Since June 16, 2000

STUDIO KAMADA

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Index

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

1. Introduction

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

2. Last update

Aug 5, 2008 23:21 JST

3. News and updates

Aug 5, 2008 (5th)

By Sinkiti Sibata / GGNFS
(23·10¹²⁷+13)/9 = 2(5)₁₂₆7_<128> = 3² · 17 · 89 · 550127 · 15161969 · C111
C111 = P35 · P77
P35 = 13962671799159788912176788641978303_<35>
P77 = 16114498505559821766333917333370677084205143841791033427451207993209327515189_<77>

Number: 25557_127 N=225001453841182686270734845345767763482321035145545368687777587106504220899885180817018327157682834904240944267 ( 111 digits) SNFS difficulty: 128 digits. Divisors found: r1=13962671799159788912176788641978303 (pp35) r2=16114498505559821766333917333370677084205143841791033427451207993209327515189 (pp77) Version: GGNFS-0.77.1-20050930-nocona Total time: 4.50 hours. Scaled time: 3.52 units (timescale=0.782). Factorization parameters were as follows: name: 25557_127 n: 225001453841182686270734845345767763482321035145545368687777587106504220899885180817018327157682834904240944267 m: 10000000000000000000000000 c5: 2300 c0: 13 skew: 0.36 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 950001) Primes: RFBsize:63951, AFBsize:64288, largePrimes:1480412 encountered Relations: rels:1464229, finalFF:157594 Max relations in full relation-set: 28 Initial matrix: 128306 x 157594 with sparse part having weight 11631696. Pruned matrix : 119660 x 120365 with weight 7163626. Total sieving time: 4.35 hours. Total relation processing time: 0.05 hours. Matrix solve time: 0.06 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,128,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 4.50 hours. --------- CPU info (if available) ----------

(23·10¹¹⁹+13)/9 = 2(5)₁₁₈7_<120> = 280032133 · 16397289482959744157_<20> · C92
C92 = P44 · P48
P44 = 96993982263781813971167216661363091550858813_<44>
P48 = 573800079124972352177927819974219178800933411769_<48>

Number: 25557_119 N=55655154697604169806028078164116264032438483353137260828203497020024427432838560478111570197 ( 92 digits) SNFS difficulty: 121 digits. Divisors found: r1=96993982263781813971167216661363091550858813 (pp44) r2=573800079124972352177927819974219178800933411769 (pp48) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 3.02 hours. Scaled time: 1.43 units (timescale=0.472). Factorization parameters were as follows: name: 25557_119 n: 55655154697604169806028078164116264032438483353137260828203497020024427432838560478111570197 m: 1000000000000000000000000 c5: 23 c0: 130 skew: 1.41 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved algebraic special-q in [400000, 650001) Primes: RFBsize:49098, AFBsize:63533, largePrimes:2228706 encountered Relations: rels:2377123, finalFF:258771 Max relations in full relation-set: 28 Initial matrix: 112696 x 258771 with sparse part having weight 25229340. Pruned matrix : 86971 x 87598 with weight 6306762. Total sieving time: 2.82 hours. Total relation processing time: 0.08 hours. Matrix solve time: 0.09 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,121,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 3.02 hours. --------- CPU info (if available) ----------

(23·10¹²⁸+13)/9 = 2(5)₁₂₇7_<129> = 83 · 920849 · 1030201 · 24436253 · C108
C108 = P34 · P74
P34 = 7593900515955794514613493406731977_<34>
P74 = 17490302870130540569518879363200396131415419419892069960190397320321006691_<74>

Number: 25557_128 N=132819619989707425690297221931201401167919173092980715094496396268807687443328293733002387041546989060658107 ( 108 digits) SNFS difficulty: 129 digits. Divisors found: r1=7593900515955794514613493406731977 (pp34) r2=17490302870130540569518879363200396131415419419892069960190397320321006691 (pp74) Version: GGNFS-0.77.1-20050930-nocona Total time: 5.15 hours. Scaled time: 4.00 units (timescale=0.778). Factorization parameters were as follows: name: 25557_128 n: 132819619989707425690297221931201401167919173092980715094496396268807687443328293733002387041546989060658107 m: 10000000000000000000000000 c5: 23000 c0: 13 skew: 0.22 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved algebraic special-q in [400000, 1050001) Primes: RFBsize:63951, AFBsize:63628, largePrimes:1510729 encountered Relations: rels:1505111, finalFF:164740 Max relations in full relation-set: 28 Initial matrix: 127646 x 164740 with sparse part having weight 12961919. Pruned matrix : 117224 x 117926 with weight 7554883. Total sieving time: 4.99 hours. Total relation processing time: 0.06 hours. Matrix solve time: 0.07 hours. Time per square root: 0.03 hours. Prototype def-par.txt line would be: snfs,129,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 5.15 hours. --------- CPU info (if available) ----------

Aug 5, 2008 (4th)

By Serge Batalov / GMP-ECM, Msieve
(23·10¹¹⁵+13)/9 = 2(5)₁₁₄7_<116> = 3 · 1590765569_<10> · C106
C106 = P41 · P66
P41 = 25989819434052094099886238319121888616577_<41>
P66 = 206041464084329287564612835952629247644214995705639504013510860663_<66>

Number: 25557_115 N=5354980447479447877412865049581996904861673252948384953709366158979594131835599541140507623419977679010551 ( 106 digits) SNFS difficulty: 116 digits. Divisors found: r1=25989819434052094099886238319121888616577 r2=206041464084329287564612835952629247644214995705639504013510860663 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.204). Factorization parameters were as follows: n: 5354980447479447877412865049581996904861673252948384953709366158979594131835599541140507623419977679010551 Y1: 1 Y0: -100000000000000000000000 c5: 23 c0: 13 skew: 0.89 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 400001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 72538 x 72764 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,116,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 0.75 hours.

(23·10¹⁷⁶+13)/9 = 2(5)₁₇₅7_<177> = 4567 · C173
C173 = P31 · C143
P31 = 1370850223332403243997479287923_<31>
C143 = [40819182982692297903201245645427546973252118080333946991250896508476928198768851369315568750971333405347653894783379624671217671886324833679377_<143>]
(23·10¹¹⁷+13)/9 = 2(5)₁₁₆7_<118> = 67 · 1069 · C113
C113 = P37 · P77
P37 = 1088529921713480335664455585324748987_<37>
P77 = 32778754467867428138643680913471158736943850231412323569027407329166201609257_<77>

Number: 25557_117 N=35680655034773125330627808882000971134350076868541607522102614461214352310787813349839514618984900877588980572659 ( 113 digits) SNFS difficulty: 118 digits. Divisors found: r1=1088529921713480335664455585324748987 r2=32778754467867428138643680913471158736943850231412323569027407329166201609257 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.287). Factorization parameters were as follows: n: 35680655034773125330627808882000971134350076868541607522102614461214352310787813349839514618984900877588980572659 Y1: 1 Y0: -100000000000000000000000 c5: 2300 c0: 13 skew: 0.36 type: snfs Factor base limits: 600000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 46/46 Sieved rational special-q in [300000, 500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 115127 x 115347 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,118,5,0,0,0,0,0,0,0,0,600000,800000,25,25,46,46,2.4,2.4,50000 total time: 1.00 hours.

(23·10¹⁴⁰+13)/9 = 2(5)₁₃₉7_<141> = 383 · 37571 · 60029 · 323957 · 543259 · 1169334002020951974997922683_<28> · C91
C91 = P41 · P50
P41 = 97007064866694932760814312825637589612503_<41>
P50 = 14819598862760793777831985088043035801154127559863_<50>

Mon Aug 4 20:04:31 2008 Msieve v. 1.36 Mon Aug 4 20:04:31 2008 random seeds: 3716472c 5ff7c185 Mon Aug 4 20:04:31 2008 factoring 1437605788178234778599655579349905454752457659865333975172464249220608012494047083105767089 (91 digits) Mon Aug 4 20:04:32 2008 no P-1/P+1/ECM available, skipping Mon Aug 4 20:04:32 2008 commencing quadratic sieve (91-digit input) Mon Aug 4 20:04:32 2008 using multiplier of 1 Mon Aug 4 20:04:32 2008 using 64kb Opteron sieve core Mon Aug 4 20:04:32 2008 sieve interval: 18 blocks of size 65536 Mon Aug 4 20:04:32 2008 processing polynomials in batches of 6 Mon Aug 4 20:04:32 2008 using a sieve bound of 1650079 (62353 primes) Mon Aug 4 20:04:32 2008 using large prime bound of 145206952 (27 bits) Mon Aug 4 20:04:32 2008 using double large prime bound of 491560817809336 (42-49 bits) Mon Aug 4 20:04:32 2008 using trial factoring cutoff of 49 bits Mon Aug 4 20:04:32 2008 polynomial 'A' values have 12 factors Mon Aug 4 21:17:32 2008 62761 relations (17292 full + 45469 combined from 684074 partial), need 62449 Mon Aug 4 21:17:33 2008 begin with 701366 relations Mon Aug 4 21:17:33 2008 reduce to 151346 relations in 10 passes Mon Aug 4 21:17:33 2008 attempting to read 151346 relations Mon Aug 4 21:17:35 2008 recovered 151346 relations Mon Aug 4 21:17:35 2008 recovered 125083 polynomials Mon Aug 4 21:17:35 2008 attempting to build 62761 cycles Mon Aug 4 21:17:35 2008 found 62761 cycles in 6 passes Mon Aug 4 21:17:35 2008 distribution of cycle lengths: Mon Aug 4 21:17:35 2008 length 1 : 17292 Mon Aug 4 21:17:35 2008 length 2 : 12526 Mon Aug 4 21:17:35 2008 length 3 : 11168 Mon Aug 4 21:17:35 2008 length 4 : 8120 Mon Aug 4 21:17:35 2008 length 5 : 5621 Mon Aug 4 21:17:35 2008 length 6 : 3514 Mon Aug 4 21:17:35 2008 length 7 : 2067 Mon Aug 4 21:17:35 2008 length 9+: 2453 Mon Aug 4 21:17:35 2008 largest cycle: 20 relations Mon Aug 4 21:17:35 2008 matrix is 62353 x 62761 (15.8 MB) with weight 3643919 (58.06/col) Mon Aug 4 21:17:35 2008 sparse part has weight 3643919 (58.06/col) Mon Aug 4 21:17:36 2008 filtering completed in 3 passes Mon Aug 4 21:17:36 2008 matrix is 57751 x 57815 (14.6 MB) with weight 3369339 (58.28/col) Mon Aug 4 21:17:36 2008 sparse part has weight 3369339 (58.28/col) Mon Aug 4 21:17:36 2008 saving the first 48 matrix rows for later Mon Aug 4 21:17:37 2008 matrix is 57703 x 57815 (9.2 MB) with weight 2595919 (44.90/col) Mon Aug 4 21:17:37 2008 sparse part has weight 1846004 (31.93/col) Mon Aug 4 21:17:37 2008 matrix includes 64 packed rows Mon Aug 4 21:17:37 2008 using block size 23126 for processor cache size 1024 kB Mon Aug 4 21:17:37 2008 commencing Lanczos iteration Mon Aug 4 21:17:37 2008 memory use: 8.4 MB Mon Aug 4 21:18:00 2008 lanczos halted after 914 iterations (dim = 57701) Mon Aug 4 21:18:00 2008 recovered 16 nontrivial dependencies Mon Aug 4 21:18:01 2008 prp41 factor: 97007064866694932760814312825637589612503 Mon Aug 4 21:18:01 2008 prp50 factor: 14819598862760793777831985088043035801154127559863 Mon Aug 4 21:18:01 2008 elapsed time 01:13:30

