4·10n+17)/3	n≤200	n=172, 178, 179, 180, 183, 185, 188, 189, 191, 193, 197, 199 (12/200)	Oct 22, 2009
144...447	(13·10n+23)/9	n≤200	n=175, 176, 177, 179, 180, 186, 189, 190, 191, 192, 196, 197 (12/200)	Oct 22, 2009
144...449	(13·10n+41)/9	n≤200	n=171, 173, 180, 183, 185, 186, 188, 190, 192, 194, 197, 198, 200 (13/200)	Oct 22, 2009
155...553	(14·10n-23)/9	n≤200	n=174, 176, 177, 182, 184, 186, 187, 188, 191, 194, 195, 196, 197, 198 (14/200)	Oct 22, 2009
155...557	(14·10n+13)/9	n≤200	n=172, 173, 175, 176, 177, 180, 182, 186, 187, 188, 189, 190, 192, 194, 195, 196 (16/200)	Oct 22, 2009
155...559	(14·10n+31)/9	n≤200	n=172, 173, 178, 181, 185, 187, 189, 191, 193, 197, 199, 200 (12/200)	Oct 22, 2009
166...663	(5·10n-11)/3	n≤200	n=171, 178, 179, 180, 182, 183, 184, 185, 186, 191, 192, 194, 195, 196, 200 (15/200)	Oct 22, 2009
166...667	(5·10n+1)/3	n≤200	n=177, 180, 182, 183, 184, 187, 188, 190, 191, 194, 197, 198 (12/200)	Oct 22, 2009
166...669	(5·10n+7)/3	n≤200	n=175, 176, 183, 192, 194, 196, 199, 200 (8/200)	Oct 22, 2009
177...773	(16·10n-43)/9	n≤200	n=174, 175, 179, 182, 183, 186, 189, 197, 198, 200 (10/200)	Oct 22, 2009
177...779	(16·10n+11)/9	n≤200	n=174, 175, 182, 185, 189, 191, 192, 193, 194, 197, 199, 200 (12/200)	Oct 22, 2009
188...883	(17·10n-53)/9	n≤200	n=175, 177, 179, 180, 181, 184, 188, 192, 193, 194, 195, 196 (12/200)	Oct 22, 2009
188...889	(17·10n+1)/9	n≤200	n=172, 175, 176, 177, 178, 180, 182, 186, 187, 191, 193, 194, 197, 198, 199 (15/200)	Oct 22, 2009
199...993	2·10n-7	n≤200	n=173, 179, 181, 182, 190, 193, 194, 195, 196, 197, 199 (11/200)	Oct 22, 2009
199...997	2·10n-3	n≤200	n=172, 178, 179, 183, 185, 187, 193, 195, 196 (9/200)	Oct 22, 2009
200...003	2·10n+3	n≤200	n=177, 179, 180, 181, 182, 186, 190, 192, 193, 194, 196, 198, 199, 200 (14/200)	Nov 6, 2009
200...009	2·10n+9	n≤200	Completed / Nov 3, 2009	Nov 6, 2009
211...113	(19·10n+17)/9	n≤200	n=174, 183, 186, 187, 188, 189, 193, 194, 196 (9/200)	Nov 6, 2009
211...117	(19·10n+53)/9	n≤200	n=174, 178, 180, 185, 186, 188, 191, 192, 195, 199 (10/200)	Nov 6, 2009
211...119	(19·10n+71)/9	n≤200	n=174, 179, 180, 182, 183, 185, 186, 188, 189, 191, 192, 194, 195, 198, 199, 200 (16/200)	Nov 6, 2009
233...339	(7·10n+17)/3	n≤200	n=175, 176, 181, 186, 188, 190, 192, 193, 196, 197 (10/200)	Nov 6, 2009
244...441	(22·10n-31)/9	n≤200	n=175, 176, 177, 178, 181, 187, 189, 190, 191, 195, 196, 198 (12/200)	Nov 6, 2009
244...443	(22·10n-13)/9	n≤205	n=175, 180, 181, 188, 189, 193, 194, 197, 198, 201, 203, 205 (12/205)	Nov 6, 2009
244...447	(22·10n+23)/9	n≤205	n=172, 173, 179, 182, 185, 186, 187, 189, 190, 192, 193, 195, 196, 198, 200, 201, 203 (17/205)	Nov 6, 2009
244...449	(22·10n+41)/9	n≤205	n=175, 177, 178, 179, 185, 188, 190, 191, 192, 193, 194, 199, 200, 202, 205 (15/205)	Nov 6, 2009
255...551	(23·10n-41)/9	n≤205	n=174, 175, 181, 182, 184, 187, 192, 193, 194, 197, 200, 202, 205 (13/205)	Nov 6, 2009
255...557	(23·10n+13)/9	n≤205	n=175, 176, 177, 181, 182, 185, 190, 192, 193, 194, 195, 196, 199 (13/205)	Nov 6, 2009
255...559	(23·10n+31)/9	n≤205	n=173, 175, 176, 178, 179, 180, 182, 183, 185, 188, 189, 190, 191, 192, 195, 197, 199, 200, 201, 202, 205 (21/205)	Nov 6, 2009
