Factorizations of repunit numbers of the form (10n-1)/9 (111111...)


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News

-  Last update: Aug 03, 2020                                    

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Aug 03, 2020   R337, c202, GNFS: the R337-polynom was created by Gimarel and Maksym Voznyy - thanks!
                  22M unique relations and 91M unique ideals are collected           
                  currently progress ~ 3.0 %:    

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jul 24, 2020   n =  459: 287743709071765679519005572592282086727787894852332081977696568112925297043603; SNFS
   details:
Fri Apr 03 17:25:47 2020  Msieve v. 1.53 (SVN unknown)
Fri Apr 03 17:25:47 2020  random seeds: a997da14 c0f798bb
Fri Apr 03 17:25:47 2020  factoring 28097663627596496902274031141491145315198561003423811939570768213737090759678697671003530296081683917890273394247547501189864859965856340788100033713344868576734124225081468514935749802816307889082656350436177478956926883 (221 digits)
Fri Apr 03 17:25:49 2020  searching for 15-digit factors
Fri Apr 03 17:25:49 2020  commencing number field sieve (221-digit input)
Fri Apr 03 17:25:49 2020  R0: -1000000000000000000000000000000000000000000000000000
Fri Apr 03 17:25:49 2020  R1: 1
Fri Apr 03 17:25:49 2020  A0: 1
Fri Apr 03 17:25:49 2020  A1: 0
Fri Apr 03 17:25:49 2020  A2: 0
Fri Apr 03 17:25:49 2020  A3: 1
Fri Apr 03 17:25:49 2020  A4: 0
Fri Apr 03 17:25:49 2020  A5: 0
Fri Apr 03 17:25:49 2020  A6: 1
Fri Apr 03 17:25:49 2020  skew 1.00, size 6.089e-015, alpha 1.996, combined = 2.206e-015 rroots = 0
Fri Apr 03 17:25:50 2020  
Fri Apr 03 17:25:50 2020  commencing relation filtering
Fri Apr 03 17:25:50 2020  setting target matrix density to 130.0
Fri Apr 03 17:25:50 2020  estimated available RAM is 65214.1 MB
Fri Apr 03 17:25:50 2020  commencing duplicate removal, pass 1
Fri Apr 03 18:04:02 2020  error -15 reading relation 145002227
...
Fri Apr 03 20:40:56 2020  skipped 157173 relations with b > 2^32
Fri Apr 03 20:40:56 2020  skipped 3 relations with composite factors
Fri Apr 03 20:40:56 2020  found 102149573 hash collisions in 737848016 relations
Fri Apr 03 20:40:56 2020  added 3 free relations
Fri Apr 03 20:40:56 2020  commencing duplicate removal, pass 2
Fri Apr 03 20:50:17 2020  found 4110 duplicates and 737843909 unique relations
Fri Apr 03 20:50:17 2020  memory use: 4262.0 MB
Fri Apr 03 20:50:18 2020  reading ideals above 599064576
Fri Apr 03 20:50:18 2020  commencing singleton removal, initial pass
Fri Apr 03 23:25:21 2020  memory use: 11024.0 MB
Fri Apr 03 23:25:22 2020  reading all ideals from disk
Fri Apr 03 23:25:59 2020  memory use: 13386.8 MB
Fri Apr 03 23:27:08 2020  commencing in-memory singleton removal
Fri Apr 03 23:28:15 2020  begin with 737843909 relations and 616314055 unique ideals
Fri Apr 03 23:44:02 2020  reduce to 504736196 relations and 361956209 ideals in 14 passes
Fri Apr 03 23:44:02 2020  max relations containing the same ideal: 41
Fri Apr 03 23:45:10 2020  reading ideals above 720000
Fri Apr 03 23:45:11 2020  commencing singleton removal, initial pass
Sat Apr 04 02:14:50 2020  memory use: 11024.0 MB
Sat Apr 04 02:14:51 2020  reading all ideals from disk
Sat Apr 04 02:15:56 2020  memory use: 23131.9 MB