(23·10¹³⁰+13)/9 = 2(5)₁₂₉7_<131> = 3 · 7 · 1911853405367337457_<19> · C111
C111 = P45 · P67
P45 = 273621240879818118935599372820806523689400881_<45>
P67 = 2326278114029065603348744181689416700387279243410338996591662514801_<67>

Number: 25557_130 N=636519104192195960835737776365832516184927682124212998818556622451324575858446919445568813294192981881484939681 ( 111 digits) SNFS difficulty: 131 digits. Divisors found: r1=273621240879818118935599372820806523689400881 r2=2326278114029065603348744181689416700387279243410338996591662514801 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.313). Factorization parameters were as follows: n: 636519104192195960835737776365832516184927682124212998818556622451324575858446919445568813294192981881484939681 Y1: 1 Y0: -100000000000000000000000000 c5: 23 c0: 13 skew: 0.89 type: snfs Factor base limits: 800000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 44/44 Sieved rational special-q in [400000, 800001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 103517 x 103765 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,131,5,0,0,0,0,0,0,0,0,800000,800000,25,25,44,44,2.2,2.2,50000 total time: 1.75 hours.

(23·10¹³⁸+13)/9 = 2(5)₁₃₇7_<139> = 12307410569462018609_<20> · C120
C120 = P30 · P34 · P57
P30 = 507750308517183330272789653297_<30>
P34 = 3474089539882015715274674665350059_<34>
P57 = 117713814807586006583552288564604273462593769995433243151_<57>

#by ECM Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=3165820906 Step 1 took 11745ms Step 2 took 11152ms ********** Factor found in step 2: 507750308517183330272789653297 Found probable prime factor of 30 digits: 507750308517183330272789653297 Composite cofactor 408948332722643277879927696871940117264041855347969617854343237250222908088195835079195909 has 90 digits # # then stopped the running snfs-138, and did QS-90 (with Msieve-1.36) # Mon Aug 4 22:13:03 2008 Msieve v. 1.36 Mon Aug 4 22:13:03 2008 random seeds: bac18a9e 3a47e97e Mon Aug 4 22:13:03 2008 factoring 408948332722643277879927696871940117264041855347969617854343237250222908088195835079195909 (90 digits) Mon Aug 4 22:13:04 2008 no P-1/P+1/ECM available, skipping Mon Aug 4 22:13:04 2008 commencing quadratic sieve (90-digit input) Mon Aug 4 22:13:04 2008 using multiplier of 11 Mon Aug 4 22:13:04 2008 using 64kb Opteron sieve core Mon Aug 4 22:13:04 2008 sieve interval: 18 blocks of size 65536 Mon Aug 4 22:13:04 2008 processing polynomials in batches of 6 Mon Aug 4 22:13:04 2008 using a sieve bound of 1578193 (60000 primes) Mon Aug 4 22:13:04 2008 using large prime bound of 126255440 (26 bits) Mon Aug 4 22:13:04 2008 using double large prime bound of 382164232656720 (42-49 bits) Mon Aug 4 22:13:04 2008 using trial factoring cutoff of 49 bits Mon Aug 4 22:13:04 2008 polynomial 'A' values have 12 factors Mon Aug 4 23:37:53 2008 60097 relations (15999 full + 44098 combined from 632948 partial), need 60096 Mon Aug 4 23:37:53 2008 begin with 648947 relations Mon Aug 4 23:37:54 2008 reduce to 146281 relations in 10 passes Mon Aug 4 23:37:54 2008 attempting to read 146281 relations Mon Aug 4 23:37:55 2008 recovered 146281 relations Mon Aug 4 23:37:55 2008 recovered 125898 polynomials Mon Aug 4 23:37:55 2008 attempting to build 60097 cycles Mon Aug 4 23:37:55 2008 found 60097 cycles in 6 passes Mon Aug 4 23:37:55 2008 distribution of cycle lengths: Mon Aug 4 23:37:55 2008 length 1 : 15999 Mon Aug 4 23:37:55 2008 length 2 : 11696 Mon Aug 4 23:37:55 2008 length 3 : 10617 Mon Aug 4 23:37:55 2008 length 4 : 7985 Mon Aug 4 23:37:55 2008 length 5 : 5632 Mon Aug 4 23:37:55 2008 length 6 : 3524 Mon Aug 4 23:37:55 2008 length 7 : 2118 Mon Aug 4 23:37:55 2008 length 9+: 2526 Mon Aug 4 23:37:55 2008 largest cycle: 23 relations Mon Aug 4 23:37:56 2008 matrix is 60000 x 60097 (15.8 MB) with weight 3662551 (60.94/col) Mon Aug 4 23:37:56 2008 sparse part has weight 3662551 (60.94/col) Mon Aug 4 23:37:56 2008 filtering completed in 3 passes Mon Aug 4 23:37:56 2008 matrix is 56117 x 56181 (14.9 MB) with weight 3461219 (61.61/col) Mon Aug 4 23:37:56 2008 sparse part has weight 3461219 (61.61/col) Mon Aug 4 23:37:57 2008 saving the first 48 matrix rows for later Mon Aug 4 23:37:57 2008 matrix is 56069 x 56181 (9.9 MB) with weight 2726773 (48.54/col) Mon Aug 4 23:37:57 2008 sparse part has weight 2024982 (36.04/col) Mon Aug 4 23:37:57 2008 matrix includes 64 packed rows Mon Aug 4 23:37:57 2008 using block size 22472 for processor cache size 1024 kB Mon Aug 4 23:37:57 2008 commencing Lanczos iteration Mon Aug 4 23:37:57 2008 memory use: 8.6 MB Mon Aug 4 23:38:21 2008 lanczos halted after 888 iterations (dim = 56069) Mon Aug 4 23:38:21 2008 recovered 19 nontrivial dependencies Mon Aug 4 23:38:22 2008 prp34 factor: 3474089539882015715274674665350059 Mon Aug 4 23:38:22 2008 prp57 factor: 117713814807586006583552288564604273462593769995433243151 elapsed time 01:25:19

(23·10¹³⁶+13)/9 = 2(5)₁₃₅7_<137> = 3³ · 7 · 260511659 · C126
C126 = P35 · P92
P35 = 35617088186151596018674980636783041_<35>
P92 = 14572630267115638925813556562718250466819225757428431015167830009407651750016178741452169627_<92>

Number: 25557_136 N=519034657328039600210553006352615630158346372995501019534847688559781900082053191302111498978559137446093228922297791128895707 ( 126 digits) SNFS difficulty: 137 digits. Divisors found: r1=35617088186151596018674980636783041 r2=14572630267115638925813556562718250466819225757428431015167830009407651750016178741452169627 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.952). Factorization parameters were as follows: n: 519034657328039600210553006352615630158346372995501019534847688559781900082053191302111498978559137446093228922297791128895707 Y1: 1 Y0: -1000000000000000000000000000 c5: 230 c0: 13 skew: 0.56 type: snfsFactor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 1625001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 146625 x 146858 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,137,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 3.00 hours.