266...663	(8·10n-11)/3	n≤205	n=175, 177, 178, 181, 182, 183, 184, 185, 189, 190, 191, 193, 194, 195, 198, 199, 200, 201, 202, 204, 205 (21/205)	Nov 6, 2009
266...669	(8·10n+7)/3	n≤225	n=202, 205, 206, 207, 208, 209, 210, 212, 213, 214, 215, 216, 217, 218, 223, 224, 225 (17/225)	Nov 6, 2009
277...771	(25·10n-61)/9	n≤205	n=175, 176, 178, 179, 180, 183, 186, 187, 188, 192, 198, 200, 201 (13/205)	Nov 6, 2009
277...773	(25·10n-43)/9	n≤205	n=174, 175, 178, 187, 188, 190, 191, 192, 193, 194, 196, 198, 199, 200, 201, 204 (16/205)	Nov 6, 2009
277...779	(25·10n+11)/9	n≤205	n=174, 175, 176, 178, 179, 180, 182, 186, 187, 188, 189, 190, 193, 195, 198, 199, 201, 203 (18/205)	Nov 7, 2009
288...881	(26·10n-71)/9	n≤205	n=174, 175, 177, 178, 179, 180, 184, 185, 189, 190, 191, 196, 200, 202, 204 (15/205)	Nov 7, 2009
288...883	(26·10n-53)/9	n≤205	n=177, 178, 179, 182, 183, 184, 187, 188, 190, 191, 192, 194, 199, 200, 201, 203, 205 (17/205)	Nov 7, 2009
288...887	(26·10n-17)/9	n≤205	n=184, 186, 189, 191, 194, 198, 199, 200, 201, 202, 205 (11/205)	Nov 7, 2009
288...889	(26·10n+1)/9	n≤205	n=174, 175, 176, 177, 180, 182, 183, 184, 185, 186, 187, 190, 191, 192, 196, 198, 199, 200, 201, 202, 204, 205 (22/205)	Nov 7, 2009
299...993	3·10n-7	n≤200	n=176, 180, 188, 191, 193, 194, 195, 196, 198 (9/200)	Nov 7, 2009
300...001	3·10n+1	n≤200	n=173, 174, 175, 176, 182, 183, 193, 194, 195, 196, 197, 200 (12/200)	Nov 5, 2009
300...007	3·10n+7	n≤200	n=178, 180, 182, 183, 187, 188, 189, 190, 192, 195, 196, 199, 200 (13/200)	Nov 5, 2009
311...117	(28·10n+53)/9	n≤205	n=176, 178, 180, 181, 184, 190, 191, 196, 199, 201, 202, 203, 204 (13/205)	Nov 5, 2009
311...119	(28·10n+71)/9	n≤205	n=175, 183, 187, 188, 190, 192, 195, 198, 199, 200, 203, 204, 205 (13/205)	Nov 5, 2009
322...221	(29·10n-11)/9	n≤205	n=173, 174, 175, 180, 181, 184, 186, 187, 188, 189, 194, 195, 196, 197, 200, 202, 203, 205 (18/205)	Nov 5, 2009
322...227	(29·10n+43)/9	n≤205	n=171, 174, 177, 182, 183, 185, 187, 189, 191, 194, 195, 198, 200, 202, 203, 204, 205 (17/205)	Nov 5, 2009
322...229	(29·10n+61)/9	n≤205	n=171, 173, 175, 177, 178, 179, 181, 182, 185, 188, 189, 191, 196, 199, 203, 204 (16/205)	Nov 5, 2009
344...447	(31·10n+23)/9	n≤205	n=174, 178, 179, 180, 181, 183, 186, 187, 188, 189, 193, 194, 196, 197, 198, 201, 203 (17/205)	Nov 6, 2009
344...449	(31·10n+41)/9	n≤205	n=174, 175, 177, 181, 182, 183, 187, 188, 190, 193, 194, 196, 197, 198, 201, 202, 204 (17/205)	Nov 6, 2009
355...551	(32·10n-41)/9	n≤205	n=174, 176, 179, 180, 184, 185, 189, 191, 192, 195, 199, 200, 202 (13/205)	Nov 6, 2009
355...557	(32·10n+13)/9	n≤205	n=174, 178, 179, 182, 183, 184, 185, 186, 190, 192, 196, 197, 198, 199, 203, 204 (16/205)	Nov 6, 2009
355...559	(32·10n+31)/9	n≤205	n=175, 182, 183, 184, 187, 191, 192, 197, 198, 203, 205 (11/205)	Nov 6, 2009
366...661	(11·10n-17)/3	n≤205	n=174, 179, 182, 186, 187, 189, 190, 192, 200, 202, 203 (11/205)	Nov 6, 2009
366...667	(11·10n+1)/3	n≤205	n=175, 176, 178, 179, 181, 183, 184, 185, 186, 188, 189, 190, 195, 197, 198, 200, 203, 204, 205 (19/205)	Nov 6, 2009