Sat Apr 04 02:18:10 2020  keeping 421785409 ideals with weight <= 200, target excess is 2724899
Sat Apr 04 02:20:25 2020  commencing in-memory singleton removal
Sat Apr 04 02:22:02 2020  begin with 504736196 relations and 421785409 unique ideals
Sat Apr 04 02:40:49 2020  reduce to 504722501 relations and 421771714 ideals in 9 passes
Sat Apr 04 02:40:49 2020  max relations containing the same ideal: 200
Sat Apr 04 02:48:26 2020  removing 14346634 relations and 12562686 ideals in 2000000 cliques
Sat Apr 04 02:48:36 2020  commencing in-memory singleton removal
Sat Apr 04 02:50:03 2020  begin with 490375867 relations and 421771714 unique ideals
...
Sat Apr 04 12:17:10 2020  begin with 170227179 relations and 172785920 unique ideals
Sat Apr 04 12:21:45 2020  reduce to 169963756 relations and 166800361 ideals in 8 passes
Sat Apr 04 12:21:45 2020  max relations containing the same ideal: 104
Sat Apr 04 12:24:49 2020  relations with 0 large ideals: 206417
Sat Apr 04 12:24:49 2020  relations with 1 large ideals: 35137
Sat Apr 04 12:24:49 2020  relations with 2 large ideals: 439347
Sat Apr 04 12:24:49 2020  relations with 3 large ideals: 3019770
Sat Apr 04 12:24:49 2020  relations with 4 large ideals: 11565343
Sat Apr 04 12:24:49 2020  relations with 5 large ideals: 27231596
Sat Apr 04 12:24:49 2020  relations with 6 large ideals: 41413029
Sat Apr 04 12:24:49 2020  relations with 7+ large ideals: 86053117
Sat Apr 04 12:24:49 2020  commencing 2-way merge
Sat Apr 04 12:28:28 2020  reduce to 110760814 relation sets and 107597419 unique ideals
Sat Apr 04 12:28:28 2020  commencing full merge
Sat Apr 04 13:56:48 2020  memory use: 14622.2 MB
Sat Apr 04 13:57:40 2020  found 49189882 cycles, need 49115619
Sat Apr 04 13:57:44 2020  weight of 49115619 cycles is about 6385166686 (130.00/cycle)
Sat Apr 04 13:57:44 2020  distribution of cycle lengths:
Sat Apr 04 13:57:44 2020  1 relations: 3045635
Sat Apr 04 13:57:44 2020  2 relations: 3191268
Sat Apr 04 13:57:44 2020  3 relations: 3385894
Sat Apr 04 13:57:44 2020  4 relations: 3381649
Sat Apr 04 13:57:44 2020  5 relations: 3400284
Sat Apr 04 13:57:44 2020  6 relations: 3327590
Sat Apr 04 13:57:44 2020  7 relations: 3252571
Sat Apr 04 13:57:44 2020  8 relations: 3123119
Sat Apr 04 13:57:44 2020  9 relations: 2976096
Sat Apr 04 13:57:44 2020  10+ relations: 20031513
Sat Apr 04 13:57:44 2020  heaviest cycle: 28 relations
Sat Apr 04 14:06:34 2020  commencing cycle optimization
Sat Apr 04 14:10:29 2020  start with 438058474 relations
Sat Apr 04 14:52:10 2020  pruned 19603883 relations
Sat Apr 04 14:52:11 2020  memory use: 11519.8 MB
Sat Apr 04 14:52:11 2020  distribution of cycle lengths:
Sat Apr 04 14:52:11 2020  1 relations: 3045635
Sat Apr 04 14:52:11 2020  2 relations: 3267379
Sat Apr 04 14:52:11 2020  3 relations: 3528083
Sat Apr 04 14:52:11 2020  4 relations: 3522005
Sat Apr 04 14:52:11 2020  5 relations: 3563405
Sat Apr 04 14:52:11 2020  6 relations: 3479104
Sat Apr 04 14:52:11 2020  7 relations: 3414085
Sat Apr 04 14:52:11 2020  8 relations: 3265392
Sat Apr 04 14:52:11 2020  9 relations: 3107054
Sat Apr 04 14:52:11 2020  10+ relations: 18923477
Sat Apr 04 14:52:11 2020  heaviest cycle: 28 relations
Sat Apr 04 15:02:14 2020  RelProcTime: 77784
Sat Apr 04 15:02:14 2020  elapsed time 21:36:27

