Factorizations of Repunit Numbers

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

News

-  Last update: May 13, 2021          

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

    
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   May 12, 2021   R1008, c249, SNFS-difficult = 288 
                  219M unique r. relations and 402M unique ideals are collected
                  currently progress ~ 30%;    
                  
                  
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   May 12, 2021   R1740M, c204, GNFS:
                  - msieve-filtering: well done
                  - msieve-linear algebra completed 17500000 of 49514384 dimensions (ETA 1058 hours)
                  - I think we found a good balance between the number of unique r. relations and the matrix size 
                  - msieve-log-file:
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                    

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


-  Found by Alfred Eichhorn 
   May 07, 2021   n= 59351: 2460450677754144414887557 * 4515884513......c59326;     ecm: B1 = 5e4; sigma = 0:4294405550077682 
   May 07, 2021   n= 95527: 13955681448587740311701347 * 1280603465......c95478;    ecm: B1 = 5e4; sigma = 0:2908964832870371


-  Found by Kurt Beschorner 
   May 07, 2021   n=11220M: 16930380233308606707892880902447984978624096501;        ecm: B1 =43e6; sigma = 0:863078287696667 
   May 07, 2021   n=100019: 2369446454946296317873849 * 3954505151......c99962;     ecm: B1 = 5e4; sigma = 0:411156440346518 


-  Found by Kurt Beschorner 
   May 02, 2021   n = 6079: 61182767215009075574812972501787;                       ecm: B1 = 1e6; sigma = 0:6573795364083891  
   May 02, 2021   n =12519: 4142429561097371437530391 * 1204600084......c7589;      Prime95: B1 = 1e6; sigma = 6003805306615619 
   May 02, 2021   n=150003: 13429267242949059517;                                   Prime95: B1 = 5e4; sigma = 5440031747720602 

     
-  Found by Kurt Beschorner 
   Apr 27, 2021   n=226007: 4096985547143801107;                                    gr-mfaktc
   Apr 27, 2021   n=226013: 1749160943839460111;                                    gr-mfaktc
   Apr 27, 2021   n=226169: 11491302653436030881;                                   gr-mfaktc
   Apr 27, 2021   n=226183: 75615602414169361;                                      gr-mfaktc
   Apr 27, 2021   n=226367: 190357122644312707;                                     gr-mfaktc
   Apr 27, 2021   n=226379: 12140022886817374639;                                   gr-mfaktc
   Apr 27, 2021   n=226549: 4783052383654238671;                                    gr-mfaktc
   Apr 27, 2021   n=226609: 1782390671362612489;                                    gr-mfaktc
   Apr 27, 2021   n=226777: 378193188098520601;                                     gr-mfaktc
   Apr 27, 2021   n=226799: 84991215983418883;                                      gr-mfaktc
   Apr 27, 2021   n=226871: 75049647428960723;                                      gr-mfaktc
   Apr 27, 2021   n=226991: 379669865999843813;                                     gr-mfaktc


-  Found by Alfred Eichhorn 
   Apr 26, 2021   n =40351: 41361445978979438195400493 * 2686344939......c40325;    ecm: B1 = 5e4; sigma = 0:7786469976376711  


-  Found by Kurt Beschorner 
   Apr 26, 2021   n = 6073: 4192625020954268448085694062613;                        ecm: B1 = 1e6; sigma = 0:7615054103756595 
   Apr 26, 2021   n =70004: 553846660793381209;                                     ecm: B1 =25e4; sigma = 3113211770127235
   Apr 26, 2021   n=100012: 194864129920036674366721 * 6637236146......c45387;      ecm: B1 =25e4; sigma = 0:3712397564149538
   

-  YOYO@home/DRPanther 
   Apr 23, 2021   n =  485: 3905050584750719584997916596589271839372757118110949321; ecm: B1 = 26e7; sigma = 0:13910476698621796582 
 
         
-  Serge Batalov, Ryan Propper
   Apr 20, 2021   n=5794777 is probable prime - congratulations!
                  see: https://mersenneforum.org/showthread.php?t=26719
                  It is not known whether there are between exponents 4300447 and 5794777 other rprimes 