377...771	(34·10n-61)/9	n≤205	n=172, 176, 179, 187, 191, 192, 193, 194, 195, 196, 197, 201, 204, 205 (14/205)	Nov 6, 2009
377...779	(34·10n+11)/9	n≤205	n=174, 176, 178, 179, 182, 183, 187, 188, 189, 197, 199, 200, 201, 203, 204, 205 (16/205)	Nov 6, 2009
388...881	(35·10n-71)/9	n≤205	n=172, 173, 174, 181, 183, 184, 185, 186, 190, 194, 195, 197, 198, 201, 202, 204, 205 (17/205)	Nov 6, 2009
388...887	(35·10n-17)/9	n≤205	n=175, 177, 183, 185, 188, 190, 195, 197, 198, 199, 200, 201, 204 (13/205)	Nov 6, 2009
388...889	(35·10n+1)/9	n≤205	n=172, 175, 176, 181, 182, 185, 186, 195, 196, 197, 200, 201, 202, 205 (14/205)	Nov 6, 2009
399...991	4·10n-9	n≤250	n=189, 191, 193, 203, 205, 207, 209, 211, 213, 221, 225, 235, 237, 239, 243, 245, 247, 249 (18/250)	Nov 6, 2009
399...997	4·10n-3	n≤200	n=174, 177, 181, 184, 185, 186, 188, 189, 190, 191, 192, 193, 199 (13/200)	Nov 6, 2009
400...001	4·10n+1	n≤250	n=202, 206, 210, 211, 213, 215, 219, 222, 225, 226, 227, 231, 233, 235, 237, 238, 239, 243, 245, 246, 247, 250 (22/250)	Nov 4, 2009
400...003	4·10n+3	n≤200	n=179, 189, 190, 191, 193, 195, 199, 200 (8/200)	Nov 4, 2009
400...007	4·10n+7	n≤200	n=171, 174, 176, 178, 179, 184, 186, 187, 188, 192, 193, 197, 199 (13/200)	Nov 6, 2009
400...009	4·10n+9	n≤250	n=184, 186, 190, 197, 201, 204, 207, 208, 209, 211, 214, 215, 218, 220, 221, 223, 224, 225, 226, 227, 228, 230, 231, 232, 233, 234, 235, 238, 239, 240, 241, 244, 245, 246, 247, 248, 249 (37/250)	Nov 4, 2009
411...113	(37·10n+17)/9	n≤205	n=171, 176, 179, 181, 183, 184, 185, 187, 188, 189, 191, 192, 193, 194, 197, 198, 199, 202 (18/205)	Nov 4, 2009
411...117	(37·10n+53)/9	n≤205	n=174, 175, 180, 181, 182, 183, 184, 185, 191, 192, 193, 194, 197, 198, 202, 203, 204, 205 (18/205)	Nov 4, 2009
411...119	(37·10n+71)/9	n≤205	n=185, 188, 189, 190, 195, 196, 197, 204 (8/205)	Nov 4, 2009
422...221	(38·10n-11)/9	n≤205	n=171, 176, 179, 180, 182, 186, 190, 193, 194, 197, 198, 199, 201, 202, 203, 204, 205 (17/205)	Nov 4, 2009
422...223	(38·10n+7)/9	n≤205	n=173, 175, 178, 179, 180, 184, 186, 187, 188, 190, 192, 194, 196, 197, 198, 199, 200, 201, 202, 203, 204 (21/205)	Nov 4, 2009
422...227	(38·10n+43)/9	n≤205	n=171, 174, 179, 182, 185, 187, 190, 191, 194, 199, 200, 201, 202 (13/205)	Nov 4, 2009
422...229	(38·10n+61)/9	n≤205	n=172, 175, 179, 183, 184, 188, 189, 193, 197, 201, 202, 204, 205 (13/205)	Nov 4, 2009
433...331	(13·10n-7)/3	n≤205	n=175, 176, 181, 183, 184, 186, 192, 193, 195, 200, 201 (11/205)	Nov 4, 2009
433...337	(13·10n+11)/3	n≤205	n=178, 179, 181, 184, 186, 187, 188, 195, 198, 199, 200, 203, 204 (13/205)	Nov 5, 2009
433...339	(13·10n+17)/3	n≤205	n=171, 179, 187, 191, 196, 197, 198, 200, 201, 202 (10/205)	Nov 5, 2009
455...553	(41·10n-23)/9	n≤205	n=172, 175, 179, 187, 188, 189, 190, 192, 193, 195, 196, 199, 201, 202, 204 (15/205)	Nov 5, 2009
455...557	(41·10n+13)/9	n≤205	n=177, 178, 179, 186, 190, 191, 192, 193, 195, 197, 198, 199, 202, 203, 204 (15/205)	Nov 5, 2009
455...559	(41·10n+31)/9	n≤205	n=174, 175, 176, 180, 183, 187, 188, 193, 194, 197, 201, 205 (12/205)	Nov 5, 2009
466...661	(14·10n-17)/3	n≤205	n=176, 177, 178, 179, 181, 183, 184, 186, 187, 188, 190, 193, 197, 198, 199, 202, 203, 205 (18/205)	Nov 5, 2009