Fri May 15 20:03:29 2020  commencing linear algebra
Fri May 15 20:04:31 2020  matrix starts at (0, 0)
Fri May 15 20:04:44 2020  matrix is 49114833 x 49115010 (24803.7 MB) with weight 7031998278 (143.17/col)
Fri May 15 20:04:44 2020  sparse part has weight 5961868268 (121.39/col)
Fri May 15 20:04:44 2020  saving the first 48 matrix rows for later
Fri May 15 20:04:57 2020  matrix includes 64 packed rows
Fri May 15 20:05:06 2020  matrix is 49114785 x 49115010 (23840.4 MB) with weight 6111460112 (124.43/col)
Fri May 15 20:05:06 2020  sparse part has weight 5758479444 (117.24/col)
Fri May 15 20:05:06 2020  using block size 8192 and superblock size 1081344 for processor cache size 11264 kB
Fri May 15 20:10:25 2020  commencing Lanczos iteration (16 threads)
Fri May 15 20:10:25 2020  memory use: 21169.4 MB
Fri May 15 20:10:29 2020  restarting at iteration 37005 (dim = 2340052)
Fri May 15 20:13:52 2020  linear algebra at 4.8%, ETA 1728h22m
Fri May 15 20:14:51 2020  checkpointing every 30000 dimensions
Thu Jul 23 18:43:22 2020  lanczos halted after 776689 iterations (dim = 49114781)
Thu Jul 23 18:44:11 2020  recovered 37 nontrivial dependencies
Thu Jul 23 18:46:29 2020  BLanczosTime: 5956980
Thu Jul 23 18:46:29 2020  elapsed time 1654:43:01
 
Thu Jul 23 19:25:05 2020  commencing square root phase
Thu Jul 23 19:25:05 2020  handling dependencies 1 to 64
Thu Jul 23 19:25:05 2020  reading relations for dependency 1
Thu Jul 23 19:25:13 2020  read 24559187 cycles
Thu Jul 23 19:26:08 2020  cycles contain 84141086 unique relations
Thu Jul 23 19:37:11 2020  read 84141086 relations
Thu Jul 23 19:44:35 2020  multiplying 84141086 relations
Thu Jul 23 20:38:56 2020  multiply complete, coefficients have about 2351.40 million bits
Thu Jul 23 20:39:10 2020  initial square root is modulo 187877
Thu Jul 23 21:36:30 2020  sqrtTime: 7885
Thu Jul 23 21:36:30 2020  p78 factor: 287743709071765679519005572592282086727787894852332081977696568112925297043603
Thu Jul 23 21:36:30 2020  p143 factor: 97648229107204235650441206754425845388055840946224275373388075321223543065113417752695410418408653172411245982360494127850309706544173670915761
Thu Jul 23 21:36:30 2020  elapsed time 02:11:27
    

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner;  the R1980M-polynom was 
           created by Maksym Voznyy in cooperation with mersenneforum - thanks!  
   Jul 07, 2019   n =1980M: 1894480662587906626213719003472037744324031299064496778010791034044578628744590947201792481; GNFS 


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jul 30, 2020   R1740M, c204, GNFS: the R1740M-polynom was created by Maksym Voznyy - thanks!
                  346M unique relations and 550M unique ideals are collected           
                  currently progress ~ 47 %:    


