Factorizations of Repunit Numbers

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

News

-  Last update: Aug 03, 2021     

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jul 28, 2021   R1008, c249, SNFS-difficult = 288 
                  729M unique r. relations and 622M unique ideals are collected
                  msieve-logfile abstract:
                  -> setting target matrix density to 130 
                  -> begin with 729425851 relations and 611973089 unique ideals
                  -> found 31674616 cycles, need 31654077
                  -> commencing linear algebra      
                  -> matrix is 31654188 x 31654077 
                  -> linear algebra at 29.0%, estimated time of arrival: 458 hours


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Aug 03, 2021   R888/c258: SNFS-difficult = 296 
                  47M unique r. relations and 156M unique ideals are collected
 
 
-  Found by Kurt Beschorner      
    Jul 29, 2021   n=245023: 110716844516934599 * 1809440376......c244984;          gr-mfaktc ***
    Jul 29, 2021   n=245087: 3943532397201103799 * 2887405166......c245049;         gr-mfaktc ***
    Jul 29, 2021   n=245129: 6549809783930302609 * 3387006285......c245098;         gr-mfaktc ***
    Jul 29, 2021   n=245299: 10206496475634241199 * 1088631259......c245280;        gr-mfaktc ***
    Jul 29, 2021   n=245321: 1164459383507898991 * 2953377175......c245283;         gr-mfaktc ***
    Jul 29, 2021   n=245521: 81298951302561431 * 1366697962......c245504;           gr-mfaktc ***
    Jul 29, 2021   n=245527: 10509999932768167319 * 1057194213......c245508;        gr-mfaktc ***
    Jul 29, 2021   n=245881: 9158062156524976133 * 1213260067......c245862;         gr-mfaktc ***

    *** all cofactors are composite: Prime95-results
    {"status":"C", "k":1, "b":10, "n":245023, "c":-1, "known-factors":["9","110716844516934599","1696539253","3269155671521"], "worktype":"PRP-3", "res64":"966EF9C7A123AE39", "residue-type":1, "res2048":"61586E5C6E...... ", "fft-length":49152, "error-code":"00000000", "security-code":"1B265ED8", "program":{"name":"Prime95", "version":"29.6", "build":7, "port":4}, "timestamp":"2021-07-29 05:32:08", "user":"ANONYMOUS"}
    {"status":"C", "k":1, "b":10, "n":245087, "c":-1, "known-factors":["9","3943532397201103799","1470523","6635788365533"], "worktype":"PRP-3", "res64":"ED5E547B66B0C9CA", "residue-type":1, "res2048":"F214E9CF2E......  ", "fft-length":49152, "error-code":"00000000", "security-code":"1BA65F58", "program":{"name":"Prime95", "version":"29.6", "build":7, "port":4}, "timestamp":"2021-07-29 04:37:54", "user":"ANONYMOUS"}
    {"status":"C", "k":1, "b":10, "n":245129, "c":-1, "known-factors":["9","6549809783930302609","500855907187"], "worktype":"PRP-3", "res64":"992F2804B0D1D18B", "residue-type":1, "res2048":"B70F37BDA1...... ", "fft-length":49152, "error-code":"00000000", "security-code":"1BFA5FAC", "program":{"name":"Prime95", "version":"29.6", "build":7, "port":4}, "timestamp":"2021-07-29 04:39:05", "user":"ANONYMOUS"}
    {"status":"C", "k":1, "b":10, "n":245299, "c":-1, "known-factors":["9","10206496475634241199"], "worktype":"PRP-3", "res64":"161C6430D07235B7", "residue-type":1, "res2048":"73B9190565......  ", "fft-length":49152, "error-code":"00000000", "security-code":"1D4E6100", "program":{"name":"Prime95", "version":"29.6", "build":7, "port":4}, "timestamp":"2021-07-29 04:40:15", "user":"ANONYMOUS"}
    {"status":"C", "k":1, "b":10, "n":245321, "c":-1, "known-factors":["9","1164459383507898991","490643","65848915136759"], "worktype":"PRP-3", "res64":"3E8C964149E95761", "residue-type":1, "res2048":"E7A3ADC541...... ", "fft-length":49152, "error-code":"00000000", "security-code":"1D7A612C", "program":{"name":"Prime95", "version":"29.6", "build":7, "port":4}, "timestamp":"2021-07-29 04:41:28", "user":"ANONYMOUS"}
    {"status":"C", "k":1, "b":10, "n":245521, "c":-1, "known-factors":["9","81298951302561431"], "worktype":"PRP-3", "res64":"03FF29BE91A35D7C", "residue-type":1, "res2048":"7EED19BBB7......  ", "fft-length":49152, "error-code":"00000000", "security-code":"1F0A62BC", "program":{"name":"Prime95", "version":"29.6", "build":7, "port":4}, "timestamp":"2021-07-29 04:42:39", "user":"ANONYMOUS"}
    {"status":"C", "k":1, "b":10, "n":245527, "c":-1, "known-factors":["9","10509999932768167319"], "worktype":"PRP-3", "res64":"42F387A24DDFA2D1", "residue-type":1, "res2048":"A6F6229D11......  ", "fft-length":49152, "error-code":"00000000", "security-code":"1F1662C8", "program":{"name":"Prime95", "version":"29.6", "build":7, "port":4}, "timestamp":"2021-07-29 04:43:50", "user":"ANONYMOUS"}
    {"status":"C", "k":1, "b":10, "n":245881, "c":-1, "known-factors":["9","9158062156524976133"], "worktype":"PRP-3", "res64":"67EEA9874152C4C8", "residue-type":1, "res2048":"D4BE5FA839......  ", "fft-length":49152, "error-code":"00000000", "security-code":"21DA658C", "program":{"name":"Prime95", "version":"29.6", "build":7, "port":4}, "timestamp":"2021-07-29 04:45:00", "user":"ANONYMOUS"}
 

-  Found by Yousuke Koide      
   Jul 28, 2021   n =  834: 84191134295847459088496323909951690425296390505413654926185730285872463; SNFS   