466...663	(14·10n-11)/3	n≤205	n=174, 176, 177, 180, 181, 182, 183, 184, 186, 187, 188, 189, 190, 191, 192, 196, 198, 199, 202, 203 (20/205)	Nov 5, 2009
466...667	(14·10n+1)/3	n≤205	n=176, 177, 181, 186, 187, 188, 189, 190, 191, 198, 201, 202, 203, 205 (14/205)	Nov 5, 2009
477...771	(43·10n-61)/9	n≤205	n=172, 175, 178, 183, 185, 186, 188, 191, 194, 195, 197, 198, 200, 203 (14/205)	Nov 5, 2009
477...779	(43·10n+11)/9	n≤205	n=174, 176, 177, 181, 187, 188, 191, 194, 195, 196, 201, 202, 205 (13/205)	Nov 5, 2009
488...881	(44·10n-71)/9	n≤205	n=175, 180, 181, 183, 184, 185, 188, 190, 191, 192, 194, 195, 197, 199, 200, 201, 202, 204 (18/205)	Nov 6, 2009
488...883	(44·10n-53)/9	n≤205	n=174, 176, 177, 179, 180, 181, 182, 183, 184, 185, 188, 189, 191, 193, 194, 197, 198, 201, 203, 204 (20/205)	Nov 5, 2009
488...887	(44·10n-17)/9	n≤205	n=172, 174, 179, 183, 184, 185, 187, 189, 190, 194, 196, 198, 199, 200, 201, 203, 205 (17/205)	Nov 5, 2009
488...889	(44·10n+1)/9	n≤205	n=174, 177, 178, 181, 183, 188, 190, 191, 193, 194, 196, 198, 199, 200, 201, 202, 203 (17/205)	Nov 5, 2009
499...991	5·10n-9	n≤200	n=175, 176, 177, 178, 181, 182, 183, 186, 187, 188, 192, 195, 196, 200 (14/200)	Nov 5, 2009
499...993	5·10n-7	n≤200	n=172, 177, 183, 185, 187, 191, 192, 198 (8/200)	Nov 6, 2009
499...997	5·10n-3	n≤200	n=173, 175, 176, 181, 183, 185, 187, 188, 189, 190, 191, 194, 195, 197, 200 (15/200)	Nov 6, 2009
500...003	5·10n+3	n≤200	n=174, 177, 178, 182, 184, 190, 193, 194, 195, 197, 199, 200 (12/200)	Nov 4, 2009
500...009	5·10n+9	n≤200	n=172, 176, 180, 181, 182, 183, 184, 185, 190, 193, 197, 198, 199, 200 (14/200)	Nov 4, 2009
511...113	(46·10n+17)/9	n≤205	n=174, 175, 182, 183, 187, 188, 189, 190, 191, 192, 193, 196, 199, 201, 203, 204, 205 (17/205)	Nov 4, 2009
511...117	(46·10n+53)/9	n≤205	n=173, 178, 179, 180, 181, 183, 184, 188, 189, 190, 191, 192, 194, 197, 199, 203, 205 (17/205)	Nov 4, 2009
511...119	(46·10n+71)/9	n≤205	n=174, 177, 179, 181, 183, 184, 185, 186, 187, 190, 191, 192, 194, 197, 201, 202, 203, 204, 205 (19/205)	Nov 4, 2009
522...221	(47·10n-11)/9	n≤205	n=173, 174, 175, 178, 180, 181, 182, 184, 185, 186, 187, 191, 194, 195, 196, 199, 203, 205 (18/205)	Nov 4, 2009
522...223	(47·10n+7)/9	n≤205	n=172, 175, 176, 180, 182, 189, 192, 198, 201, 203, 205 (11/205)	Nov 4, 2009
522...227	(47·10n+43)/9	n≤205	n=173, 175, 176, 178, 183, 184, 187, 190, 191, 192, 196, 199, 201, 202, 203, 205 (16/205)	Nov 4, 2009
522...229	(47·10n+61)/9	n≤205	n=176, 177, 178, 180, 181, 183, 185, 189, 190, 192, 194, 200, 201, 202, 204, 205 (16/205)	Nov 4, 2009
533...339	(16·10n+17)/3	n≤205	n=172, 173, 174, 176, 179, 181, 184, 185, 187, 188, 189, 191, 192, 198, 199, 201, 202, 204, 205 (19/205)	Nov 4, 2009
544...441	(49·10n-31)/9	n≤205	n=175, 177, 179, 180, 181, 182, 183, 184, 186, 189, 190, 192, 193, 194, 195, 200, 201, 204 (18/205)	Nov 4, 2009
544...443	(49·10n-13)/9	n≤205	n=174, 175, 176, 179, 181, 187, 189, 191, 192, 195, 197, 201, 203, 204 (14/205)	Nov 4, 2009
544...447	(49·10n+23)/9	n≤205	n=172, 176, 179, 182, 184, 186, 188, 191, 193, 194, 196, 199, 201, 202, 203, 204, 205 (17/205)	Nov 4, 2009