(17·10¹⁸⁹+1)/9 = 1(8)₁₈₈9_<190> = 59 · 71 · 1617391 · 12524207 · 3607698986231981_<16> · 370127884625109553441_<21> · C137
C137 = P31 · P36 · P71
P31 = 1756706333511604963524042522871_<31>
P36 = 668814360582016023721300568011912207_<36>
P71 = 14188743452434643875801927553951755349395681019380535143529908397628329_<71>
(23·10¹⁷¹+13)/9 = 2(5)₁₇₀7_<172> = 47 · 89 · 224293807 · C160
C160 = P30 · P130
P30 = 420665653593367124551131807829_<30>
P130 = 6475049984190779352600188491788559885012137408499137509465838676005670925080692961463905247359951019310758928110457579498055421593_<130>
(23·10¹³⁷+13)/9 = 2(5)₁₃₆7_<138> = 1193 · C135
C135 = P53 · P82
P53 = 24825801948309814186567834093884243731110843768686833_<53>
P82 = 8628625030368435551953354953972853797741901598228835301547475858040231276993102253_<82>

Number: 25557_137 N=214212536090155536928378504237682779174816056626618236006333240197448076743969451429635838688646735587221756542795939275402812703734749 ( 135 digits) SNFS difficulty: 138 digits. Divisors found: r1=24825801948309814186567834093884243731110843768686833 r2=8628625030368435551953354953972853797741901598228835301547475858040231276993102253 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.946). Factorization parameters were as follows: n: 214212536090155536928378504237682779174816056626618236006333240197448076743969451429635838688646735587221756542795939275402812703734749 Y1: 1 Y0: -1000000000000000000000000000 c5: 2300 c0: 13 skew: 0.36 type: snfsFactor base limits: 1000000/800000 Large primes per side: 3 Large prime bits: 25/25 Max factor residue bits: 43/43 Sieved rational special-q in [500000, 2450001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 172185 x 172417 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: snfs,138,5,0,0,0,0,0,0,0,0,1000000,800000,25,25,43,43,2.3,2.3,75000 total time: 5.25 hours.

(23·10¹⁹¹+13)/9 = 2(5)₁₉₀7_<192> = 17 · 61 · 600577511 · C180
C180 = P33 · P147
P33 = 581223556439835774287202811285249_<33>
P147 = 705983086990766454288312162598464346964091589028038512031272672754584909109068532226533435641467045849482264569501155389959859487896366390090168799_<147>

Aug 5, 2008 (3rd)

Factorizations of 255...557 were extended to n=205. Exposed composite numbers had passed ECM(B1=250000) 430 times. Unknown prime factors probably have 30 or more digits.

Aug 5, 2008 (2nd)

By Serge Batalov / GMP-ECM
(8·10¹⁷⁹-17)/9 = (8)₁₇₈7_<179> = 3² · 193 · 15809 · 552241 · 1674912378443233_<16> · 3436763031126603253_<19> · C133
C133 = P30 · P103
P30 = 681730178728744701011924498497_<30>
P103 = 1493689791486146713478996194570842049379770863848290072870963693810359525801102136426038074592658672243_<103>
(43·10¹⁸⁷-7)/9 = 4(7)_187<188> = 157 · 167 · 857 · 398681 · 15621247 · 153367745358551_<15> · 38912178926543071_<17> · C137
C137 = P33 · P105
P33 = 563109820432391065038572286966239_<33>
P105 = 101595641665225801482855126843463077933095944176748411552258185690480521896642701682667226673118857591243_<105>
(67·10¹⁷⁹+23)/9 = 7(4)₁₇₈7_<180> = 3 · 11 · 127721089 · 12689264677_<11> · 11278525964270232939888763_<26> · C136
C136 = P31 · P105
P31 = 1503577311371110536299145909067_<31>
P105 = 820807237203065576049616360230827773873672515282532295733748443458210584183593438540403638917367057872443_<105>
(10¹⁸¹+11)/3 = (3)₁₈₀7_<181> = 7 · 17 · 37426643 · 314567063 · 5853728102221_<13> · 954343568843543_<15> · C135
C135 = P30 · P33 · P74
P30 = 105981447101665873606353102413_<30>
P33 = 173528881158073536221773584328933_<33>
P74 = 23157877513186904238703485740025834562034755077344962107936455349631017881_<74>

Aug 5, 2008

By matsui / GGNFS
(2·10¹⁸⁵+1)/3 = (6)₁₈₄7_<185> = 21143 · C181
C181 = P81 · P100
P81 = 900453601285265582520047067012732576071069650788340131680486043607858213615331267_<81>
P100 = 3501714962000928317461759364309288753778079923142299914269367242522743703784043573496181765706887407_<100>

N=3153131848208232827255671695911964558798026139463021646250137949518359110186192435636696148449447413643601507197023443535291428211070645919059105456494663324346907565939869775654669 ( 181 digits) SNFS difficulty: 185 digits. Divisors found: r1=900453601285265582520047067012732576071069650788340131680486043607858213615331267 (pp81) r2=3501714962000928317461759364309288753778079923142299914269367242522743703784043573496181765706887407 (pp100) Version: GGNFS-0.77.1-20060513-pentium-m Total time: 298.03 hours. Scaled time: 848.78 units (timescale=2.848). Factorization parameters were as follows: n: 3153131848208232827255671695911964558798026139463021646250137949518359110186192435636696148449447413643601507197023443535291428211070645919059105456494663324346907565939869775654669 m: 10000000000000000000000000000000000000 c5: 2 c0: 1 skew: 0.87 type: snfs Factor base limits: 7400000/7400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [3700000, 10800001) Primes: RFBsize:501962, AFBsize:501936, largePrimes:6574782 encountered Relations: rels:7037035, finalFF:1136338 Max relations in full relation-set: 28 Initial matrix: 1003963 x 1136338 with sparse part having weight 79195228. Pruned matrix : 896127 x 901210 with weight 62006881. Total sieving time: 291.34 hours. Total relation processing time: 0.13 hours. Matrix solve time: 6.33 hours. Time per square root: 0.22 hours. Prototype def-par.txt line would be: snfs,185,5,0,0,0,0,0,0,0,0,7400000,7400000,27,27,48,48,2.6,2.6,100000 total time: 298.03 hours.

Aug 4, 2008 (3rd)

By Robert Backstrom / GMP-ECM, GGNFS, Msieve
(23·10¹⁶⁴-41)/9 = 2(5)₁₆₃1_<165> = 17 · 14783 · 6954611 · C153
C153 = P39 · P40 · P75
P39 = 127092897952617830861128387381793123491_<39>
P40 = 5984338350534202483602163442377911766177_<40>
P75 = 192248766671982198740268835298401979782919136451461142361013167032834159033_<75>

GMP-ECM 6.2.1 [powered by GMP 4.2.1] [ECM] Input number is 146218049130642441234495363713913754675210966706539923532522558284754745799883843367386080454093351306607004960263989647786921657401273701595788872021931 (153 digits) Using B1=4366000, B2=8561918830, polynomial Dickson(6), sigma=1627898278 Step 1 took 52484ms Step 2 took 17660ms ********** Factor found in step 2: 5984338350534202483602163442377911766177 Found probable prime factor of 40 digits: 5984338350534202483602163442377911766177 Composite cofactor 24433452884158869463121391219856044588647399397141519895148690044715795722505127594463645181432631902409302144203 has 113 digits Number: n N=24433452884158869463121391219856044588647399397141519895148690044715795722505127594463645181432631902409302144203 ( 113 digits) Divisors found: Mon Aug 4 22:19:36 2008 prp39 factor: 127092897952617830861128387381793123491 Mon Aug 4 22:19:36 2008 prp75 factor: 192248766671982198740268835298401979782919136451461142361013167032834159033 Mon Aug 4 22:19:36 2008 elapsed time 00:39:09 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 21.39 hours. Scaled time: 17.93 units (timescale=0.838). Factorization parameters were as follows: name: KA_2_5_163_1 n: 24433452884158869463121391219856044588647399397141519895148690044715795722505127594463645181432631902409302144203 skew: 22181.66 # norm 3.00e+15 c5: 92520 c4: -6744153222 c3: -45832076939516 c2: 3355354381773925699 c1: 26376496291199123709754 c0: 55897100324407256183969376 # alpha -5.88 Y1: 32923335533 Y0: -3050351678222518898863 # Murphy_E 7.42e-10 # M 24431814637208274680734783426277441947002447691196750391363360992421760360967572735589642666701638520266722683606 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 3500000/3500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved special-q in [100000, 1500001) Primes: RFBsize:250150, AFBsize:249815, largePrimes:6780508 encountered Relations: rels:6430342, finalFF:544879 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 21.19 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 21.39 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).

(2·10¹⁹¹+61)/9 = (2)₁₉₀9_<191> = 17 · C190
C190 = P35 · C156
P35 = 10852771508056059135206234116514171_<35>
C156 = [120447531905866413108914601272250048343140105606651999784883636087529705448811959016585189877632383393661040361642471439530256902961775524681574643452982847_<156>]

Aug 4, 2008 (2nd)

By Serge Batalov / GMP-ECM, pol51, Msieve
(43·10¹⁹³-7)/9 = 4(7)_193<194> = 919 · 445461301538551_<15> · 893558958002816352193_<21> · 4284288203992414224517391893_<28> · C128
C128 = P33 · P96
P33 = 150826515975256399552220025155339_<33>
P96 = 202125386244925252749734893061275680905056146225460546218343135651883483612166284107990237484503_<96>
(10¹⁸⁴+71)/9 = (1)₁₈₃9_<184> = 3 · 29 · 199 · 1697 · 919179139 · 1299592780666421554668910151_<28> · 9343168720031962523222369884197334253_<37> · C103
C103 = P40 · P64
P40 = 1586931314118813407557567732512708559877_<40>
P64 = 2135224521200188890616493683567821754642212756737532735710790131_<64>

Number: 11119_184 N=3388454655366929914498505057165802657142065274822407340167831244985945664751645516070076150034794173887 ( 103 digits) Divisors found: r1=1586931314118813407557567732512708559877 r2=2135224521200188890616493683567821754642212756737532735710790131 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.316). Factorization parameters were as follows: name: 11119_184 n: 3388454655366929914498505057165802657142065274822407340167831244985945664751645516070076150034794173887 skew: 31960.24 # norm 9.10e+13 c5: 480 c4: -138581412 c3: -2970890933000 c2: 125334112112828449 c1: 728602337992886243758 c0: -14786800388206937397895095 # alpha -5.22 Y1: 7082309663 Y0: -93272580525981859492 # Murphy_E 2.34e-09 # M 3088295724384864144699871818544359448147530931965530510173465076385594779988601548584947108074515787463 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1850001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 273090 x 273338 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 5.90 hours.