-  Found by Kurt Beschorner      
   Jul 28, 2021   n=244003: 14987734041242686351;                                   gr-mfaktc
   Jul 28, 2021   n=244043: 11835424759410615787;                                   gr-mfaktc
   Jul 28, 2021   n=244091: 415489380407954201;                                     gr-mfaktc
   Jul 28, 2021   n=244109: 96108266578102439;                                      gr-mfaktc
   Jul 28, 2021   n=244247: 1564011899110093427;                                    gr-mfaktc
   Jul 28, 2021   n=244379: 3159094113684406369;                                    gr-mfaktc
   Jul 28, 2021   n=244639: 1752417698563513369;                                    gr-mfaktc
   Jul 28, 2021   n=244841: 2142766097052150751;                                    gr-mfaktc
   Jul 28, 2021   n=244861: 514999041650481013;                                     gr-mfaktc

 
-  Found by Kurt Beschorner      
   Jul 26, 2021   n = 6005: 420717903891686501333521683198569142151 * 2892781919......c4735; ecm: B1 = 1e6; sigma = 0:4074722048380764  
   Jul 26, 2021   n =15023: 507351723014476264139916677 * 1773917302......c14734;   ecm: B1 =25e4; sigma = 0:1694655298603566  
   Jul 26, 2021   n=100207: 336079933200659172489515626991 * 3306091799......c100177; ecm: B1 = 5e4; sigma = 8183157438565096 
   Jul 26, 2021   n=100229: 65298258132561265731089 * 1417123228......c98748;       ecm: B1 = 5e4; sigma = 0:7977182807505599   
   Jul 26, 2021   n=243343: 13060888043755415723;                                   gr-mfaktc   
   Jul 26, 2021   n=243401: 359380958196228533;                                     gr-mfaktc   
   Jul 26, 2021   n=243517: 110721045185156587;                                     gr-mfaktc   
   Jul 26, 2021   n=243613: 16042914083123033563;                                   gr-mfaktc   
   Jul 26, 2021   n=243647: 628879386496510133;                                     gr-mfaktc   
   Jul 26, 2021   n=243703: 142340437902241037;                                     gr-mfaktc   
   Jul 26, 2021   n=243871: 77084466962976071;                                      gr-mfaktc   
	   

-  Found by Alfred Eichhorn 
   Jul 22, 2021   n =96527: 865621802419894774873159 * 1283598804......c96503;      mprime: B1 = 5e4; sigma = 6670886850754605   


-  Found by Kurt Beschorner      
   Jul 22, 2021   n = 7003: 2795275541644314229026155745397;                        ecm: B1 = 1e6; sigma = 0:6526693758661186 
   Jul 22, 2021   n = 7003: 57386559453693196421241258187529490893 * 3195719953......c6651; ecm: B1 = 1e6; sigma = 0:8513032473632757 
   Jul 22, 2021   n=100189: 342589204796374215133 * 1298751345......c100150;        ecm: B1 = 5e4; sigma = 0:8751326778434432 
   Jul 22, 2021   n=100271: 24675304796250323893 * 7103395288......c100234;         ecm: B1 = 5e4; sigma = 0:678085146272887 


-  Found by Kurt Beschorner      
   Jul 17, 2021   n=241093: 276566898690889837;                                     gr-mfaktc 
   Jul 17, 2021   n=241313: 79676760715519477;                                      gr-mfaktc 
   Jul 17, 2021   n=241333: 204233580814082471;                                     gr-mfaktc 
   Jul 17, 2021   n=241537: 2528464638367786333;                                    gr-mfaktc  
   Jul 17, 2021   n=241663: 1373673328034823169;                                    gr-mfaktc 
   Jul 17, 2021   n=241691: 2126040112959700841;                                    gr-mfaktc 
   Jul 17, 2021   n=241823: 110443798279493681;                                     gr-mfaktc 
   Jul 17, 2021   n=241823: 781365898344783881;                                     gr-mfaktc 
   Jul 17, 2021   n=241847: 15408065431021647413;                                   gr-mfaktc 
   Jul 17, 2021   n=241979: 153549751903355917;                                     gr-mfaktc 
   Jul 17, 2021   n=242069: 295913901213459653;                                     gr-mfaktc 
   Jul 17, 2021   n=242173: 10777260488125071883;                                   gr-mfaktc 
   Jul 17, 2021   n=242201: 4510933454560404563;                                    gr-mfaktc 
   Jul 17, 2021   n=242371: 129046478396027747;                                     gr-mfaktc 
   Jul 17, 2021   n=242399: 1840817793859081991;                                    gr-mfaktc 
   Jul 17, 2021   n=242677: 545839518252207133;                                     gr-mfaktc 
   Jul 17, 2021   n=242681: 17148411301288926289;                                   gr-mfaktc 
   Jul 17, 2021   n=242989: 9127170726763614529;                                    gr-mfaktc 


-  Found by Kurt Beschorner      
   Jul 16, 2021   n=100141: 388021169898847081 * 1116983830......c99451;            ecm: B1 = 5e4; sigma = 0:8238397063673048 


-  Found by Kurt Beschorner      
   Jul 15, 2021   n=100117: 2031193439072401;                                       ecm: B1 = 5e4; sigma = 608325200118047 
   Jul 15, 2021   n=100117: 2696440775225444243;                                    ecm: B1 = 5e4; sigma = 0:985066099169757  
   Jul 15, 2021   n=100117: 22599314490035872963133 * 7271182961......c98120;       ecm: B1 = 5e4; sigma = 0:3481519970690305 
   Jul 15, 2021   n=100123: 9495986790660578628569 * 9477687994......c98346;        ecm: B1 = 5e4; sigma = 0:7706668740098573
   Jul 15, 2021   n=100151: 195182992328029698780209 * 5884141361......c100119;     ecm: B1 = 5e4; sigma = 0:3412315986731954 
   Jul 15, 2021   n=100159: 2294077591908190603 *  3923145420......c97398;          ecm: B1 = 5e4; sigma = 0:3145807232861379 