544...449	(49·10n+41)/9	n≤205	n=179, 180, 181, 182, 183, 185, 189, 190, 191, 192, 193, 195, 202, 203, 204 (15/205)	Nov 6, 2009
566...663	(17·10n-11)/3	n≤205	n=173, 174, 176, 178, 181, 182, 184, 187, 188, 189, 190, 192, 197, 198, 199, 203, 204, 205 (18/205)	Nov 4, 2009
566...669	(17·10n+7)/3	n≤205	n=172, 175, 177, 178, 179, 181, 184, 186, 188, 189, 191, 193, 194, 196, 197, 198, 199, 201, 202, 203 (20/205)	Nov 4, 2009
577...771	(52·10n-61)/9	n≤205	n=175, 176, 179, 181, 182, 183, 188, 190, 192, 194, 195, 196, 197, 198, 199, 201, 202, 204 (18/205)	Nov 4, 2009
577...773	(52·10n-43)/9	n≤205	n=172, 174, 177, 179, 180, 182, 185, 186, 187, 188, 189, 190, 191, 194, 196, 198, 199, 201, 202, 203, 204, 205 (22/205)	Nov 4, 2009
577...779	(52·10n+11)/9	n≤205	n=171, 176, 179, 185, 186, 187, 191, 192, 193, 194, 198, 202, 203, 205 (14/205)	Nov 4, 2009
588...881	(53·10n-71)/9	n≤205	n=172, 174, 176, 177, 179, 180, 182, 184, 186, 187, 188, 189, 190, 198, 199, 200, 201, 202, 203, 205 (20/205)	Nov 4, 2009
588...887	(53·10n-17)/9	n≤205	n=173, 174, 175, 181, 182, 183, 185, 186, 188, 189, 190, 192, 193, 196, 199, 204, 205 (17/205)	Nov 4, 2009
588...889	(53·10n+1)/9	n≤205	n=175, 177, 181, 182, 184, 186, 188, 189, 191, 192, 194, 196, 198, 200, 201, 203, 205 (17/205)	Nov 4, 2009
599...993	6·10n-7	n≤200	n=174, 177, 178, 181, 182, 186, 187, 188, 191, 192, 195, 198, 199, 200 (14/200)	Nov 4, 2009
600...001	6·10n+1	n≤250	n=201, 203, 204, 206, 207, 208, 209, 210, 212, 213, 215, 216, 217, 218, 219, 220, 222, 223, 226, 227, 228, 231, 232, 233, 234, 235, 237, 238, 239, 240, 242, 243, 245, 246, 247, 249 (36/250)	Nov 4, 2009
600...007	6·10n+7	n≤200	n=174, 175, 177, 181, 184, 186, 189, 190, 191, 193, 196, 197, 199 (13/200)	Nov 4, 2009
611...113	(55·10n+17)/9	n≤205	n=174, 176, 177, 178, 182, 184, 185, 186, 187, 189, 195, 196, 197, 202, 204, 205 (16/205)	Nov 4, 2009
611...117	(55·10n+53)/9	n≤205	n=174, 175, 176, 177, 180, 181, 182, 183, 185, 187, 188, 189, 190, 193, 195, 196, 201, 203 (18/205)	Nov 4, 2009
611...119	(55·10n+71)/9	n≤205	n=175, 177, 178, 179, 180, 184, 185, 187, 188, 189, 193, 194, 195, 198, 200, 202, 203, 204 (18/205)	Nov 4, 2009
622...221	(56·10n-11)/9	n≤205	n=172, 177, 181, 184, 187, 188, 191, 193, 195, 196, 197, 200, 202, 203, 204, 205 (16/205)	Nov 4, 2009
622...227	(56·10n+43)/9	n≤205	n=177, 180, 182, 183, 185, 187, 188, 192, 194, 195, 196, 197, 198, 201 (14/205)	Nov 4, 2009
622...229	(56·10n+61)/9	n≤205	n=171, 172, 178, 179, 181, 182, 183, 184, 188, 189, 193, 194, 195, 197, 198, 202, 203, 204, 205 (19/205)	Nov 4, 2009
633...331	(19·10n-7)/3	n≤205	n=171, 173, 174, 177, 182, 187, 189, 191, 192, 193, 194, 195, 196, 198, 199, 201, 202 (17/205)	Nov 4, 2009
633...337	(19·10n+11)/3	n≤205	n=173, 174, 177, 179, 180, 183, 186, 187, 188, 190, 193, 195, 196, 198, 200, 203, 204 (17/205)	Nov 4, 2009
644...441	(58·10n-31)/9	n≤205	n=176, 180, 183, 184, 185, 186, 187, 190, 191, 192, 194, 197, 198, 199, 200, 201, 203, 204, 205 (19/205)	Nov 4, 2009
644...443	(58·10n-13)/9	n≤205	n=176, 178, 181, 184, 187, 188, 193, 194, 196, 197, 199, 200, 202, 203, 204, 205 (16/205)	Nov 4, 2009