-  Found by Kurt Beschorner 
   Apr 16, 2021   n = 6047: 15726038561834089683346100723;                          ecm: B1 = 1e6; sigma = 0:3954038962062933 
   Apr 16, 2021   n = 6047: 55601862060496756187615026748638027;                    ecm: B1 = 1e6; sigma = 0:7983712199898554   
   Apr 16, 2021   n =12507: 60416314772560190835246784695757 * 3606042102......c7470; ecm: B1 = 1e6; sigma = 0:8282807134168857 
   Apr 16, 2021   n =19525: 1252208919866796487751 * 4056432245......c13961;        ecm: B1 = 5e4; sigma = 4539103865474074 
   Apr 16, 2021   n =97625: 188114671994937753430312751;                            ecm: B1 = 5e4; sigma = 0:6891315861581545  
   Apr 16, 2021   n=224033: 8413719147198343369;                                    gr-mfaktc
   Apr 16, 2021   n=224047: 1580226132429404483;                                    gr-mfaktc
   Apr 16, 2021   n=224101: 9199687762655955401;                                    gr-mfaktc
   Apr 16, 2021   n=224209: 7376612001366597239;                                    gr-mfaktc
   Apr 16, 2021   n=224233: 2148033672261722761;                                    gr-mfaktc
   Apr 16, 2021   n=224251: 5881042730274935681;                                    gr-mfaktc
   Apr 16, 2021   n=224267: 11508449042404230199;                                   gr-mfaktc
   Apr 16, 2021   n=224309: 806019344878636601;                                     gr-mfaktc
   Apr 16, 2021   n=224449: 348516204990509557;                                     gr-mfaktc
   Apr 16, 2021   n=224737: 178682103504143123;                                     gr-mfaktc
   Apr 16, 2021   n=224813: 2233964174952416717;                                    gr-mfaktc
   Apr 16, 2021   n=225161: 945106445733686281;                                     gr-mfaktc
   Apr 16, 2021   n=225227: 2104622090878328843;                                    gr-mfaktc
   Apr 16, 2021   n=225353: 7307600761666111601;                                    gr-mfaktc
   Apr 16, 2021   n=225373: 974339825755665601;                                     gr-mfaktc
   Apr 16, 2021   n=225509: 213743166541889773;                                     gr-mfaktc
   Apr 16, 2021   n=225523: 82959711460243883;                                      gr-mfaktc
   Apr 16, 2021   n=225581: 12687816497137019591;                                   gr-mfaktc
   Apr 16, 2021   n=225637: 115075555092146347;                                     gr-mfaktc
   Apr 16, 2021   n=225721: 143204535436858963;                                     gr-mfaktc
   Apr 16, 2021   n=225769: 235775674520884439;                                     gr-mfaktc
   Apr 16, 2021   n=225889: 335262685529613551;                                     gr-mfaktc

 
-  Found by Alfred Eichhorn 
   Apr 13, 2021   n =40289: 861341134157064323034529 * 1289977997......c40265;      ecm: B1 = 5e4; sigma = 7301371137223312  


-  Found by Kurt Beschorner 
   Apr 13, 2021   n =12507: 799466547815794573409504041 * 2178637747......c7502;    ecm: B1 = 1e6; sigma = 0:633755798596697 


-  Found by Kurt Beschorner 
   Apr 12, 2021   n = 1285: 16125873110496868884553362758627283290407985434481 * 2893837681......P922; ecm: B1 =43e6; sigma = 0:8766000215669500 
   Apr 12, 2021   n =18812: 17057447125458406802349961 * 5558959398......c9340;     ecm:     B1 =25e4; sigma = 0:978503384498149  


-  Found by Kurt Beschorner 
   Apr 07, 2021   n =12507: 1995095101053242532179551 * 1741747998......c7529;      ecm:     B1 = 1e6; sigma = 2060213348392852  
   Apr 07, 2021   n=150001: 393118534934461079 * 3623568004......c149976;           Prime95: B1 = 1e6; sigma = 6780472448998231 
   Apr 07, 2021   n=222107: 105497433013879409;                                     gr-mfaktc
   Apr 07, 2021   n=222323: 5173343292703218209;                                    gr-mfaktc
   Apr 07, 2021   n=222329: 228636709971904163;                                     gr-mfaktc
   Apr 07, 2021   n=222367: 6923539429746581911;                                    gr-mfaktc
   Apr 07, 2021   n=222493: 604572265759833641;                                     gr-mfaktc
   Apr 07, 2021   n=222601: 328259257873588999;                                     gr-mfaktc
   Apr 07, 2021   n=222799: 576922891852245791;                                     gr-mfaktc
   Apr 07, 2021   n=222823: 6811293491968284601;                                    gr-mfaktc
   Apr 07, 2021   n=222953: 503654209714706867;                                     gr-mfaktc
   Apr 07, 2021   n=222979: 1662163092024441493;                                    gr-mfaktc
   Apr 07, 2021   n=223049: 2862340440158492933;                                    gr-mfaktc
   Apr 07, 2021   n=223229: 14466968209954984123;                                   gr-mfaktc
   Apr 07, 2021   n=223367: 2608226886855414791;                                    gr-mfaktc
   Apr 07, 2021   n=223711: 1441207977103906159;                                    gr-mfaktc
   Apr 07, 2021   n=223757: 785618164779654641;                                     gr-mfaktc
   Apr 07, 2021   n=223781: 1175927490682718237;                                    gr-mfaktc
   Apr 07, 2021   n=223849: 272482638327241249;                                     gr-mfaktc
   Apr 07, 2021   n=223921: 1076535960856348711;                                    gr-mfaktc