-  Found by Kurt Beschorner      
   Jul 13, 2021   n=100127: 377832246320161 * 2382009499......c99442;               ecm: B1 = 5e4; sigma = 0:5916218765991568
   Jul 13, 2021   n=238009: 2569595782097577361;                                    gr-mfaktc
   Jul 13, 2021   n=238109: 362971620900461357;                                     gr-mfaktc
   Jul 13, 2021   n=238141: 76775463617073517;                                      gr-mfaktc
   Jul 13, 2021   n=238213: 8443565067133467533;                                    gr-mfaktc
   Jul 13, 2021   n=238321: 110254347735257027;                                     gr-mfaktc
   Jul 13, 2021   n=238321: 6345506079461820191;                                    gr-mfaktc
   Jul 13, 2021   n=238363: 4151966938041650191;                                    gr-mfaktc
   Jul 13, 2021   n=238373: 647067953641564321;                                     gr-mfaktc
   Jul 13, 2021   n=238463: 72987184124448791;                                      gr-mfaktc
   Jul 13, 2021   n=238519: 3164480296920479987;                                    gr-mfaktc
   Jul 13, 2021   n=238519: 9306113223942348311;                                    gr-mfaktc
   Jul 13, 2021   n=238529: 389772471859069751;                                     gr-mfaktc
   Jul 13, 2021   n=238801: 906082008506696237;                                     gr-mfaktc
   Jul 13, 2021   n=238829: 539570526711522067;                                     gr-mfaktc
   Jul 13, 2021   n=238841: 14448740812829463449;                                   gr-mfaktc
   Jul 13, 2021   n=238877: 1098478068109533043;                                    gr-mfaktc
   Jul 13, 2021   n=238939: 153826472157965951;                                     gr-mfaktc
   Jul 13, 2021   n=238967: 6665190548976354037;                                    gr-mfaktc
   Jul 13, 2021   n=238991: 178598081962577609;                                     gr-mfaktc
   Jul 13, 2021   n=239017: 1654584046272041707;                                    gr-mfaktc
   Jul 13, 2021   n=239017: 2765395497803466001;                                    gr-mfaktc
   Jul 13, 2021   n=239137: 1158162972130192267;                                    gr-mfaktc
   Jul 13, 2021   n=239179: 1942906275108923477;                                    gr-mfaktc
   Jul 13, 2021   n=239243: 266973401035237307;                                     gr-mfaktc
   Jul 13, 2021   n=239383: 705283043511250961;                                     gr-mfaktc
   Jul 13, 2021   n=239489: 266636372492249401;                                     gr-mfaktc
   Jul 13, 2021   n=239539: 775749901631316679;                                     gr-mfaktc
   Jul 13, 2021   n=239597: 15777435163246474121;                                   gr-mfaktc
   Jul 13, 2021   n=239623: 323810598620003773;                                     gr-mfaktc
   Jul 13, 2021   n=239711: 1639072928354663071;                                    gr-mfaktc
   Jul 13, 2021   n=239713: 341855301555073693;                                     gr-mfaktc
   Jul 13, 2021   n=239843: 14363619840611921471;                                   gr-mfaktc
   Jul 13, 2021   n=239857: 15272788487208549013;                                   gr-mfaktc
   Jul 13, 2021   n=239873: 1809085772154686117;                                    gr-mfaktc
   Jul 13, 2021   n=239893: 1515179303732296831;                                    gr-mfaktc
   Jul 13, 2021   n=239933: 5007590462986303603;                                    gr-mfaktc
   Jul 13, 2021   n=240011: 581140835030942213;                                     gr-mfaktc
   Jul 13, 2021   n=240049: 1084330497971699591;                                    gr-mfaktc
   Jul 13, 2021   n=240173: 136934337649369849;                                     gr-mfaktc
   Jul 13, 2021   n=240319: 3241859460135507803;                                    gr-mfaktc
   Jul 13, 2021   n=240379: 331030660952250563;                                     gr-mfaktc
   Jul 13, 2021   n=240433: 397376014873846187;                                     gr-mfaktc
   Jul 13, 2021   n=240491: 196509787303099397;                                     gr-mfaktc
   Jul 13, 2021   n=240503: 133312749006870721;                                     gr-mfaktc
   Jul 13, 2021   n=240769: 15139366593251813351;                                   gr-mfaktc
   Jul 13, 2021   n=240883: 2829718729425809173;                                    gr-mfaktc
   Jul 13, 2021   n=240893: 1591525588832804719;                                    gr-mfaktc 


-  Found by Alfred Eichhorn 
   Jul 12, 2021   n =96401: 2879432598959913813557347 * 3858784926......c96376;      ecm: B1 = 5e4; sigma = 2455032047814037   
   Jul 12, 2021   n =96457: 412145967998115070364051763403 * 2695916489......c96427; ecm: B1 = 5e4; sigma = 523617785980939  


-  Found by Kurt Beschorner      
   Jul 11, 2021   n = 1269: 541520087299201982040396188910708534378319;             ecm: B1 =43e6; sigma = 0:932524933627175
   Jul 11, 2021   n =30001: 5336322542252166455873929;                              ecm: B1 =25e4; sigma = 0:2603019868468078   
   Jul 11, 2021   n =30001: 279579714362022366270782281;                            ecm: B1 =25e4; sigma = 0:6308082884044570   
 