644...447	(58·10n+23)/9	n≤205	n=173, 174, 177, 178, 180, 181, 182, 183, 184, 188, 189, 190, 192, 193, 195, 196, 199, 202, 203, 204, 205 (21/205)	Nov 4, 2009
644...449	(58·10n+41)/9	n≤205	n=176, 178, 181, 182, 183, 184, 185, 186, 191, 193, 196, 197, 198, 199, 201, 202 (16/205)	Nov 4, 2009
655...551	(59·10n-41)/9	n≤205	n=171, 172, 173, 174, 180, 181, 183, 189, 190, 191, 196, 197, 198, 199, 200, 201, 203, 204 (18/205)	Nov 4, 2009
655...553	(59·10n-23)/9	n≤205	n=171, 181, 183, 186, 189, 191, 192, 193, 194, 196, 201, 205 (12/205)	Nov 4, 2009
655...557	(59·10n+13)/9	n≤200	n=152, 155, 158, 160, 161, 164, 170, 171, 172, 173, 175, 179, 182, 183, 186, 187, 190, 192, 193, 195, 196, 199, 200 (23/200)	Nov 4, 2009
655...559	(59·10n+31)/9	n≤200	n=155, 156, 158, 159, 161, 162, 164, 167, 168, 171, 172, 173, 176, 182, 183, 184, 186, 187, 188, 191, 193, 194, 195, 197, 198 (25/200)	Nov 6, 2009
677...773	(61·10n-43)/9	n≤200	n=155, 160, 166, 169, 172, 175, 177, 185, 187, 190, 194, 195, 196, 197, 198, 199 (16/200)	Nov 4, 2009
677...779	(61·10n+11)/9	n≤150	n=146 (1/150)	Nov 4, 2009
688...881	(62·10n-71)/9	n≤150	Completed / Nov 5, 2009	Nov 6, 2009
688...883	(62·10n-53)/9	n≤150	Completed / Nov 4, 2009	Nov 5, 2009
688...887	(62·10n-17)/9	n≤150	Completed / Nov 7, 2009	Nov 8, 2009
688...889	(62·10n+1)/9	n≤150	Completed / Nov 4, 2009	Nov 5, 2009
699...991	7·10n-9	n≤200	n=177, 179, 183, 185, 188, 189, 192, 193, 195 (9/200)	Nov 4, 2009
699...997	7·10n-3	n≤200	n=180, 182, 184, 188, 189, 192, 196, 197, 198, 199 (10/200)	Nov 4, 2009
700...001	7·10n+1	n≤200	n=172, 177, 180, 181, 184, 185, 186, 191, 193, 195, 196, 197, 199 (13/200)	Oct 21, 2009
700...003	7·10n+3	n≤200	n=173, 179, 180, 181, 183, 184, 186, 195, 196, 197, 198 (11/200)	Nov 7, 2009
700...009	7·10n+9	n≤200	n=183, 185, 186, 190, 193, 194, 197, 198, 200 (9/200)	Oct 21, 2009
711...113	(64·10n+17)/9	n≤200	n=154, 156, 161, 164, 165, 168, 169, 170, 173, 174, 175, 177, 178, 181, 182, 184, 185, 186, 187, 191, 192, 193, 194, 195, 196, 197, 200 (27/200)	Nov 8, 2009
711...119	(64·10n+71)/9	n≤200	n=153, 157, 166, 169, 171, 174, 175, 176, 178, 179, 180, 181, 186, 187, 188, 189, 190, 191, 192, 194, 195, 196, 197, 198, 199, 200 (26/200)	Oct 31, 2009
722...221	(65·10n-11)/9	n≤200	n=151, 153, 156, 158, 161, 162, 164, 165, 166, 172, 175, 180, 182, 183, 186, 189, 190, 191, 192, 195, 197 (21/200)	Nov 5, 2009
722...223	(65·10n+7)/9	n≤200	n=152, 156, 157, 159, 160, 163, 165, 166, 168, 172, 182, 185, 187, 192, 195, 196, 197, 198, 199, 200 (20/200)	Nov 8, 2009
722...229	(65·10n+61)/9	n≤200	n=156, 159, 162, 164, 166, 167, 168, 170, 171, 172, 174, 175, 177, 178, 181, 182, 183, 184, 185, 186, 188, 191, 192, 193, 194, 196, 198 (27/200)	Nov 5, 2009
733...331	(22·10n-7)/3	n≤200	n=154, 158, 159, 160, 161, 164, 166, 167, 172, 177, 178, 180, 182, 187, 188, 189, 190, 191, 192, 193, 195, 196, 197, 198, 199, 200 (26/200)	Nov 6, 2009
733...339	(22·10n+17)/3	n≤200	n=157, 163, 165, 166, 168, 169, 170, 171, 172, 175, 176, 178, 181, 183, 186, 187, 188, 189, 192, 193, 194, 195, 196, 197, 200 (25/200)	Nov 6, 2009