-  Found by Kurt Beschorner 
   Apr 03, 2021   n =20001: 131917264692353678368249438519 * 3385514184......c12923; ecm: B1 =25e4; sigma = 0:284690055275574  
   

-  Found by Kurt Beschorner 
   Apr 01, 2021   n =12505: 895207758250401992676289744561 * 4090092249...c9560;    ecm: B1 = 1e6; sigma = 0:4631770911328880  
   Apr 01, 2021   n =19893: 162887837523447121255604881 * 6097680711......c12483;   ecm: B1 =25e4; sigma = 0:6038576895983461    
   Apr 01, 2021   n=100007: 59484631881686555439227 * 2521479011......c98852;       ecm: B1 = 5e4; sigma = 0:1784171070427286  
   Apr 01, 2021   n=220141: 465305480620402759;                                     gr-mfaktc
   Apr 01, 2021   n=220169: 925561132383830053;                                     gr-mfaktc
   Apr 01, 2021   n=220177: 1902193122450285307;                                    gr-mfaktc
   Apr 01, 2021   n=220243: 529581123289169293;                                     gr-mfaktc
   Apr 01, 2021   n=220589: 433845254277255893;                                     gr-mfaktc
   Apr 01, 2021   n=220757: 723017486623244089;                                     gr-mfaktc
   Apr 01, 2021   n=220757: 1238844447052010483;                                    gr-mfaktc
   Apr 01, 2021   n=220771: 250805438525074679;                                     gr-mfaktc
   Apr 01, 2021   n=220811: 1937671020624853601;                                    gr-mfaktc
   Apr 01, 2021   n=220903: 172785003750913003;                                     gr-mfaktc
   Apr 01, 2021   n=221047: 15169474912038495119;                                   gr-mfaktc
   Apr 01, 2021   n=221101: 407125505561229361;                                     gr-mfaktc
   Apr 01, 2021   n=221101: 3535939223405258471;                                    gr-mfaktc
   Apr 01, 2021   n=221281: 18388940488682412533;                                   gr-mfaktc
   Apr 01, 2021   n=221411: 73648296792386929;                                      gr-mfaktc
   Apr 01, 2021   n=221461: 5136406953298928441;                                    gr-mfaktc
   Apr 01, 2021   n=221497: 2740775806421328119;                                    gr-mfaktc
   Apr 01, 2021   n=221659: 132654430076122627;                                     gr-mfaktc
   Apr 01, 2021   n=221729: 119838327663140717;                                     gr-mfaktc
   Apr 01, 2021   n=221953: 874763746343211227;                                     gr-mfaktc
 

-  Found by Alfred Eichhorn 
   Mar 28, 2021   n =39989: 284793838539222508987728986561 * 3901457688......c39959; ecm: B1 = 5e4; sigma = 9042961611972796  
   Mar 28, 2021   n =40031: 15528140726021009080339759 * 3315212522......c39983;     ecm: B1 = 5e4; sigma = 2446785030476167


-  Found by Kurt Beschorner 
   Mar 26, 2021   n = 9285: 121167118788342318909335442231775438016191 * 2226782692......c4893; ecm: B1 = 3e6; sigma = 0:5397596929722729

-  Found by Kurt Beschorner 
   Mar 24, 2021   n = 2231: 127269517286008733272752480463187 * 7008647119......c1970;    ecm: B1 =11e6; sigma = 0:2945844318283144  