(16·10¹⁹⁹-43)/9 = 1(7)₁₉₈3_<200> = 13² · 197 · 41046419 · 3191682259_<10> · 200516406221467309_<18> · C161
C161 = P40 · P56 · P66
P40 = 4390892260316240532684572528091436747139_<40>
P56 = 23900525030689996426582940228851626653088952483784974829_<56>
P66 = 193695479051958499150090176237277153417415656132662983103787245979_<66>

# first ECM # Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1416775493 Step 1 took 24354ms Step 2 took 19253ms ********** Factor found in step 2: 4390892260316240532684572528091436747139 Found probable prime factor of 40 digits: 4390892260316240532684572528091436747139 Composite cofactor 4629423645412823967849086103516114227366096388384060554523226454110605387301721011151681397173112326997089098521746462591 has 121 digits # # then Msieve-1.36/gnfs-121 # Number: 17773_199 N=4629423645412823967849086103516114227366096388384060554523226454110605387301721011151681397173112326997089098521746462591 ( 121 digits) Divisors found: r1=23900525030689996426582940228851626653088952483784974829 r2=193695479051958499150090176237277153417415656132662983103787245979 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.299). Factorization parameters were as follows: name: 17773_199 n: 4629423645412823967849086103516114227366096388384060554523226454110605387301721011151681397173112326997089098521746462591 skew: 43909.78 # norm 6.12e+16 c5: 13800 c4: 29054540302 c3: -1619554790749659 c2: -70244931498683416923 c1: 55355974140314250897651 c0: 1392762997799671933665557405 # alpha -5.70 Y1: 9197936842171 Y0: -201892988572876655833536 # Murphy_E 2.30e-10 # M 4486796550059614013416217299982389050995435682256387198880252966082610771759153383949597551122257473790454129900955193894 type: gnfs rlim: 5000000 alim: 5000000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5000000/5000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2500000, 9500001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 830699 x 830947 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,120,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5000000,5000000,27,27,50,50,2.5,2.5,100000 total time: 2.5 days

(16·10²¹⁴-61)/9 = 1(7)₂₁₃1_<215> = 13 · 863 · 18661 · 369819256019_<12> · 584833068852155422531_<21> · 4516565897012282883697690057920883_<34> · C140
C140 = P53 · P88
P53 = 16814750565378686502204377710527501824320586545945603_<53>
P88 = 5169733908173540534007921788791377675334362229095173255753307146459503895142109161685829_<88>

# gnfs,140 # pol51 polynomial selection time: 2 or 3 days (while ECM was run for a week or two) # Number: 17771_214 N=86927786155318407263273710266523202940690097929584601977940218641236715258445415008714444666356629075405450626239173034367866144188409959887 ( 140 digits) Divisors found: r1=16814750565378686502204377710527501824320586545945603 r2=5169733908173540534007921788791377675334362229095173255753307146459503895142109161685829 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.735). Factorization parameters were as follows: name: 17771_214 n: 86927786155318407263273710266523202940690097929584601977940218641236715258445415008714444666356629075405450626239173034367866144188409959887 skew: 267143.89 # norm 1.97e+19 c5: 698880 c4: -1489690686532 c3: -176616113976832028 c2: 103006324549653347616719 c1: 3712851734270791622017222272 c0: -432658741100514020527612440105864 # alpha -6.29 Y1: 13968147388773457 Y0: -659105787539946137530863055 # Murphy_E 1.94e-11 # M 49579079600743972072443184556436418407617530021357634358500716158197635856463288739352084719618552259657530257163309696054721363836328031333 type: gnfs rlim: 12000000 alim: 12000000 lpbr: 27 lpba: 27 mfbr: 54 mfba: 54 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 12000000/12000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 54/54 Sieved rational special-q in [6000000, 37700001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 16715895 relations #### (beware of huge redundancy! up to 25-30% in the end) 12175171 unique relations and about 10717437 large ideals Max relations in full relation-set: 20 Initial matrix: Pruned matrix : 2296340 x 2296588 (this one, Lanczos = 31hrs) Pruned matrix : 1881104 x 1881352 (with most oversieving, Lanczos = 15hrs, -> ...Sun Aug 3 03:17:51 2008 lanczos error: only trivial dependencies found !! tried twice) Pruned matrix : 2052464 x 2052685 (alternative run with oversieving and pruning, Lanczos = 19hrs, still running for studying purposes) Total sieving time: 17 days Total relation processing time: 2.00 hours. Matrix solve time: 31.00 hours. Time per square root: 1.60 hours. * 3 deps Prototype def-par.txt line would be: gnfs,139,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,12000000,12000000,27,27,54,54,2.6,2.6,100000 total time: 19 days # in retrospect, obervations - rlim/alim should be higher still # 28 bit would have been probably better in terms of redundancy of sieving

Note: C140 is the largest composite number factored by GNFS so far in our tables.

Aug 4, 2008

By Tyler Cadigan / Msieve, GGNFS
(5·10¹⁹⁸-11)/3 = 1(6)₁₉₇3_<199> = 17 · 73 · 14417612748337_<14> · 15591863092514077_<17> · 2050925281672230869_<19> · 798492457907659976598191_<24> · C124
C124 = P59 · P65
P59 = 58029655586752866277654340982152770761209260744213665747727_<59>
P65 = 62865872733823391060391929387855942847658010265702276841724324879_<65>

Number: 16663_198 N=3648084942904409231781740133863005618024633980723139006909650256997407933041732927137820715390571584310230633883275803800033 ( 124 digits) Divisors found: r1=58029655586752866277654340982152770761209260744213665747727 r2=62865872733823391060391929387855942847658010265702276841724324879 Version: Total time: 82.43 hours. Scaled time: 205.57 units (timescale=2.494). Factorization parameters were as follows: name: 16663_198 n: 3648084942904409231781740133863005618024633980723139006909650256997407933041732927137820715390571584310230633883275803800033 skew: 212888.11 # norm 1.22e+017 c5: 10740 c4: 7370305606 c3: -2467585952064540 c2: -248933528645380281069 c1: 34811739326102006425315528 c0: 1611754352640371786855945807871 # alpha -5.96 Y1: 22584968622799 Y0: -805768826493317965725508 # Murphy_E 1.69e-010 # M 2314935598007029659498302023408434039733754485237880886588822343019923669131832398564903343895745163314827211213456861106685 type: gnfs rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.5 alambda: 2.5 qintsize: 1000000Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [2700000, 6700001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 715840 x 716088 Total sieving time: 82.43 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,123,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5, total time: 82.43 hours. --------- CPU info (if available) ----------

Aug 3, 2008 (3rd)

By Robert Backstrom / GGNFS, Msieve
(23·10¹⁶⁶-41)/9 = 2(5)₁₆₅1_<167> = 3² · C166
C166 = P72 · P94
P72 = 643496646045034314863036088356290602835699348302317420935391877062800651_<72>
P94 = 4412620003991111484688047460906035814232134281081696744784440167395589300355555901131709979989_<94>

Number: n N=2839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839 ( 166 digits) SNFS difficulty: 167 digits. Divisors found: Sun Aug 3 15:17:18 2008 prp72 factor: 643496646045034314863036088356290602835699348302317420935391877062800651 Sun Aug 3 15:17:18 2008 prp94 factor: 4412620003991111484688047460906035814232134281081696744784440167395589300355555901131709979989 Sun Aug 3 15:17:18 2008 elapsed time 01:27:42 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 88.42 hours. Scaled time: 74.18 units (timescale=0.839). Factorization parameters were as follows: name: KA_2_5_165_1 n: 2839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839506172839 type: snfs deg: 5 c5: 230 c0: -41 skew: 0.71 m: 1000000000000000000000000000000000 rlim: 5800000 alim: 5800000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5800000/5800000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 4600001) Primes: RFBsize:399993, AFBsize:399420, largePrimes:5834136 encountered Relations: rels:5996928, finalFF:828084 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 88.21 hours. Total relation processing time: 0.21 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,167,5,0,0,0,0,0,0,0,0,5800000,5800000,27,27,48,48,2.5,2.5,100000 total time: 88.42 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).