 
-  Found by Kurt Beschorner      
   Jun 30, 2021   n =15001: 30355533034317967107263711969;                          ecm: B1 =25e4; sigma = 2661518256649941  
   Jun 30, 2021   n=236069: 6424278810074045573;                                    gr-mfaktc
   Jun 30, 2021   n=236111: 7531708499269976213;                                    gr-mfaktc
   Jun 30, 2021   n=236129: 787374677201670307;                                     gr-mfaktc
   Jun 30, 2021   n=236143: 4472211474423644443;                                    gr-mfaktc
   Jun 30, 2021   n=236333: 757167448818129053;                                     gr-mfaktc
   Jun 30, 2021   n=236429: 185085704036150041;                                     gr-mfaktc
   Jun 30, 2021   n=236429: 633437347791738253;                                     gr-mfaktc
   Jun 30, 2021   n=236449: 4417636050017680759;                                    gr-mfaktc
   Jun 30, 2021   n=236471: 7606105384782029173;                                    gr-mfaktc
   Jun 30, 2021   n=236477: 1551884702389503763;                                    gr-mfaktc
   Jun 30, 2021   n=236477: 13661912104344954757;                                   gr-mfaktc
   Jun 30, 2021   n=236653: 4412748924476617787;                                    gr-mfaktc
   Jun 30, 2021   n=236813: 267860366681733197;                                     gr-mfaktc
   Jun 30, 2021   n=236981: 5663039717296466653;                                    gr-mfaktc
   Jun 30, 2021   n=236983: 10589313220210655243;                                   gr-mfaktc
   Jun 30, 2021   n=236993: 2414130867930324329;                                    gr-mfaktc
   Jun 30, 2021   n=237217: 474809484002521631;                                     gr-mfaktc
   Jun 30, 2021   n=237257: 139546212248594689;                                     gr-mfaktc
   Jun 30, 2021   n=237343: 127169437648354391;                                     gr-mfaktc
   Jun 30, 2021   n=237361: 590333831014186997;                                     gr-mfaktc
   Jun 30, 2021   n=237379: 274554208356219107;                                     gr-mfaktc
   Jun 30, 2021   n=237859: 242931418649563573;                                     gr-mfaktc
   Jun 30, 2021   n=237911: 4151629306304769563;                                    gr-mfaktc
   Jun 30, 2021   n=237967: 256417148280763241;                                     gr-mfaktc
   Jun 30, 2021   n=237971: 75445571398158991;                                      gr-mfaktc
   Jun 30, 2021   n=237997: 8938606754426253679;                                    gr-mfaktc 


-  Found by Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jun 27, 2021   n =1740M: 38500497070688096027556817882565728990416892548263819672284096593431517949011701136219584563960572421; GNFS   
                  The poly-file was created by Maksym Voznyy - thanks  
Sat Apr 17 09:21:05 2021  Msieve v. 1.53 (SVN unknown)
Sat Apr 17 09:21:05 2021  random seeds: ca4ab918 5ab96ba7
Sat Apr 17 09:21:05 2021  factoring 131530344752500531973366175234450924350818650273749175535608297557535517691257001851075669039105083565947532142733020300358168725328898559788675357243034349825598797613375635300708831058228182388355784661 (204 digits)
Sat Apr 17 09:21:06 2021  searching for 15-digit factors
Sat Apr 17 09:21:07 2021  commencing number field sieve (204-digit input)
Sat Apr 17 09:21:07 2021  R0: -3373811031078855887988445262998571743799
Sat Apr 17 09:21:07 2021  R1: 11509880545207076757558
Sat Apr 17 09:21:07 2021  A0: -1011605031457446800403474711756529386281885525624
Sat Apr 17 09:21:07 2021  A1: -156658770946669316726156600541248344076761
Sat Apr 17 09:21:07 2021  A2: -813140174642815037619795427014835
Sat Apr 17 09:21:07 2021  A3: 14070112777299305509364632
Sat Apr 17 09:21:07 2021  A4: 9754532376000330
Sat Apr 17 09:21:07 2021  A5: 10832400
Sat Apr 17 09:21:07 2021  skew 165672963.55, size 4.433e-020, alpha -8.434, combined = 2.467e-015 rroots = 3
Sat Apr 17 09:21:07 2021  commencing relation filtering
Sat Apr 17 09:21:07 2021  setting target matrix density to 130.0
Sat Apr 17 09:21:07 2021  estimated available RAM is 130983.0 MB
Sat Apr 17 09:21:07 2021  commencing duplicate removal, pass 1
Sat Apr 17 11:22:02 2021  found 100488337 hash collisions in 731371426 relations
Sat Apr 17 11:22:35 2021  added 20415 free relations
Sat Apr 17 11:22:35 2021  commencing duplicate removal, pass 2
Sat Apr 17 11:32:33 2021  found 107 duplicates and 731391734 unique relations
Sat Apr 17 11:32:33 2021  memory use: 4262.0 MB
Sat Apr 17 11:32:33 2021  reading ideals above 557645824
Sat Apr 17 11:32:33 2021  commencing singleton removal, initial pass
Sat Apr 17 13:21:46 2021  memory use: 11024.0 MB
Sat Apr 17 13:21:47 2021  reading all ideals from disk
Sat Apr 17 13:21:56 2021  memory use: 13589.9 MB
Sat Apr 17 13:23:04 2021  commencing in-memory singleton removal
Sat Apr 17 13:24:15 2021  begin with 731391734 relations and 615009841 unique ideals
...
Sun Apr 18 05:08:01 2021  reduce to 173281768 relations and 170225889 ideals in 6 passes
Sun Apr 18 05:08:01 2021  max relations containing the same ideal: 110
Sun Apr 18 05:12:16 2021  relations with 0 large ideals: 9183
Sun Apr 18 05:12:16 2021  relations with 1 large ideals: 29252
Sun Apr 18 05:12:16 2021  relations with 2 large ideals: 447816
Sun Apr 18 05:12:16 2021  relations with 3 large ideals: 3154807
Sun Apr 18 05:12:16 2021  relations with 4 large ideals: 12252963
Sun Apr 18 05:12:16 2021  relations with 5 large ideals: 28991048
Sun Apr 18 05:12:16 2021  relations with 6 large ideals: 43939783
Sun Apr 18 05:12:16 2021  relations with 7+ large ideals: 84456916
Sun Apr 18 05:12:16 2021  commencing 2-way merge
Sun Apr 18 05:17:20 2021  reduce to 112664275 relation sets and 109608396 unique ideals
Sun Apr 18 05:17:20 2021  commencing full merge
Sun Apr 18 06:46:56 2021  memory use: 13331.7 MB
Sun Apr 18 06:47:48 2021  found 49742886 cycles, need 49516596   <<<=== matrix size ===>>>
Sun Apr 18 06:47:52 2021  weight of 49516596 cycles is about 6437691509 (130.01/cycle)
Sun Apr 18 06:47:52 2021  distribution of cycle lengths:
Sun Apr 18 06:47:52 2021  1 relations: 3155824
Sun Apr 18 06:47:52 2021  2 relations: 3360458
Sun Apr 18 06:47:52 2021  3 relations: 3577094
Sun Apr 18 06:47:52 2021  4 relations: 3559942
Sun Apr 18 06:47:52 2021  5 relations: 3617633
Sun Apr 18 06:47:52 2021  6 relations: 3516452
Sun Apr 18 06:47:52 2021  7 relations: 3438818
Sun Apr 18 06:47:52 2021  8 relations: 3283726
Sun Apr 18 06:47:52 2021  9 relations: 3111659
Sun Apr 18 06:47:52 2021  10+ relations: 18894990
Sun Apr 18 06:47:52 2021  heaviest cycle: 28 relations
Sun Apr 18 06:57:04 2021  commencing cycle optimization
Sun Apr 18 07:00:46 2021  start with 420510148 relations
Sun Apr 18 07:43:37 2021  pruned 18910701 relations
Sun Apr 18 07:43:37 2021  memory use: 11452.8 MB
Sun Apr 18 07:43:38 2021  distribution of cycle lengths:
Sun Apr 18 07:43:38 2021  1 relations: 3155824
Sun Apr 18 07:43:38 2021  2 relations: 3457913
Sun Apr 18 07:43:38 2021  3 relations: 3737619
Sun Apr 18 07:43:38 2021  4 relations: 3713619
Sun Apr 18 07:43:38 2021  5 relations: 3793731
Sun Apr 18 07:43:38 2021  6 relations: 3680313
Sun Apr 18 07:43:38 2021  7 relations: 3608148
Sun Apr 18 07:43:38 2021  8 relations: 3432946
Sun Apr 18 07:43:38 2021  9 relations: 3240856
Sun Apr 18 07:43:38 2021  10+ relations: 17695627
Sun Apr 18 07:43:38 2021  heaviest cycle: 28 relations
Sun Apr 18 07:55:34 2021  RelProcTime: 81267
Sun Apr 18 07:55:34 2021  elapsed time 22:34:29   