-  Found by Kurt Beschorner 
   Mar 23, 2021   n = 6029: 459714139684213098474058511602532231 * 3103904642......c5972; ecm: B1 = 1e6; sigma = 0:5767151061
   Mar 23, 2021   n =12255: 4897985075684847789326555366233201 * 1079448216......c5988;   ecm: B1 = 1e6; sigma = 0:8775605246208353 
   Mar 23, 2021   n =14291: 6039237541399466426719 * 1490254347......c13779;        ecm: B1 = 5e4; sigma = 3513949041793941  
   Mar 23, 2021   n=218357: 2690881573780188277;                                    gr-mfaktc
   Mar 23, 2021   n=218423: 142604952511460837;                                     gr-mfaktc
   Mar 23, 2021   n=218437: 3630746879089334951;                                    gr-mfaktc
   Mar 23, 2021   n=218447: 187571225207482481;                                     gr-mfaktc
   Mar 23, 2021   n=218453: 6466974568295418449;                                    gr-mfaktc
   Mar 23, 2021   n=218579: 2308667747769448547;                                    gr-mfaktc
   Mar 23, 2021   n=218737: 1259089952831991481;                                    gr-mfaktc
   Mar 23, 2021   n=218849: 748394254720802201;                                     gr-mfaktc
   Mar 23, 2021   n=219019: 581568790783580801;                                     gr-mfaktc    
   Mar 23, 2021   n=219059: 324375436583765803;                                     gr-mfaktc    
   Mar 23, 2021   n=219097: 216806336018574361;                                     gr-mfaktc    
   Mar 23, 2021   n=219119: 76221314990483053;                                      gr-mfaktc    
   Mar 23, 2021   n=219217: 359932060960957879;                                     gr-mfaktc    
   Mar 23, 2021   n=219437: 1088226020470197013;                                    gr-mfaktc    
   Mar 23, 2021   n=219523: 743459349217286249;                                     gr-mfaktc    
   Mar 23, 2021   n=219851: 6201071715484499239;                                    gr-mfaktc    
   Mar 23, 2021   n=219881: 2040172648096777787;                                    gr-mfaktc    
   Mar 23, 2021   n=219937: 3068762748834315893;                                    gr-mfaktc   
  

-  Found by Kurt Beschorner 
   Mar 19, 2021   n =17509: 32231159497750136397559 * 6435717701......c17443;       ecm: B1 = 5e4; sigma = 0:6831872783432326
   Mar 19, 2021   n =33344: 14555126684990568267049793 * 6870431440......c16615;    ecm: B1 =25e4; sigma = 860331931532703


-  Found by Kurt Beschorner 
   Mar 17, 2021   n=216061: 444294179035386679;                                     gr-mfaktc
   Mar 17, 2021   n=216173: 2620145763709472083;                                    gr-mfaktc
   Mar 17, 2021   n=216173: 4492558041766676551;                                    gr-mfaktc
   Mar 17, 2021   n=216217: 79272808155104089;                                      gr-mfaktc
   Mar 17, 2021   n=216259: 481206912003367973;                                     gr-mfaktc
   Mar 17, 2021   n=216263: 6713050763412206831;                                    gr-mfaktc
   Mar 17, 2021   n=216289: 242877599855516081;                                     gr-mfaktc
   Mar 17, 2021   n=216397: 918570902304602483;                                     gr-mfaktc
   Mar 17, 2021   n=216553: 1056821536320251609;                                    gr-mfaktc
   Mar 17, 2021   n=216607: 280177866272310089;                                     gr-mfaktc
   Mar 17, 2021   n=216791: 112237611780555067;                                     gr-mfaktc
   Mar 17, 2021   n=216803: 1221839307263193919;                                    gr-mfaktc
   Mar 17, 2021   n=216841: 265297751967254843;                                     gr-mfaktc
   Mar 17, 2021   n=216901: 83010407277496357;                                      gr-mfaktc
   Mar 17, 2021   n=216919: 612630691893583483;                                     gr-mfaktc
   Mar 17, 2021   n=216919: 5648418101747030627;                                    gr-mfaktc
   Mar 17, 2021   n=216967: 2212548886227952523;                                    gr-mfaktc
   Mar 17, 2021   n=216991: 580775976090633203;                                     gr-mfaktc
   Mar 17, 2021   n=217241: 5525663368197964493;                                    gr-mfaktc
   Mar 17, 2021   n=217333: 1303822388089141169;                                    gr-mfaktc
   Mar 17, 2021   n=217337: 131154899865549871;                                     gr-mfaktc
   Mar 17, 2021   n=217351: 3307729271035393999;                                    gr-mfaktc
   Mar 17, 2021   n=217361: 470796671813983213;                                     gr-mfaktc
   Mar 17, 2021   n=217409: 1273104982048073929;                                    gr-mfaktc
   Mar 17, 2021   n=217429: 1236262173601177157;                                    gr-mfaktc
   Mar 17, 2021   n=217457: 1552635369950503037;                                    gr-mfaktc
   Mar 17, 2021   n=217577: 347981830922553559;                                     gr-mfaktc
   Mar 17, 2021   n=217691: 8968429992518669293;                                    gr-mfaktc