Aug 3, 2008 (2nd)

By suberi / GMP-ECM
(46·10¹⁶⁷-1)/9 = 5(1)_167<168> = 70626533 · 213771611 · 38387318408683_<14> · C138
C138 = P41 · P98
P41 = 10652708041146778174216248100844005311463_<41>
P98 = 82784609590842840754482542867744143167470530984746443938052838133532893663609041186948295276030693_<98>
(46·10¹⁷⁴-1)/9 = 5(1)_174<175> = 35159 · 58943237 · 1746625507597_<13> · C151
C151 = P30 · C121
P30 = 248922781670497343680620477691_<30>
C121 = [5672576765062949804877898588549304541456787458112679112216952341251445580533290906546230462728475408918734991394065086371_<121>]

Aug 3, 2008

By Serge Batalov / GMP-ECM, Msieve, pol51
(4·10¹⁹⁰+23)/9 = (4)₁₈₉7_<190> = 9569335559270336914133_<22> · 2204456588025119545885777787_<28> · C141
C141 = P33 · P108
P33 = 914614705542996095283314411688089_<33>
P108 = 230354111071823462818299073248460216708575614431593821351666507826249002338559777821243718681313328757074913_<108>
3·10¹⁸¹-7 = 2(9)₁₈₀3_<182> = 1936760724982998289_<19> · 68808646991249141025719_<23> · C141
C141 = P37 · P105
P37 = 1724512309637715528857993530467193207_<37>
P105 = 130537703533059377398780785440600547165396660129485394210598345885209061956376547057033455498259978403289_<105>
(16·10¹⁹⁶+11)/9 = 1(7)₁₉₅9_<197> = 10099 · 160006301767452572991787889_<27> · 888035983002108169065398017_<27> · C140
C140 = P31 · P53 · P57
P31 = 4803801617306383518347006989561_<31>
P53 = 14715761835396161314812187666323650894319358275041849_<53>
P57 = 175252263317018383575140193534337967914768654073004843553_<57>
(22·10¹⁸¹+41)/9 = 2(4)₁₈₀9_<182> = 23897095845197_<14> · 776272617318286786491553225607_<30> · C139
C139 = P34 · P36 · P69
P34 = 1769770208978296859658331890070637_<34>
P36 = 894919377524823262965410505209487619_<36>
P69 = 831993602705134771540965249704583123198561362548116161848843063999477_<69>

#ecm: # Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=1689418823 Step 1 took 18414ms Step 2 took 16307ms ********** Factor found in step 2: 894919377524823262965410505209487619 Found probable prime factor of 36 digits: 894919377524823262965410505209487619 Composite cofactor 1472437492128072456080341721656210925078116385346784875563765316598223832211646356703426379933261056849 has 103 digits # #then pol51, and Msieve/gnfs-103 # Number: 24449_181 N=1472437492128072456080341721656210925078116385346784875563765316598223832211646356703426379933261056849 ( 103 digits) Divisors found: r1=1769770208978296859658331890070637 r2=831993602705134771540965249704583123198561362548116161848843063999477 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.725). Factorization parameters were as follows: name: 24449_181 n: 1472437492128072456080341721656210925078116385346784875563765316598223832211646356703426379933261056849 skew: 12109.92 # norm 1.11e+14 c5: 13800 c4: 229021120 c3: -5546394553982 c2: 39015717440707647 c1: 265001117184500868642 c0: -1409292541606116852827712 # alpha -5.56 Y1: 57257448043 Y0: -40330119583764690079 # Murphy_E 2.48e-09 # M 555219686948494539915267439001639650635907604410780913489476571794940846402885098730478554425179319560 type: gnfs rlim: 2300000 alim: 2300000 lpbr: 26 lpba: 26 mfbr: 49 mfba: 49 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor base limits: 2300000/2300000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 49/49 Sieved algebraic special-q in [1150000, 1850001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 231148 x 231396 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,102,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,2300000,2300000,26,26,49,49,2.6,2.6,100000 total time: 4.50 hours.

(23·10¹⁸⁵+1)/3 = 7(6)₁₈₄7_<186> = 11 · 409 · 3919 · 9019884346492579823_<19> · 81540614634217442591_<20> · C140
C140 = P33 · P108
P33 = 334871162855198257095061908037933_<33>
P108 = 176547927865901998870134175492592669582800548196356188701886100127196219234273530578226419288591470033352403_<108>
(10¹⁸⁴+71)/9 = (1)₁₈₃9_<184> = 3 · 29 · 199 · 1697 · 919179139 · 1299592780666421554668910151_<28> · C140
C140 = P37 · C103
P37 = 9343168720031962523222369884197334253_<37>
C103 = [3388454655366929914498505057165802657142065274822407340167831244985945664751645516070076150034794173887_<103>]
6·10¹⁸⁹+1 = 6(0)₁₈₈1_<190> = 42589 · 5780291335866737_<16> · 107788304148617970061487122159_<30> · C141
C141 = P30 · P41 · P71
P30 = 174013302696433020274845304681_<30>
P41 = 18309085696764041534162136664724986762411_<41>
P71 = 70971393580825121102733841341176453634821357709829428898091709401554553_<71>

Using B1=3000000, B2=14267859070, polynomial Dickson(12), sigma=2803236752 Step 1 took 20722ms Step 2 took 16429ms ********** Factor found in step 2: 174013302696433020274845304681 Found probable prime factor of 30 digits: 174013302696433020274845304681 Composite cofactor 1299421327090096537092650364554015119148292501873377738981166234391431318448786187635106425292624877709866307283 has 112 digits # # then Msieve/gnfs-112 # Number: 60001_189 N=1299421327090096537092650364554015119148292501873377738981166234391431318448786187635106425292624877709866307283 ( 112 digits) Divisors found: r1=18309085696764041534162136664724986762411 r2=70971393580825121102733841341176453634821357709829428898091709401554553 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.188). Factorization parameters were as follows: name: 60001_189 n: 1299421327090096537092650364554015119148292501873377738981166234391431318448786187635106425292624877709866307283 skew: 52578.04 # norm 2.72e+15 c5: 16440 c4: 1619746172 c3: -135511103262470 c2: -4014692173401370183 c1: 183805157963031787936530 c0: 1031049847200277256970651600 # alpha -5.96 Y1: 828435965947 Y0: -2396440646982282764377 # Murphy_E 7.97e-10 # M 1136488550539358265641494014969627028960530201153737973603644946454438107607609201185415837558953909792296923205 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor 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, 3550001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 437477 x 437725 Total sieving time: 0.00 hours. Total relation processing time: 0.00 hours. Matrix solve time: 0.00 hours. Time per square root: 0.00 hours. Prototype def-par.txt line would be: gnfs,111,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 16.0 hours.

Aug 2, 2008 (3rd)

By Serge Batalov / GMP-ECM
(23·10¹⁹⁴+1)/3 = 7(6)₁₉₃7_<195> = 13 · 139 · 78459255911_<11> · 234102535388474561689151_<24> · C158
C158 = P32 · C126
P32 = 28755254470177769678351594744207_<32>
C126 = [803305815778793560119943241710039446370201891384089344299540163842961294333911367771016525950573017814190338673989871897500803_<126>]
(5·10¹⁹⁸-23)/9 = (5)₁₉₇3_<198> = 79 · 1787 · 92166227 · 62964716122813547478189355909_<29> · C156
C156 = P33 · C124
P33 = 119356565544646731891786102577789_<33>
C124 = [5681466871324695058688910174023721450274408912155790860885985665340075745372042729625565314195995410292414361378012735405343_<124>]
(43·10¹⁹³-7)/9 = 4(7)_193<194> = 919 · 445461301538551_<15> · 893558958002816352193_<21> · C156
C156 = P28 · C128
P28 = 4284288203992414224517391893_<28>
C128 = [30485867797475088755064300991906426987241836546815788111296849337158228409230973644957546968604924308437984135196279273180211517_<128>]

Aug 2, 2008 (2nd)

By Sinkiti Sibata / GGNFS
(23·10¹⁵⁴-41)/9 = 2(5)₁₅₃1_<155> = 3 · 91411 · 125717 · 99479243282099_<14> · C130
C130 = P33 · P47 · P51
P33 = 340181494077011694290357817506041_<33>
P47 = 69952169448817622365476237996541279017803003027_<47>
P51 = 313131860083472179775867830221927950460921636582587_<51>

Number: 25551_154 N=7451421490539368400745666140791923586210703006310976378376855205625717878891916365540177939686299220679430926588394932343158718809 ( 130 digits) SNFS difficulty: 156 digits. Divisors found: r1=340181494077011694290357817506041 (pp33) r2=69952169448817622365476237996541279017803003027 (pp47) r3=313131860083472179775867830221927950460921636582587 (pp51) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 57.77 hours. Scaled time: 27.27 units (timescale=0.472). Factorization parameters were as follows: name: 25551_154 n: 7451421490539368400745666140791923586210703006310976378376855205625717878891916365540177939686299220679430926588394932343158718809 m: 10000000000000000000000000000000 c5: 23 c0: -410 skew: 1.78 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3000001) Primes: RFBsize:216816, AFBsize:216777, largePrimes:5650674 encountered Relations: rels:5572838, finalFF:509244 Max relations in full relation-set: 28 Initial matrix: 433658 x 509244 with sparse part having weight 42472284. Pruned matrix : 400314 x 402546 with weight 29842667. Total sieving time: 51.37 hours. Total relation processing time: 0.28 hours. Matrix solve time: 5.99 hours. Time per square root: 0.13 hours. Prototype def-par.txt line would be: snfs,156,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 57.77 hours. --------- CPU info (if available) ----------

(23·10¹⁷⁹-41)/9 = 2(5)₁₇₈1_<180> = 311 · 605993 · 9486007 · 14509530323_<11> · 29282668291_<11> · 62155026673_<11> · 348398479188686501_<18> · C116
C116 = P55 · P61
P55 = 4498980788192811699189568905957540794386101261910526893_<55>
P61 = 3453371022627095076155775850110344684731257028691845350307583_<61>

Number: 25551_179 N=15536649885301064370678981856573830216220820743461352404945988973856041528897128938405796842530844335414223143329619 ( 116 digits) Divisors found: r1=4498980788192811699189568905957540794386101261910526893 (pp55) r2=3453371022627095076155775850110344684731257028691845350307583 (pp61) Version: GGNFS-0.77.1-20050930-nocona Total time: 47.90 hours. Scaled time: 36.41 units (timescale=0.760). Factorization parameters were as follows: name: 25551_179 n: 15536649885301064370678981856573830216220820743461352404945988973856041528897128938405796842530844335414223143329619 skew: 29412.77 # norm 3.98e+15 c5: 13440 c4: 7304861420 c3: -37829521335628 c2: -4586753777585773893 c1: 32509909704735860085894 c0: 381949982671101480999382968 # alpha -5.47 Y1: 523520788439 Y0: -16315113794246774390069 # Murphy_E 4.96e-10 # M 2833285247338597467203869810197414061555862670509082923762924242923193033919568095952457100773799659651415061182693 type: gnfs rlim: 4500000 alim: 4500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.4 alambda: 2.4 qintsize: 60000 Factor base limits: 4500000/4500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 50/50 Sieved algebraic special-q in [2250000, 3630001) Primes: RFBsize:315948, AFBsize:316793, largePrimes:7713552 encountered Relations: rels:7941927, finalFF:902430 Max relations in full relation-set: 28 Initial matrix: 632821 x 902430 with sparse part having weight 72590726. Pruned matrix : 404955 x 408183 with weight 39044189. Total sieving time: 45.03 hours. Total relation processing time: 0.38 hours. Matrix solve time: 2.20 hours. Time per square root: 0.30 hours. Prototype def-par.txt line would be: gnfs,115,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,4500000,4500000,27,27,50,50,2.4,2.4,60000 total time: 47.90 hours. --------- CPU info (if available) ----------