744...441	(67·10n-31)/9	n≤200	n=151, 153, 154, 156, 160, 163, 166, 171, 174, 175, 176, 177, 180, 185, 186, 189, 190, 196, 197, 198 (20/200)	Nov 8, 2009
744...443	(67·10n-13)/9	n≤200	n=153, 155, 158, 160, 162, 165, 166, 168, 170, 172, 177, 178, 179, 180, 181, 182, 186, 189, 190, 191, 192, 193, 196 (23/200)	Nov 6, 2009
744...449	(67·10n+41)/9	n≤200	n=154, 156, 160, 161, 164, 167, 171, 172, 173, 175, 176, 177, 179, 180, 181, 183, 184, 185, 187, 188, 189, 190, 193, 194, 195, 196, 197, 200 (28/200)	Nov 8, 2009
755...551	(68·10n-41)/9	n≤100	Completed / Jan 6, 2005	Oct 21, 2009
755...553	(68·10n-23)/9	n≤100	Completed / Dec 6, 2004	Oct 21, 2009
755...559	(68·10n+31)/9	n≤100	Completed / Nov 29, 2004	Oct 21, 2009
766...661	(23·10n-17)/3	n≤100	Completed / Jan 7, 2005	Oct 21, 2009
766...663	(23·10n-11)/3	n≤100	Completed / Jan 7, 2005	Oct 21, 2009
766...669	(23·10n+7)/3	n≤100	Completed / Jan 7, 2005	Oct 21, 2009
788...883	(71·10n-53)/9	n≤100	Completed / Jan 7, 2005	Oct 21, 2009
788...889	(71·10n+1)/9	n≤100	Completed / Dec 6, 2004	Oct 21, 2009
799...991	8·10n-9	n≤200	n=177, 186, 188, 189, 191, 196, 197 (7/200)	Oct 21, 2009
799...993	8·10n-7	n≤200	n=173, 176, 178, 180, 185, 187, 190, 192, 193, 197, 198, 199, 200 (13/200)	Oct 21, 2009
800...003	8·10n+3	n≤200	n=173, 174, 179, 180, 182, 183, 184, 186, 188, 190, 191, 192, 193, 195, 197, 199, 200 (17/200)	Oct 22, 2009
800...009	8·10n+9	n≤200	n=178, 179, 191, 192, 193, 195, 196 (7/200)	Oct 22, 2009
811...113	(73·10n+17)/9	n≤100	Completed / Jan 7, 2005	Oct 22, 2009
811...117	(73·10n+53)/9	n≤100	Completed / Jan 7, 2005	Oct 22, 2009
811...119	(73·10n+71)/9	n≤100	Completed / Jan 6, 2005	Oct 22, 2009
822...221	(74·10n-11)/9	n≤100	Completed / Jan 7, 2005	Oct 22, 2009
822...223	(74·10n+7)/9	n≤100	Completed / Jan 7, 2005	Oct 22, 2009
822...227	(74·10n+43)/9	n≤100	Completed / Jan 7, 2005	Oct 22, 2009
822...229	(74·10n+61)/9	n≤100	Completed / Jan 6, 2005	Oct 22, 2009
833...339	(25·10n+17)/3	n≤100	Completed / Jan 7, 2005	Oct 22, 2009
844...441	(76·10n-31)/9	n≤100	Completed / Jan 7, 2005	Oct 22, 2009
844...443	(76·10n-13)/9	n≤100	Completed / Jan 7, 2005	Oct 22, 2009
844...447	(76·10n+23)/9	n≤100	Completed / Jan 6, 2005	Oct 22, 2009
844...449	(76·10n+41)/9	n≤100	Completed / Jan 7, 2005	Oct 22, 2009
855...551	(77·10n-41)/9	n≤100	Completed / Dec 6, 2004	Oct 22, 2009
855...553	(77·10n-23)/9	n≤100	Completed / Jan 8, 2005	Oct 22, 2009
855...557	(77·10n+13)/9	n≤100	Completed / Dec 6, 2004	Oct 22, 2009
855...559	(77·10n+31)/9	n≤100	Completed / Jan 8, 2005	Oct 22, 2009
866...663	(26·10n-11)/3	n≤200	n=154, 157, 158, 161, 163, 166, 167, 169, 172, 173, 175, 176, 179, 186, 188, 190, 194, 196, 198, 199, 200 (21/200)	Nov 8, 2009
866...669	(26·10n+7)/3	n≤100	Completed / Jan 8, 2005	Oct 22, 2009
877...771	(79·10n-61)/9	n≤100	Completed / Jan 8, 2005	Oct 22, 2009
877...773	(79·10n-43)/9	n≤100	Completed / Nov 29, 2004	Oct 22, 2009
877...779	(79·10n+11)/9	n≤100	Completed / Jan 8, 2005	Oct 22, 2009
899...993	9·10n-7	n≤200	n=172, 175, 176, 177, 179, 183, 185, 186, 187, 189, 190, 193, 197, 198, 200 (15/200)	Oct 22, 2009
900...001	9·10n+1	n≤200	n=176, 178, 179, 181, 182, 185, 187, 188, 191, 195, 196, 199, 200 (13/200)	Oct 23, 2009