Sun Apr 18 13:08:48 2021  commencing linear algebra
Sun Apr 18 13:09:21 2021  matrix starts at (0, 0)
Sun Apr 18 13:09:43 2021  matrix is 49515207 x 49515384 (25087.3 MB) with weight 7663161458 (154.76/col)
Sun Apr 18 13:09:43 2021  sparse part has weight 5982295350 (120.82/col)
Sun Apr 18 13:09:43 2021  saving the first 48 matrix rows for later
Sun Apr 18 13:10:04 2021  matrix includes 64 packed rows
Sun Apr 18 13:10:17 2021  matrix is 49515159 x 49515384 (24662.9 MB) with weight 6640042109 (134.10/col)
Sun Apr 18 13:10:17 2021  sparse part has weight 5970081534 (120.57/col)
Sun Apr 18 13:10:17 2021  using block size 8192 and superblock size 6291456 for processor cache size 65536 kB
Sun Apr 18 13:21:12 2021  commencing Lanczos iteration (24 threads)
Sun Apr 18 13:21:12 2021  memory use: 21476.5 MB
Sun Apr 18 13:21:13 2021  restarting at iteration 475 (dim = 30041)
Sun Apr 18 13:31:04 2021  linear algebra at 0.1%, ETA 5351h30m
Sun Apr 18 13:32:33 2021  checkpointing every 20000 dimensions
 
Sat Jun 26 18:08:38 2021  commencing square root phase
Sat Jun 26 18:08:38 2021  handling dependencies 1 to 64
Sat Jun 26 18:08:38 2021  reading relations for dependency 1
Sat Jun 26 18:08:48 2021  read 24754092 cycles
Sat Jun 26 18:09:54 2021  cycles contain 85888658 unique relations
Sat Jun 26 18:22:11 2021  read 85888658 relations
Sat Jun 26 18:37:31 2021  multiplying 85888658 relations
Sat Jun 26 20:57:52 2021  multiply complete, coefficients have about 5739.19 million bits
Sat Jun 26 20:58:37 2021  initial square root is modulo 2729533
Sat Jun 26 23:36:20 2021  sqrtTime: 19662
Sat Jun 26 23:36:20 2021  p101 factor: 38500497070688096027556817882565728990416892548263819672284096593431517949011701136219584563960572421
Sat Jun 26 23:36:20 2021  p103 factor: 3416328483006512256320335979072423448945322454006830297255949627404017992115810552611056496561408407441
Sat Jun 26 23:36:20 2021  elapsed time 05:27:44
 

-  Found by Kurt Beschorner                         
   Jun 24, 2021   n=234029: 8215370869268922169;                                    gr-mfaktc
   Jun 24, 2021   n=234121: 175395088478556043;                                     gr-mfaktc
   Jun 24, 2021   n=234131: 172639745979901667;                                     gr-mfaktc
   Jun 24, 2021   n=234131: 5977212639625303031;                                    gr-mfaktc
   Jun 24, 2021   n=234203: 3242243999061254431;                                    gr-mfaktc
   Jun 24, 2021   n=234259: 72105849739243483;                                      gr-mfaktc
   Jun 24, 2021   n=234281: 79278472847868089;                                      gr-mfaktc
   Jun 24, 2021   n=234319: 5099855027160436321;                                    gr-mfaktc
   Jun 24, 2021   n=234589: 3177000334628616479;                                    gr-mfaktc
   Jun 24, 2021   n=234727: 1084288024769638361;                                    gr-mfaktc
   Jun 24, 2021   n=234733: 3495165735723576199;                                    gr-mfaktc
   Jun 24, 2021   n=234743: 663883390524909991;                                     gr-mfaktc
   Jun 24, 2021   n=234799: 4583823600816158879;                                    gr-mfaktc
   Jun 24, 2021   n=234893: 1778800899523469561;                                    gr-mfaktc
   Jun 24, 2021   n=234977: 167402589309145493;                                     gr-mfaktc
   Jun 24, 2021   n=234979: 165149830933217597;                                     gr-mfaktc
   Jun 24, 2021   n=235009: 912564477544461683;                                     gr-mfaktc
   Jun 24, 2021   n=235117: 7052228219721068191;                                    gr-mfaktc
   Jun 24, 2021   n=235489: 237723582774944249;                                     gr-mfaktc
   Jun 24, 2021   n=235489: 4081219474141274711;                                    gr-mfaktc
   Jun 24, 2021   n=235519: 79773865942460801;                                      gr-mfaktc
   Jun 24, 2021   n=235553: 4951741202918725987;                                    gr-mfaktc
   Jun 24, 2021   n=235849: 98955952217075203;                                      gr-mfaktc