-  Found by Kurt Beschorner 
   May 26, 2020   n = 9089: 30418264146162968969429117;                            B1= 1e6;  sigma = 4274930699985848 
   May 29, 2020   n = 9093: 101908180340763230295104537071;                        B1= 3e6;  sigma = 3681890424543276 
   Jun 11, 2020   n = 9129: 58716953887634579999893;                               B1= 3e6;  sigma = 581214424774345  
   Jun 16, 2020   n=299947: 4179348094038241;                                      B1= 5e4;  sigma = 7664573366871508 
   Jun 24, 2020   n = 9135: 11344306940218749065447446471;                         B1= 3e6;  sigma = 6758203416202594
   Jul 20, 2020   n = 9159: 7458071133126696400638318787;                          B1= 3e6;  sigma = 5685064070024516 
   Jul 22, 2020   n = 9107: 2102333137776831192401353613;                          B1= 1e6;  sigma = 3467006848464782 
   Aug 02, 2020   n = 9113: 17245749127283658743551012523;                         B1= 1e6;  sigma = 1521521902935765

  
-  Found by ECMNET/Sam Wagstaff
   Feb 21, 2020   n =  337: 906533749251005245151122204670351312590267105760052002862150546121; ecm 
 
  
-  Found by Alfred Eichhorn 
   May 04, 2020   n =31873:  2889000206988332683096031387 * 3846005647......c31845; B1= 5e4; sigma = 5296134971648714 
   May 04, 2020   n =53653:  2364313679577837740321267 * 3545833684......c53611;   B1= 5e4; sigma = 4112093875386518
   May 14, 2020   n =31981:  72196917331341724987875079 * 1539000766......c31955;  B1= 5e4; sigma = 6893105606345854
   May 14, 2020   n =32027:  570756320932474796608885321 * 1946734657......c32000; B1= 5e4; sigma = 8805025147452105
   May 14, 2020   n =53717:  400508678524420115806230649 * 2774249774......c53690; B1= 5e4; sigma = 0:6028819601082278 
   May 27, 2020   n =32341:  108356997611851134571717413721 * 1025417034......c32312; B1= 5e4; sigma = 7462963621981876
   May 27, 2020   n =90373:  4614344401493455210003273963 * 2407950110......c90345;   B1= 5e4; sigma = 6334765406592556
   May 27, 2020   n =90397:  105845847549750221725067 * 1049744639......c90374;    B1= 5e4; sigma = 9003930757188247
   Jun 08, 2020   n =32603:  45903897617432364294119 * 2420515835......c32580;     B1= 5e4; sigma = 3075270328928611
   Jun 08, 2020   n =53917:  294269401779639493852213 * 3775829577......c53893;    B1= 5e4; sigma = 5866403170814528   
   Jun 08, 2020   n =90619:  2345630318122074716729 * 4736940439......c90597;      B1= 5e4; sigma = 7480871379203208
   Jun 16, 2020   n =32887:  214754296621034269611689 * 5173871389......c32863;    B1= 5e4; sigma = 5776684445425926 
   Jun 22, 2020   n =32957:  3034964556511025727319 * 3661034883......c32935;      B1= 5e4; sigma = 6759563567141852 
   Jun 22, 2020   n =54311:  99226280343250370040079 * 1119775030......c54288;     B1= 5e4; sigma = 5492623138501617 
   Jun 22, 2020   n =90947:  4836116397715960105187489 * 2297527643......c90922;   B1= 5e4; sigma = 6875843154026388 
   Jul 01, 2020   n =33113:  24353329584974226507401 * 4562460780......c33090;     B1= 5e4; sigma = 7127985045140319
   Jul 01, 2020   n =54361:  665592461889878795163841 * 1669356512......c54337;    B1= 5e4; sigma = 5447122642957776 
   Jul 15, 2020   n =33563:  6048976971971164235785867 * 1836857895......c33538;   B1= 5e4; sigma = 8315090112117856
   Jul 30, 2020   n =33851:  1089612291588859083100799 * 1019730705......c33827;   B1= 5e4; sigma = 6941267710365863
   