Aug 2, 2008

By Robert Backstrom / GMP-ECM
(23·10¹⁶⁹-41)/9 = 2(5)₁₆₈1_<170> = 3 · 7 · 19 · C167
C167 = P38 · P129
P38 = 99115019415880121677092502404222247027_<38>
P129 = 646208937806761842825739606924013230081780096425955573149216008366271383509656353669041781599017902484058310271913115315734810187_<129>

Aug 1, 2008 (6th)

By Robert Backstrom / GGNFS, Msieve
(82·10¹⁸⁷-1)/9 = 9(1)_187<188> = 7 · 13 · C187
C187 = P73 · P114
P73 = 3026480116245698243462872523183807295562073549268169183952528712774717527_<73>
P114 = 330820280578284578811104218819679244326107204280567814363792995482310812487533307731049138903576211787733292120323_<114>

Number: n N=1001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221 ( 187 digits) SNFS difficulty: 188 digits. Divisors found: Fri Aug 01 22:10:03 2008 prp73 factor: 3026480116245698243462872523183807295562073549268169183952528712774717527 Fri Aug 01 22:10:03 2008 prp114 factor: 330820280578284578811104218819679244326107204280567814363792995482310812487533307731049138903576211787733292120323 Fri Aug 01 22:10:03 2008 elapsed time 06:58:34 (Msieve 1.36) Version: GGNFS-0.77.1-20051202-athlon Total time: 125.80 hours. Scaled time: 258.01 units (timescale=2.051). Factorization parameters were as follows: name: KA_9_1_187 n: 1001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221001221 type: snfs skew: 0.16 deg: 5 c5: 8200 c0: -1 m: 10000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 9300001) Primes: RFBsize:602489, AFBsize:603036, largePrimes:10948587 encountered Relations: rels:10948800, finalFF:1233699 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 125.35 hours. Total relation processing time: 0.45 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,188,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000 total time: 125.80 hours. --------- CPU info (if available) ----------

Aug 1, 2008 (5th)

By Serge Batalov / Msieve
(22·10²⁰⁰-31)/9 = 2(4)₁₉₉1_<201> = C201
C201 = P53 · P70 · P79
P53 = 47713862744287860379304252114030623412334743979315223_<53>
P70 = 2395392072792774623211423837351600973074529935809359597689484971362983_<70>
P79 = 2138744897728437264421864974178897354836969223259709418858727405909337720973849_<79>

# ok, dudes! If there's a thing called a nice split, # there must be a thing called an ugly split. Well, it's OK. # Doing a full 43M ECM wouldn't have helped -- # SNFS-201 is easier than GNFS-149 # # C201 = P53 . P70 . P79 (no smaller factors!) # # plain SNFS, 29-bit LPs, 1 CPU, 2Gb of memory, 23 days # Number: 24441_200 N=244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441 ( 201 digits) SNFS difficulty: 201 digits. Divisors found: r1=47713862744287860379304252114030623412334743979315223 r2=2395392072792774623211423837351600973074529935809359597689484971362983 r3=2138744897728437264421864974178897354836969223259709418858727405909337720973849 Version: Msieve 1.36 Total time: 23 days Scaled time: ? units (timescale=2.738). Factorization parameters were as follows: n: 244444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444444441 name: 24441_200 #res: 1872 Y0: -10000000000000000000000000000000000000000 Y1: 1 c5: 22 c0: -31 skew: 1.07 type: snfs lpbr: 29 lpba: 29 mfbr: 57 mfba: 57 rlambda: 2.5 alambda: 2.5 rlim: 16000000 alim: 16000000 Factor base limits: 16000000/16000000 Large primes per side: 3 Large prime bits: 29/29 Max factor residue bits: 57/57 Sieved rational special-q in [8000000, 16900001) Relations: 40323955 relations 37001703 unique relations and about 33452936 large ideals Max relations in full relation-set: 20 Initial matrix: 3454542 x 3455788 (1045.7 MB) with weight 328806948 (95.15/col) sparse part has weight 236099120 (68.32/col) Pruned matrix : 3395676 x 3395924 (991.3 MB) with weight 250430313 (73.74/col) sparse part has weight 225898752 (66.52/col) Total sieving time: exactly 20 days on 1cpu. Total relation processing time: 2.00 hours. Matrix solve time: 67.50 hours. (a bit under 3 days) Time per square root: 1.11 hours. Times 5. (One Newton failed to converge.) elapsed time 05:35:31 Prototype def-par.txt line would be: snfs,201,5,0,0,0,0,0,0,0,0,16000000,16000000,29,29,57,57,2.5,2.5,100000 total time: 23 days.

Aug 1, 2008 (4th)

By Serge Batalov / GMP-ECM
(5·10¹⁹⁸-23)/9 = (5)₁₉₇3_<198> = 79 · 1787 · 92166227 · C185
C185 = P29 · C156
P29 = 62964716122813547478189355909_<29>
C156 = [678120373017004965696027723355266137898901427492400737189655707913532453650073593892558088509716301805095025038393270924775790361244152143461824320103726627_<156>]
(8·10²⁰⁰+7)/3 = 2(6)₁₉₉9_<201> = 10181399 · 126355837 · 36206518457_<11> · 28184782664921_<14> · C162
C162 = P30 · P132
P30 = 697368348053808161867372475367_<30>
P132 = 291274374180553751645366386448159892837438428245940571965196990275330307174828818699791027080461993416672152709678515211741667562337_<132>

Aug 1, 2008 (3rd)

By Sinkiti Sibata / GGNFS, GMP-ECM
(23·10¹⁵⁶-41)/9 = 2(5)₁₅₅1_<157> = 109 · 1949 · 615887 · 79671967 · C138
C138 = P60 · P78
P60 = 568072473549876077847951681943235841700911865100362592901083_<60>
P78 = 431555511214783572160697906549520112228842379475734051031125209152188991775173_<78>

Number: 25551_156 N=245154806729863389877554529829728473478831042552701224896737949891351647068415901547655165076105391748463107205434374654549956804164212359 ( 138 digits) SNFS difficulty: 157 digits. Divisors found: r1=568072473549876077847951681943235841700911865100362592901083 (pp60) r2=431555511214783572160697906549520112228842379475734051031125209152188991775173 (pp78) Version: GGNFS-0.77.1-20050930-nocona Total time: 60.42 hours. Scaled time: 46.29 units (timescale=0.766). Factorization parameters were as follows: name: 25551_156 n: 245154806729863389877554529829728473478831042552701224896737949891351647068415901547655165076105391748463107205434374654549956804164212359 m: 10000000000000000000000000000000 c5: 230 c0: -41 skew: 0.71 type: snfs Factor base limits: 3000000/3000000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved algebraic special-q in [1500000, 3600001) Primes: RFBsize:216816, AFBsize:216312, largePrimes:5870783 encountered Relations: rels:5897251, finalFF:541008 Max relations in full relation-set: 28 Initial matrix: 433195 x 541008 with sparse part having weight 56507710. Pruned matrix : 387613 x 389842 with weight 39426318. Total sieving time: 57.85 hours. Total relation processing time: 0.21 hours. Matrix solve time: 2.25 hours. Time per square root: 0.12 hours. Prototype def-par.txt line would be: snfs,157,5,0,0,0,0,0,0,0,0,3000000,3000000,27,27,48,48,2.3,2.3,100000 total time: 60.42 hours. --------- CPU info (if available) ----------

8·10²⁰⁶-1 = 7(9)_206<207> = 2844937 · 95500513 · 69076890761242761822409_<23> · C170
C170 = P47 · P124
P47 = 41135749498277498847659154913591669404231513839_<47>
P124 = 1036237806348703114978686943063529149880910428973216429428407074021642801060804673132690587919795720559017683362400311580929_<124>

Factor79991_206 Input number is 42626418822604840172098173334880818320537225294947181741042961592958391680695314798229314971658518580998472053287968986315776968375378540443044665760795283585213031976431 Run 1845 out of 2350: Using B1=3000000, B2=5706890290, polynomial Dickson(6), sigma=1065804300 Step 1 took 66862ms Step 2 took 21278ms ********** Factor found in step 2: 41135749498277498847659154913591669404231513839 Found probable prime factor of 47 digits: 41135749498277498847659154913591669404231513839 Probable prime cofactor 1036237806348703114978686943063529149880910428973216429428407074021642801060804673132690587919795720559017683362400311580929 has 124 digits

Aug 1, 2008 (2nd)

By Robert Backstrom / GGNFS, Msieve
(8·10¹⁸⁶+7)/3 = 2(6)₁₈₅9_<187> = 19 · C186
C186 = P64 · P122
P64 = 9461561365491417751494369249651340254835341510781699493399324537_<64>
P122 = 14833796640042493150323341558774456583384342378431564682298156460186483076837772252833910763261999400743782662308014748023_<122>