-  Found by Kurt Beschorner                         
   Jun 17, 2021   n =30000: 39991809070061802000001;                                ecm: B1 = 1e6; sigma = 3166126587942973  
   Jun 17, 2021   n=232051: 15694378910538830933;                                   gr-mfaktc
   Jun 17, 2021   n=232189: 149085212391132373;                                     gr-mfaktc
   Jun 17, 2021   n=232457: 1567248364848128089;                                    gr-mfaktc
   Jun 17, 2021   n=232633: 4904496424011583001;                                    gr-mfaktc
   Jun 17, 2021   n=232663: 4749088138061708627;                                    gr-mfaktc
   Jun 17, 2021   n=232681: 190828233459808667;                                     gr-mfaktc
   Jun 17, 2021   n=232919: 5863051280626541591;                                    gr-mfaktc
   Jun 17, 2021   n=233113: 384812996873138479;                                     gr-mfaktc
   Jun 17, 2021   n=233141: 3630426445017744079;                                    gr-mfaktc
   Jun 17, 2021   n=233267: 229132242762607319;                                     gr-mfaktc
   Jun 17, 2021   n=233267: 1115208077263318853;                                    gr-mfaktc
   Jun 17, 2021   n=233417: 12837922552213112489;                                   gr-mfaktc
   Jun 17, 2021   n=233423: 747305485147290317;                                     gr-mfaktc
   Jun 17, 2021   n=233437: 792032739766505723;                                     gr-mfaktc
   Jun 17, 2021   n=233713: 922721612868790799;                                     gr-mfaktc
   Jun 17, 2021   n=233777: 608804644035314653;                                     gr-mfaktc
   Jun 17, 2021   n=233921: 6103315421725379237;                                    gr-mfaktc
   Jun 17, 2021   n=233993: 2354872647586577507;                                    gr-mfaktc


-  Found by Kurt Beschorner                         
   Jun 11, 2021   n=10180M: 618469348886528986386736868045981 * 5896029167......P1967; ecm: B1 =11e6; sigma = 0:138044562091769  
   Jun 11, 2021   n=94020M: 2548383691858034221;                                    ecm: B1 =25e4; sigma = 0:5896773875895457563  
   Jun 11, 2021   n=94020M: 851237404580697489961;                                  ecm: B1 =25e4; sigma = 0:3125704586924728109  


-  Found by Kurt Beschorner                         
   Jun 09, 2021   n =5700M: 214098531848960682375313931062057408227354489641401;    ecm: B1 =43e6; sigma = 0:1218120574389352  

  
-  Correction: find out by Makoto Kamada
   Jun 07, 2021  false:       Jun 07, 2021   n=231821: 125487823297597151;  
   Jun 07, 2021  correct:     Jun 07, 2021   n=231821: 125482329778597151;  

                                                                 
                                      
-  Found by Kurt Beschorner                         
   Jun 07, 2021   n=64260M: 602071447910713201;                                     ecm: B1 = 1e6; sigma = 0:12677614305988117273  
   Jun 07, 2021   n=230047: 78746051978526241;                                      gr-mfaktc
   Jun 07, 2021   n=230357: 76975545777987107;                                      gr-mfaktc
   Jun 07, 2021   n=230501: 108202949009734121;                                     gr-mfaktc
   Jun 07, 2021   n=230779: 1912711472817779831;                                    gr-mfaktc
   Jun 07, 2021   n=230833: 173854061031735089;                                     gr-mfaktc
   Jun 07, 2021   n=230833: 7601940260842208693;                                    gr-mfaktc
   Jun 07, 2021   n=230861: 7570887592320937889;                                    gr-mfaktc
   Jun 07, 2021   n=230873: 990360663046504163;                                     gr-mfaktc
   Jun 07, 2021   n=230891: 17402402026623709729;                                   gr-mfaktc
   Jun 07, 2021   n=230939: 1600193497863035707;                                    gr-mfaktc
   Jun 07, 2021   n=230959: 15894295946527067431;                                   gr-mfaktc
   Jun 07, 2021   n=230969: 122066208528063403;                                     gr-mfaktc
   Jun 07, 2021   n=231197: 13619230688484914711;                                   gr-mfaktc
   Jun 07, 2021   n=231223: 4908568512167867957;                                    gr-mfaktc
   Jun 07, 2021   n=231289: 905543379182487961;                                     gr-mfaktc
   Jun 07, 2021   n=231299: 755953308156952043;                                     gr-mfaktc
   Jun 07, 2021   n=231409: 2094336088340204987;                                    gr-mfaktc
   Jun 07, 2021   n=231431: 1411453396656092837;                                    gr-mfaktc
   Jun 07, 2021   n=231493: 425846617734441289;                                     gr-mfaktc
   Jun 07, 2021   n=231631: 13760790439576993357;                                   gr-mfaktc
   Jun 07, 2021   n=231779: 363515424375507329;                                     gr-mfaktc
   Jun 07, 2021   n=231799: 6436226881590743591;                                    gr-mfaktc
   Jun 07, 2021   n=231821: 125487823297597151; corrected: Jun 08,2021              gr-mfaktc
 
      
-  Found by Alfred Eichhorn 
   Jun 05, 2021   n =41077: 1963136230803261055657813 * 5659877769......c41052;     ecm: B1 = 5e4; sigma = 7820758842106039 