900...007	9·10n+7	n≤200	n=172, 178, 187, 188, 190, 193, 194, 195, 197, 198 (10/200)	Oct 23, 2009
911...113	(82·10n+17)/9	n≤100	Completed / Dec 7, 2004	Oct 23, 2009
911...117	(82·10n+53)/9	n≤100	Completed / Jan 8, 2005	Oct 23, 2009
922...221	(83·10n-11)/9	n≤100	Completed / Jan 8, 2005	Oct 23, 2009
922...223	(83·10n+7)/9	n≤200	n=156, 161, 165, 167, 168, 171, 173, 174, 175, 179, 180, 184, 185, 188, 189, 191, 192, 193, 194, 196, 197, 200 (22/200)	Nov 8, 2009
922...227	(83·10n+43)/9	n≤100	Completed / Jan 8, 2005	Oct 23, 2009
933...337	(28·10n+11)/3	n≤100	Completed / Dec 1, 2004	Oct 23, 2009
944...441	(85·10n-31)/9	n≤100	Completed / Dec 7, 2004	Oct 23, 2009
944...443	(85·10n-13)/9	n≤100	Completed / Jan 8, 2005	Oct 23, 2009
944...447	(85·10n+23)/9	n≤100	Completed / Jan 8, 2005	Oct 23, 2009
955...551	(86·10n-41)/9	n≤100	Completed / Jan 8, 2005	Oct 23, 2009
955...553	(86·10n-23)/9	n≤100	Completed / Nov 29, 2004	Oct 23, 2009
955...557	(86·10n+13)/9	n≤100	Completed / Jan 8, 2005	Oct 23, 2009
966...661	(29·10n-17)/3	n≤100	Completed / Jan 6, 2005	Oct 23, 2009
966...667	(29·10n+1)/3	n≤100	Completed / Jan 8, 2005	Oct 23, 2009
977...771	(88·10n-61)/9	n≤100	Completed / Jan 8, 2005	Oct 23, 2009
977...773	(88·10n-43)/9	n≤100	Completed / Dec 7, 2004	Oct 23, 2009
988...881	(89·10n-71)/9	n≤100	Completed / Jan 8, 2005	Oct 23, 2009
988...883	(89·10n-53)/9	n≤100	Completed / Jan 8, 2005	Oct 23, 2009
988...887	(89·10n-17)/9	n≤100	Completed / Jan 8, 2005	Oct 23, 2009

10. List of near-repdigit-related prime numbers

• primesize.txt sorted by size, 100 digits or more
• primecount.txt sorted by count
• primedifficulty.txt sorted by difficulty

11. Expression generator of near-repdigit-related numbers

For example, enter "33331" or "3w1" to the left box, and click "→" button. The corresponding expression appears in the right box. More complex labels, such as "1w2w3w", are also available. This program is written in JavaScript.

12. Implementations

• GMP-ECM - INRIAGforge: GMP-ECM (Elliptic Curve Method): Project Info
• GGNFS - GGNFS suite | Get GGNFS suite at SourceForge.net
• Msieve - Msieve | Get Msieve at SourceForge.net
• PFGW - OpenPFGW | Get OpenPFGW at SourceForge.net
• Primo - Primo - Primality Proving
• YAFU - bbuhrow - YAFU's Homepage
• Windows Factoring Software Binaries (64bit & 32bit) (Jeff Gilchrist)

13. Related links

• Bob Backstrom - Sydney PCUG, Web Design, Large Factors, Digital Photos, Electronics (Bob Backstrom)
• Factorizations of Repunit Numbers of the form (10ⁿ-1)/9 (Kurt Beschorner)
• Richard Brent - Factor Tables (Richard Brent)
• Plateau and Depression Primes (Patrick De Geest)
• Factoring and Prime Identification (Torbjörn Granlund)
• Repunit - Top (Yousuke Koide)
• Factorizations of Cyclotomic Numbers (Hisanori Mishima)
• GGNFS (Chris Monico)
• Integer Factorizations and (Cyclotomic) Polynomials (Alfred Reich)
• The Cunningham Project (Sam Wagstaff)
• The ECMNET Project (Paul Zimmermann)
• AMS Online Books/Factorizations of b^{n}+/- 1, b=2,3,5,6,7,10,11,12 Up to High Powers/conm22 (AMS Online Books)
• Open Directory - Science: Math: Number Theory: Factoring (dmoz)