Number: n N=140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140351 ( 186 digits) SNFS difficulty: 186 digits. Divisors found: Fri Aug 01 04:57:51 2008 prp64 factor: 9461561365491417751494369249651340254835341510781699493399324537 Fri Aug 01 04:57:51 2008 prp122 factor: 14833796640042493150323341558774456583384342378431564682298156460186483076837772252833910763261999400743782662308014748023 Fri Aug 01 04:57:51 2008 elapsed time 08:20:34 (Msieve 1.36) Version: GGNFS-0.77.1-20060513-athlon-xp Total time: 75.43 hours. Scaled time: 98.52 units (timescale=1.306). Factorization parameters were as follows: name: KA_2_6_185_9 n: 140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140350877192982456140351 type: snfs skew: 0.61 deg: 5 c5: 80 c0: 7 m: 10000000000000000000000000000000000000 rlim: 9000000 alim: 9000000 lpbr: 28 lpba: 28 mfbr: 50 mfba: 50 rlambda: 2.5 alambda: 2.5 qintsize: 50000 Factor base limits: 9000000/9000000 Large primes per side: 3 Large prime bits: 28/28 Max factor residue bits: 50/50 Sieved special-q in [100000, 6350001) Primes: RFBsize:602489, AFBsize:603715, largePrimes:10590638 encountered Relations: rels:10590627, finalFF:1235224 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 74.89 hours. Total relation processing time: 0.54 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,186,5,0,0,0,0,0,0,0,0,9000000,9000000,28,28,50,50,2.5,2.5,100000 total time: 75.43 hours. --------- CPU info (if available) ---------- Cygwin on AMD 64 3200+

(23·10¹⁵⁸-41)/9 = 2(5)₁₅₇1_<159> = 203982161 · C151
C151 = P66 · P85
P66 = 171689635527179533850177211158120096687991880816145824295203094123_<66>
P85 = 7297079191886613832743568747111087572188527660082593836965018158316475096972563946317_<85>

Number: n N=1252832866867978497176307273044114654494495504219879088130434874427845460248632014225771221021408610116428541785845457120907526592757077201253670194991 ( 151 digits) SNFS difficulty: 159 digits. Divisors found: Fri Aug 1 10:14:11 2008 prp66 factor: 171689635527179533850177211158120096687991880816145824295203094123 Fri Aug 1 10:14:11 2008 prp85 factor: 7297079191886613832743568747111087572188527660082593836965018158316475096972563946317 Fri Aug 1 10:14:11 2008 elapsed time 00:58:14 (Msieve 1.36) Version: GGNFS-0.77.1-20050930-k8 Total time: 35.26 hours. Scaled time: 29.51 units (timescale=0.837). Factorization parameters were as follows: name: KA_2_5_157_1 n: 1252832866867978497176307273044114654494495504219879088130434874427845460248632014225771221021408610116428541785845457120907526592757077201253670194991 type: snfs deg: 5 c5: 23000 c0: -41 skew: 0.28 m: 10000000000000000000000000000000 rlim: 5500000 alim: 5500000 lbpr: 28 lbpa: 28 mbpr: 48 mbpa: 48 rlambda: 2.5 alambda: 2.5 qintsize: 100000 Factor base limits: 5500000/5500000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 48/48 Sieved special-q in [100000, 2100001) Primes: RFBsize:380800, AFBsize:381098, largePrimes:5429667 encountered Relations: rels:5543974, finalFF:780100 Max relations in full relation-set: 28 Initial matrix: Pruned matrix : Total sieving time: 35.09 hours. Total relation processing time: 0.17 hours. Matrix solve time: 0.00 hours. Total square root time: 0.00 hours, sqrts: 0. Prototype def-par.txt line would be: snfs,159,5,0,0,0,0,0,0,0,0,5500000,5500000,27,27,48,48,2.5,2.5,100000 total time: 35.26 hours. --------- CPU info (if available) ---------- CPU0: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 CPU1: AMD Athlon(tm) 64 X2 Dual Core Processor 6000+ stepping 03 Memory: 2074672k/2097088k available (2382k kernel code, 21604k reserved, 681k data, 296k init, 1179584k highmem, 0k BadRAM) Calibrating delay loop... 5963.77 BogoMIPS (lpj=2981888) Calibrating delay loop... 6045.69 BogoMIPS (lpj=3022848) Total of 2 processors activated (12009.47 BogoMIPS).

Aug 1, 2008

By Tyler Cadigan / Msieve, GGNFS
(10¹⁹⁸+53)/9 = (1)₁₉₇7_<198> = 3 · 11618966467_<11> · 272033009875993867_<18> · 30874217309083734095351287845727_<32> · C138
C138 = P49 · P89
P49 = 9453997590293827952520076434647256044623334210059_<49>
P89 = 40145390515984245549625564941684431539990421548183675478964571944721581807941671195434707_<89>

Number: 11117_198 N=379534425199519751802558862062259553534112280564965144585212678040651849592463853984445240166695146589693057988042923980473715294957117713 ( 138 digits) Divisors found: r1=9453997590293827952520076434647256044623334210059 r2=40145390515984245549625564941684431539990421548183675478964571944721581807941671195434707 Version: Total time: 621.18 hours. Scaled time: 1600.17 units (timescale=2.576). Factorization parameters were as follows: name: 11117_198 n: 379534425199519751802558862062259553534112280564965144585212678040651849592463853984445240166695146589693057988042923980473715294957117713 skew: 113421.69 # norm 6.07e+018 c5: 4597020 c4: 112946341846 c3: -142581740199761914 c2: 9306396615802705483023 c1: 924174800200196017988522392 c0: -13806708124835709986443831217980 # alpha -5.94 Y1: 6237782020208299 Y0: -152529859043766825334703079 # Murphy_E 2.62e-011 # M 105204987891615758404166717436433383277087204802518042147842137078868339598661102665100403548164843043068382038692909504027948782527384386 type: gnfs rlim: 5400000 alim: 5400000 lpbr: 27 lpba: 27 mfbr: 51 mfba: 51 rlambda: 2.5 alambda: 2.5 qintsize: 1000000Factor base limits: 5400000/5400000 Large primes per side: 3 Large prime bits: 27/27 Max factor residue bits: 51/51 Sieved algebraic special-q in [2700000, 13700001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: relations Max relations in full relation-set: Initial matrix: Pruned matrix : 1309332 x 1309580 Total sieving time: 621.18 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: gnfs,137,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,5400000,5400000,27,27,51,51,2.5,2.5, total time: 621.18 hours. --------- CPU info (if available) ----------

Jul 31, 2008

By Serge Batalov / pol51, Msieve
(23·10¹⁸⁸-41)/9 = 2(5)₁₈₇1_<189> = 43 · 683 · 1123 · 11003 · 129491 · 13776430890486919_<17> · 1998967854737700046309_<22> · 4118359186990383026851_<22> · C113
C113 = P44 · P69
P44 = 65615481280730819870909029109781563549335597_<44>
P69 = 730790082739108945520358150329693309160286713343015176689118525792073_<69>

Number: 25551_188 N=47951142994111730052600594373683969756210565578842353767390601851826733211778758756378457047403995719847319322581 ( 113 digits) Divisors found: r1=65615481280730819870909029109781563549335597 r2=730790082739108945520358150329693309160286713343015176689118525792073 Version: Total time: 0.00 hours. Scaled time: 0.00 units (timescale=2.315). Factorization parameters were as follows: name: 25551_188 n: 47951142994111730052600594373683969756210565578842353767390601851826733211778758756378457047403995719847319322581 skew: 39942.85 # norm 4.55e+15 c5: 34440 c4: 33787766 c3: -289153465319201 c2: 86740494851837328 c1: 170200457961466906677222 c0: 1225255008348063687936417840 # alpha -6.30 Y1: 624020572153 Y0: -4253506998509198027219 # Murphy_E 7.21e-10 # M 13308855079719020252483670510147535496065937586070006992997317244223463936867911346371720820664892712291005385604 type: gnfs rlim: 3500000 alim: 3500000 lpbr: 27 lpba: 27 mfbr: 50 mfba: 50 rlambda: 2.6 alambda: 2.6 qintsize: 100000 Factor 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, 3650001) Primes: rational ideals filtering, algebraic ideals filtering, Relations: 7790604 relations (7008594 unique relations and about 7083638 large ideals) Max relations in full relation-set: 20 Initial matrix: 486909 x 487115 (149.7 MB) with weight 49914063 (102.47/col) Pruned matrix : 484228 x 484476 Total sieving time: 12.00 hours. Total relation processing time: 00:06:58 Matrix solve time: 01:06:27 Time per square root: 00:14:26 Prototype def-par.txt line would be: gnfs,112,5,maxs1,maxskew,goodScore,efrac,j0,j1,eStepSize,maxTime,3500000,3500000,27,27,50,50,2.6,2.6,100000 total time: 13.6 hours.