              
-  Found by Kurt Beschorner                         
   Jun 02, 2021   n =7500L: 48207545174782975493383750875127027725001;              ecm: B1 = 43e6; sigma = 0:7630000256316624  

           
-  Found by Kurt Beschorner                         
   May 29, 2021   n=229037: 1705505054821867489;                                    gr-mfaktc
   May 29, 2021   n=229093: 2127882148430908853;                                    gr-mfaktc
   May 29, 2021   n=229213: 1810307076949938649;                                    gr-mfaktc
   May 29, 2021   n=229403: 5828609083556274467;                                    gr-mfaktc
   May 29, 2021   n=229409: 4618383564203001041;                                    gr-mfaktc
   May 29, 2021   n=229423: 1091544121886699249;                                    gr-mfaktc
   May 29, 2021   n=229459: 10516067428353219107;                                   gr-mfaktc
   May 29, 2021   n=229487: 321768362056466323;                                     gr-mfaktc
   May 29, 2021   n=229549: 1979476283829342031;                                    gr-mfaktc
   May 29, 2021   n=229627: 190740618900172049;                                     gr-mfaktc
   May 29, 2021   n=229631: 437239814010372563;                                     gr-mfaktc
   May 29, 2021   n=229763: 1860799902294640787;                                    gr-mfaktc
   May 29, 2021   n=229771: 967687791963421729;                                     gr-mfaktc


-  Found by Kurt Beschorner                         
   May 28, 2021   n = 9315: 1979969702769616223206181829684818071;                  ecm: B1 = 3e6; sigma = 0:8529503709117214  

      
-  Found by Kurt Beschorner                         
   May 27, 2021   n=64260L: 6622965059352315389973181;                              ecm: B1 = 1e6; sigma = 0:17596343613092824574  
   May 27, 2021   n=228077: 94192546200714569;                                      gr-mfaktc 
   May 27, 2021   n=228139: 1374856240189138013;                                    gr-mfaktc 
   May 27, 2021   n=228203: 3548885022024523031;                                    gr-mfaktc 
   May 27, 2021   n=228353: 673783478249915641;                                     gr-mfaktc 
   May 27, 2021   n=228577: 625813082621162693;                                     gr-mfaktc 
   May 27, 2021   n=228581: 238830631022126917;                                     gr-mfaktc 
   May 27, 2021   n=228587: 3296141936466731921;                                    gr-mfaktc 
   May 27, 2021   n=228593: 4726383715694368471;                                    gr-mfaktc 
   May 27, 2021   n=228619: 5605249366191505391;                                    gr-mfaktc 
   May 27, 2021   n=228737: 7974300034061926277;                                    gr-mfaktc 
   May 27, 2021   n=228841: 8817512666875110893;                                    gr-mfaktc 
   May 27, 2021   n=228869: 541100869023505517;                                     gr-mfaktc 
   May 27, 2021   n=228869: 984479243838930677;                                     gr-mfaktc 
   May 27, 2021   n=228953: 5156302757530016359;                                    gr-mfaktc
   
   
-  Found by Kurt Beschorner 
   May 22, 2021   n =16667: 3947239369512426079 * 1052426686......c14245;           ecm: B1 = 5e4; sigma = 0:954925097974726 
   May 22, 2021   n=150003: 13429267242949059517;                                   ecm: B1 = 5e4; sigma = 0:3101963270112704 


-  Found by Kurt Beschorner        
   May 19, 2021   n=100037: 29637670240923588791513413;                             ecm: B1 = 5e4; sigma = 0:4048588861662294
   May 19, 2021   n=227053: 15467400284016675311;                                   gr-mfaktc
   May 19, 2021   n=227089: 136467873861783077;                                     gr-mfaktc
   May 19, 2021   n=227399: 247033911979333729;                                     gr-mfaktc
   May 19, 2021   n=227419: 1137737547523054921;                                    gr-mfaktc
   May 19, 2021   n=227471: 1211892962522104609;                                    gr-mfaktc
   May 19, 2021   n=227489: 2482595654373204329;                                    gr-mfaktc
   May 19, 2021   n=227533: 75246664153403641;                                      gr-mfaktc
   May 19, 2021   n=227627: 629676137742006991;                                     gr-mfaktc
   May 19, 2021   n=227653: 4560148890672159563;                                    gr-mfaktc
   May 19, 2021   n=227707: 8065404759495333031;                                    gr-mfaktc
   May 19, 2021   n=227797: 299215061031313439;                                     gr-mfaktc
   May 19, 2021   n=227951: 5884508779162389203;                                    gr-mfaktc
   May 19, 2021   n=227989: 539450085886803323;                                     gr-mfaktc

 
-  Found by Yousuke Koide  
   May 15, 2021   n =1620L: 216228542818328308783433809596084627890392881018159564738348653328755727601; SNFS 


-  Found by Kurt Beschorner 
   May 13, 2021   n = 6001: 4891012142136348517404673727015993959;                  ecm: B1 = 1e6; sigma =0:6324268175647661 

       
-  Serge Batalov, Ryan Propper
   May 09, 2021   n=8177207 is probable prime - congratulations!
                  see: https://mersenneforum.org/showthread.php?p=578079#post578079

ECM efforts
with Rn: 1 < n < 2000 (Aug 03, 2021)	with Rn: 1999 < n < 3000 (Jul 23, 2021)
with Rn: 2999 < n < 4000 (Jul 23, 2021)	with Rn: 3999 < n < 5000 (Jul 23, 2019)
with Rn: 4999 < n < 6000 (Jul 23, 2021)	with Rn: 5999 < n < 7000 (Jul 26, 2021)
with Rn: 6999 < n < 8000 (Jul 26, 2021)	with Rn: 7999 < n < 9000 (Jul 23, 2021)
with Rn: 8999 < n <10000 (Jul 23, 2021)	with Rn: 9999 < n <11000 (Jul 23, 2021)
with Rn: 10999 < n <12000 (Jul 23, 2021)	with Rn: 11999 < n <14980L/M (Aug 03, 2021)

currently ECM-efforts by yoyo@home: ecm-curves
B1 = 43e6/8600 curves/ numbers < 1001 digits	1255 working	1463 working	1475 working	7980L working	8460M working
B1 = 11e7/18400 curves/ numbers < 701 digits	611 working	617 working	619 working	625 working	641 working
B1 = 26e7/46000 curves/ numbers < 450 digits	469 working	475 working	521 working	1136 working	1160 working
B1 = 85e7/75000 curves/ numbers < 250 digits	609 working	735 working	1188 working	1200 working	1320 working