   
-  Found by Yousuke Koide
   Apr 05, 2020   n =  816: 3178246571075235723080972275640135632212436318968968029466533249264048115754831736073020454216579035062833710671458881; SNFS 


-  Found by Danilo Nitsche
   Apr 16, 2020   n=299933: 470768613790117 * composite cofactor 531112...c299899; mfaktc


-  Found by YOYO@home 
   YOYO@home/cellman 
   May 19, 2020   n = 1233: 2071133703625587214227323104568507030381670852043;     B1= 43e6; sigma = 0:12155937095413581933


ECM efforts
with Rn:      323 < n < 2000 (Jul 24, 2020) with Rn:     1999 < n < 3000 (Feb 14, 2020)
with Rn:     2999 < n < 4000 (Jun 12, 2019) with Rn:     3999 < n < 5000 (Jun 12, 2019)
with Rn:     4999 < n < 6000 (Mar 15, 2020) with Rn:     5999 < n < 7000 (May 11, 2020)
with Rn:     6999 < n < 8000 (May 11, 2020) with Rn:     7999 < n < 9000 (Jun 25, 2020)
with Rn:     8999 < n <10000 (Aug 02, 2020) with Rn:     9999 < n <11000 (Jun 12, 2019)
with Rn:   10999 < n <12000 (Jun 12, 2019) with Rn:   11999 < n <12501 (Mar 16, 2019)



currently ECM-efforts by   yoyo@home:    ecm-curves
B1 = 43e6/8600 curves/
numbers < 1001 digits		 1233
working		 1235
working		 1251
working		 1255
working		 1257
working
B1 = 11e7/18400 curves/
numbers < 701 digits		 571
working		 577
working		 589
working		 593
working		 879
working
B1 = 26e7/46000 curves/
numbers < 450 digits		 467
working		 521
working		 1136
working		 1142
working		 1160
working
B1 = 85e7/75000 curves/
numbers < 250 digits		 471
working		 585
working		 609
working		 675
working		 735
working



Factorizations
Repunits: R1        - R2500 (Jul 24, 2020) Repunits:  R2501 - R5000 (Feb 14, 2020)
Repunits: R5001   - R7500 (Apr 22, 2020) Repunits: R7501 - R10000 (Aug 02, 2020)
Repunits: R10001 - R12500 (Jun 12, 2019) Repunits: R12540LM - R14980LM (Apr 13, 2019)




Rprime project; base 10

last update: Jul 05, 2020

project page  

Status:       3 - 1M     1M - 2M     2M - 3M     3M - 4M     4M - 5M    
Details:     3 - 1M     1M - 2M     2M - 3M     3M - 4M     4M - 5M    

active members: Danilo Nitsche, Edo Rajh, Fan Ming, Kurt Beschorner

all contributors:     Danilo Nitsche, Paul Bourdelais, Charles, Bo Chen, Alfred Eichhorn, FactorDB.com, Giovanni Di Maria, Fan Ming, Phil,
                                Richard Kapek, Pavlos, Edo Rajh, Alfred Reich, Nejc Skoberne, Sebastian, MattStath, Maksym Voznyy, wims, Kurt Beschorner
Overview
 
    Exponent     Primes/PRP                     found by ...
    - 10ˆ20     R19 = prime
    - 10ˆ100     R23 = prime
    - 10ˆ1000     R317 = prime
    - 10ˆ10000     R1031 = prime                 WD (Dec 1985)
    - 10ˆ50000     R49081 = PRP                 Harvey Dubner (Sep 1999)
    - 10ˆ100000     R86453 = PRP                 Lew Baxter (Oct 2000)
    - 10ˆ250000     R109297 = PRP               Paul Bourdelais - Harvey Dubner (Apr 2007)
    - 10ˆ500000     R270343 = PRP               Maksym Voznyy - Anton Budnyy (Jul 2007)
    - 10ˆ 4197139     no further probable primes




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