Jul 30, 2008

By Sinkiti Sibata / GMP-ECM, GGNFS
8·10²⁰³-1 = 7(9)_203<204> = 139 · 661 · 691 · 221101 · 7609211 · 8030409029_<10> · 58953836021010431_<17> · C158
C158 = P35 · P123
P35 = 15964735925805978713074497549589901_<35>
P123 = 990954857884280807155141937143358514822699724692261377137730212333798710863533568558966350673543013087657806107656416640019_<123>
(23·10¹⁶⁰-41)/9 = 2(5)₁₅₉1_<161> = 3 · 421 · 1303290019_<10> · 16757517846851_<14> · 33410740941589932192257971_<26> · C110
C110 = P51 · P60
P51 = 141201378282839605551482507237147623978827958693229_<51>
P60 = 196384032376405294052137230651200422806370915812525870825887_<60>

Number: 25551_160 N=27729696044290224460609024058949846655012187821821005718326741022823024412724637968075461477077242655504819123 ( 110 digits) Divisors found: r1=141201378282839605551482507237147623978827958693229 (pp51) r2=196384032376405294052137230651200422806370915812525870825887 (pp60) Version: GGNFS-0.77.1-20050930-pentium4 Total time: 34.78 hours. Scaled time: 16.45 units (timescale=0.473). Factorization parameters were as follows: name: 25551_160 n: 27729696044290224460609024058949846655012187821821005718326741022823024412724637968075461477077242655504819123 skew: 19703.02 # norm 2.58e+15 c5: 97200 c4: 2699482653 c3: -193815028071876 c2: -1584280404140977288 c1: 22126732270643781438316 c0: -44916850879699875155644045 # alpha -6.32 Y1: 17675023289 Y0: -778136368901680828542 # Murphy_E 1.04e-09 # M 5474228949482118542256893329492702222648847949467955749282916956767404137793286945529386778071697693401222665 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: RFBsize:230209, AFBsize:230705, largePrimes:7471164 encountered Relations: rels:7388085, finalFF:642533 Max relations in full relation-set: 28 Initial matrix: 460991 x 642533 with sparse part having weight 52550874. Pruned matrix : 312266 x 314634 with weight 26599352. Total sieving time: 30.88 hours. Total relation processing time: 0.45 hours. Matrix solve time: 3.16 hours. Time per square root: 0.28 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: 34.78 hours. --------- CPU info (if available) ----------

(23·10¹⁴⁸-41)/9 = 2(5)₁₄₇1_<149> = 3³ · 17 · 151 · 1283 · 75011929299489064304755445730298699_<35> · C106
C106 = P48 · P59
P48 = 242428544050253915914646918889394792594740748663_<48>
P59 = 15803560686756702280080903994808482373671375272389819798509_<59>

Number: 25551_148 N=3831234208100258225905784789352281618753028879135330243405513044277690944977878017308340945272902471143467 ( 106 digits) SNFS difficulty: 149 digits. Divisors found: r1=242428544050253915914646918889394792594740748663 (pp48) r2=15803560686756702280080903994808482373671375272389819798509 (pp59) Version: GGNFS-0.77.1-20050930-nocona Total time: 42.02 hours. Scaled time: 32.06 units (timescale=0.763). Factorization parameters were as follows: name: 25551_148 n: 3831234208100258225905784789352281618753028879135330243405513044277690944977878017308340945272902471143467 m: 100000000000000000000000000000 c5: 23000 c0: -41 skew: 0.28 type: snfs Factor base limits: 1500000/1500000 Large primes per side: 3 Large prime bits: 26/26 Max factor residue bits: 45/45 Sieved algebraic special-q in [750000, 5650001) Primes: RFBsize:114155, AFBsize:113913, largePrimes:3272514 encountered Relations: rels:3445255, finalFF:267676 Max relations in full relation-set: 28 Initial matrix: 228135 x 267676 with sparse part having weight 36440840. Pruned matrix : 218281 x 219485 with weight 28929745. Total sieving time: 41.16 hours. Total relation processing time: 0.20 hours. Matrix solve time: 0.59 hours. Time per square root: 0.07 hours. Prototype def-par.txt line would be: snfs,149,5,0,0,0,0,0,0,0,0,1500000,1500000,26,26,45,45,2.3,2.3,100000 total time: 42.02 hours. --------- CPU info (if available) ----------

4. Wanted

See Wanted.

5. Records

See Records.

6. Contributors

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

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

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

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

Contributions by e-mails are also acceptable.

7. Forms

Repunit

(1)_w

Near-repdigit

(R)_wD

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

D(R)_w

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

Near-repdigit Palindrome

(R)_wD(R)_w

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

Plateau and Depression

D(R)_wD

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

D<R

Plateau ('台地' in Japanese)

D>R

Depression ('窪地' in Japanese)

Generalized quasi-repdigit

D(R)_wE

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

8. Factor Table Search

Examples

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

9. Factor tables

Representations

number_<xxx>

Subscript <xxx> is length of adjacent number.

[number_<xxx>]

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

Near-repdigit (R)wD
Number	General term	Room	Condition	Status / Not factored	Last update
11...113	(10n+17)/9	14.33%	n≤200	176, 179, 181, 183, 184, 185, 187, 188, 189, 192, 193, 195, 199 (13/200)	Jul 5, 2008
11...117	(10n+53)/9	16.19%	n≤200	180, 183, 184, 185, 186, 189, 194, 196 (8/200)	Aug 1, 2008
11...119	(10n+71)/9	15.44%	n≤200	171, 176, 177, 178, 179, 180, 183, 187, 188, 189, 190, 191, 193, 195, 199, 200 (16/200)	Aug 4, 2008
22...221	(2·10n-11)/9	16.84%	n≤200	167, 170, 174, 175, 176, 179, 183, 185, 186, 187, 188, 189, 191, 196, 199, 200 (16/200)	Jan 14, 2008
22...223	(2·10n+7)/9	23.92%	n≤200	171, 173, 174, 175, 176, 179, 182, 183, 184, 186, 189, 193, 195, 196, 198, 199, 200 (17/200)	Jul 14, 2008
22...227	(2·10n+43)/9	13.19%	n≤200	167, 171, 179, 183, 184, 185, 186, 189, 190, 192, 194, 196, 197, 199, 200 (15/200)	Apr 13, 2008
22...229	(2·10n+61)/9	14.02%	n≤200	171, 180, 181, 182, 183, 184, 186, 189, 190, 191, 194, 195, 196, 198, 199, 200 (16/200)	Aug 5, 2008
33...331	(10n-7)/3	34.06%	n≤200	168, 174, 182, 183, 189, 190, 195, 196, 199, 200 (10/200)	Jul 9, 2008
33...337	(10n+11)/3	15.23%	n≤200	170, 173, 174, 176, 178, 179, 180, 184, 185, 186, 187, 191, 192, 193, 194, 196, 197, 198, 199, 200 (20/200)	Aug 5, 2008
44...441	(4·10n-31)/9	16.25%	n≤200	172, 173, 174, 175, 176, 180, 181, 185, 193, 195, 196, 197, 198, 200 (14/200)	Jul 11, 2008
44...443	(4·10n-13)/9	14.66%	n≤200	170, 172, 175, 176, 177, 178, 179, 180, 184, 185, 188, 189, 191, 193, 195, 196, 197, 198, 200 (19/200)	Jul 17, 2008
44...447	(4·10n+23)/9	14.05%	n≤200	178, 179, 181, 183, 184, 185, 188, 192, 193, 195, 196, 197, 199, 200 (14/200)	Aug 3, 2008
44...449	(4·10n+41)/9	16.53%	n≤200	170, 172, 174, 176, 178, 179, 180, 183, 184, 186, 188, 189, 190, 191, 193, 199, 200 (17/200)	Jul 12, 2008
55...551	(5·10n-41)/9	16.91%	n≤200	169, 177, 180, 181, 183, 184, 187, 189, 190, 192, 196, 198, 199, 200 (14/200)	May 21, 2008
55...553	(5·10n-23)/9	14.82%	n≤200	166, 170, 171, 174, 176, 178, 179, 180, 182, 185, 187, 188, 192, 193, 195, 196, 198, 200 (18/200)	Aug 2, 2008
55...557	(5·10n+13)/9	16.11%	n≤200	170, 174, 175, 176, 179, 180, 181, 182, 183, 185, 187, 188, 191, 192, 193, 194, 198, 200 (18/200)	Jul 18, 2008
55...559	(5·10n+31)/9	11.42%	n≤200	165, 172, 173, 174, 179, 180, 181, 182, 183, 184, 190, 191, 194, 196 (14/200)	Jul 12, 2008
66...661	(2·10n-17)/3	31.84%	n≤200	171, 172, 174, 175, 176, 183, 186, 190, 193, 194, 195, 197, 199, 200 (14/200)	Jul 25, 2008
66...667	(2·10n+1)/3	27.28%	n≤200	172, 175, 176, 180, 183, 186, 187, 189, 191, 195, 197, 198, 200 (13/200)	Aug 5, 2008
77...771	(7·10n-61)/9	21.08%	n≤200	170, 178, 179, 181, 182, 184, 187, 189, 190, 191, 193, 194, 195, 196, 197, 198, 199 (17/200)	Jul 14, 2008
77...773	(7·10n-43)/9	18.49%	n≤200	169, 175, 179, 180, 186, 188, 195, 197, 199, 200 (10/200)	May 10, 2008
77...779	(7·10n+11)/9	12.22%	n≤200	171, 173, 177, 178, 180, 181, 182, 183, 185, 187, 191, 192, 193, 194, 196, 199, 200 (17/200)	Jun 21, 2008
88...881	(8·10n-71)/9	15.92%	n≤200	168, 170, 171, 172, 173, 174, 176, 177, 179, 180, 182, 184, 186, 187, 188, 191, 193, 196, 197, 198, 199 (21/200)	Jul 22, 2008
88...883	(8·10n-53)/9	24.96%	n≤200	170, 172, 174, 176, 177, 178, 179, 181, 182, 184, 185, 186, 189, 194, 195, 196, 197, 198, 199 (19/200)	Jun 14, 2008
88...887	(8·10n-17)/9	18.49%	n≤200	173, 180, 181, 182, 183, 184, 186, 187, 188, 189, 196, 198, 199, 200 (14/200)	Aug 5, 2008
88...889	(8·10n+1)/9	12.94%	n≤200	169, 170, 172, 182, 184, 188, 191, 193, 196, 197, 199 (11/200)	Jul 11, 2008
99...991	10n-9	18.02%	n≤200	191, 193 (2/200)	Jun 15, 2008
99...997	10n-3	21.47%	n≤200	178, 181, 183, 186, 189, 192, 193, 195, 196, 198, 199 (11/200)	Jul 17, 2008