Factorizations
Repunits: R1 - R2500 (Jul 28, 2021)	Repunits: R2501 - R5000 (Jun 17, 2021)
Repunits: R5001 - R7500 (Jul 26, 2021)	Repunits: R7501 - R10000 (May 28, 2021)
Repunits: R10001 - R12500 (Jun 11, 2021)	Repunits: R12501 - R14980L/M (Sep 19, 2020)

Rprime project; base 10

last update: Jun 11, 2021

old project page - out of date

Status: 3 - 1M 1M - 2M 2M - 3M 3M - 4M 4M - 5M 5M - 6M 6M - 7M 7M - 8M 8M - 9M 9M - 10M
Details: 3 - 1M 1M - 2M 2M - 3M 3M - 4M 4M - 5M 5M - 6M 6M - 7M 7M - 8M 8M - 9M 9M - 10M

active members:
- Danilo Nitsche, Paul Bourdelais , Benjamin Chaffin, Edo Rajh, Kurt Beschorner

Activities of Ryan Propper and Serge Batalov
- testing of all rprimes from exponent 10M up to 12M using TF (64 bits; evantually 67 - 68 bits)
- check of the remaining rprimes (without found factors) for primilarity (prp)

all contributors: Danilo Nitsche, Paul Bourdelais, Charles, Bo Chen, Alfred Eichhorn, FactorDB.com, Giovanni Di Maria, Fan Ming,
Phil, Richard Kapek, kkmrkkblmbrbk (aka GP2), 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)
- 10ˆ7500000	R5794777 = PRP S. Batalov - Ryan Propper (Apr 2021)
- 10ˆ10000000	R8177207 = PRP S. Batalov - Ryan Propper (May 2021)

Visitors since Oct 27, 2020: zur Webseite

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

related links news ecm efforts currently efforts by YOYO factor tables Rprime project

Related links:

News

Rprime project; base 10

last update: Jun 11, 2021

old project page - out of date

Status: 3 - 1M 1M - 2M 2M - 3M 3M - 4M 4M - 5M 5M - 6M 6M - 7M 7M - 8M 8M - 9M 9M - 10M
Details: 3 - 1M 1M - 2M 2M - 3M 3M - 4M 4M - 5M 5M - 6M 6M - 7M 7M - 8M 8M - 9M 9M - 10M

active members:
- Danilo Nitsche, Paul Bourdelais , Benjamin Chaffin, Edo Rajh, Kurt Beschorner

Activities of Ryan Propper and Serge Batalov
- testing of all rprimes from exponent 10M up to 12M using TF (64 bits; evantually 67 - 68 bits)
- check of the remaining rprimes (without found factors) for primilarity (prp)

all contributors: Danilo Nitsche, Paul Bourdelais, Charles, Bo Chen, Alfred Eichhorn, FactorDB.com, Giovanni Di Maria, Fan Ming,
Phil, Richard Kapek, kkmrkkblmbrbk (aka GP2), Pavlos, Edo Rajh, Alfred Reich, Nejc Skoberne, Sebastian, MattStath,
Maksym Voznyy, wims, Kurt Beschorner

Overview

Top of page

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

related links news ecm efforts currently efforts by YOYO factor tables Rprime project

Related links:

News

Rprime project; base 10

last update: Jun 11, 2021

old project page - out of date Status: 3 - 1M 1M - 2M 2M - 3M 3M - 4M 4M - 5M 5M - 6M 6M - 7M 7M - 8M 8M - 9M 9M - 10M Details: 3 - 1M 1M - 2M 2M - 3M 3M - 4M 4M - 5M 5M - 6M 6M - 7M 7M - 8M 8M - 9M 9M - 10M

active members: - Danilo Nitsche, Paul Bourdelais , Benjamin Chaffin, Edo Rajh, Kurt Beschorner

Activities of Ryan Propper and Serge Batalov - testing of all rprimes from exponent 10M up to 12M using TF (64 bits; evantually 67 - 68 bits) - check of the remaining rprimes (without found factors) for primilarity (prp)

all contributors: Danilo Nitsche, Paul Bourdelais, Charles, Bo Chen, Alfred Eichhorn, FactorDB.com, Giovanni Di Maria, Fan Ming, Phil, Richard Kapek, kkmrkkblmbrbk (aka GP2), Pavlos, Edo Rajh, Alfred Reich, Nejc Skoberne, Sebastian, MattStath, Maksym Voznyy, wims, Kurt Beschorner

Overview

Top of page

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

old project page - out of date

Status: 3 - 1M 1M - 2M 2M - 3M 3M - 4M 4M - 5M 5M - 6M 6M - 7M 7M - 8M 8M - 9M 9M - 10M
Details: 3 - 1M 1M - 2M 2M - 3M 3M - 4M 4M - 5M 5M - 6M 6M - 7M 7M - 8M 8M - 9M 9M - 10M

active members:
- Danilo Nitsche, Paul Bourdelais , Benjamin Chaffin, Edo Rajh, Kurt Beschorner

Activities of Ryan Propper and Serge Batalov
- testing of all rprimes from exponent 10M up to 12M using TF (64 bits; evantually 67 - 68 bits)
- check of the remaining rprimes (without found factors) for primilarity (prp)

all contributors: Danilo Nitsche, Paul Bourdelais, Charles, Bo Chen, Alfred Eichhorn, FactorDB.com, Giovanni Di Maria, Fan Ming,
Phil, Richard Kapek, kkmrkkblmbrbk (aka GP2), Pavlos, Edo Rajh, Alfred Reich, Nejc Skoberne, Sebastian, MattStath,
Maksym Voznyy, wims, Kurt Beschorner