-  Found by Alfred Eichhorn 
   Mar 15, 2021   n =39551: 127249419826060634887483 * 8731757776......c39527;      ecm: B1 = 5e4; sigma = 427721010480129  


-  Found by Kurt Beschorner 
   Mar 10, 2021   n=41460M: 42584355582188611283977899841 * 2317811797......c5459;  ecm: B1 = 1e6; sigma = 0:598575133130437                                


-  Found by Kurt Beschorner 
   Mar 09, 2021   n= 20709: 81963692022889 * 1234827143......c12491;                ecm: B1 =25e4                                
   Mar 09, 2021   n=41460M: 115221706621203870779319181 * 987025217......c5487;     Prime95: B1 = 1e6; sigma = 1195145782977316                                
   Mar 09, 2021   n=100029: 74765744916449557 * 1743797697......c66659;             Prime95: B1 = 5e4; sigma = 7101287492144763
   Mar 09, 2021   n=214517: 169849724698220431;                                     gr-mfaktc
   Mar 09, 2021   n=214559: 87609636802595987;                                      gr-mfaktc
   Mar 09, 2021   n=214771: 2714844054728703643;                                    gr-mfaktc
   Mar 09, 2021   n=214807: 189994165251144599;                                     gr-mfaktc
   Mar 09, 2021   n=214891: 813853396098087481;                                     gr-mfaktc
   Mar 09, 2021   n=215063: 8532813612588490013;                                    gr-mfaktc
   Mar 09, 2021   n=215273: 633951089398102243;                                     gr-mfaktc
   Mar 09, 2021   n=215309: 6966379602380889671;                                    gr-mfaktc
   Mar 09, 2021   n=215393: 318869250481125803;                                     gr-mfaktc
   Mar 09, 2021   n=215447: 642429912177243227;                                     gr-mfaktc
   Mar 09, 2021   n=215461: 309820478254881877;                                     gr-mfaktc
   Mar 09, 2021   n=215687: 4059623872828785997;                                    gr-mfaktc
   Mar 09, 2021   n=215689: 513375898736447293;                                     gr-mfaktc


-  Found by Kurt Beschorner 
   Mar 03, 2021   n= 15625: 27018407327495281843751 * 3701180413......c12478;       Prime95: B1=25e4; sigma = 2934847061157984     
   Mar 03, 2021   n=212501: 2611533311537741893;                                    gr-mfaktc
   Mar 03, 2021   n=212561: 81333213955703357;                                      gr-mfaktc
   Mar 03, 2021   n=212669: 1870192711203654031;                                    gr-mfaktc
   Mar 03, 2021   n=212671: 131771572842190283;                                     gr-mfaktc
   Mar 03, 2021   n=212981: 109591767200010877;                                     gr-mfaktc
   Mar 03, 2021   n=212987: 90453943927871123;                                      gr-mfaktc
   Mar 03, 2021   n=212987: 1152268668213861719;                                    gr-mfaktc
   Mar 03, 2021   n=213043: 4037359481605357883;                                    gr-mfaktc
   Mar 03, 2021   n=213253: 146443392906383203;                                     gr-mfaktc
   Mar 03, 2021   n=213289: 3713522190482076277;                                    gr-mfaktc
   Mar 03, 2021   n=213307: 574323045203972521;                                     gr-mfaktc
   Mar 03, 2021   n=213599: 88642799975401627;                                      gr-mfaktc
   Mar 03, 2021   n=213623: 4383369634089460591;                                    gr-mfaktc
   Mar 03, 2021   n=213637: 2357988751072066997;                                    gr-mfaktc
   Mar 03, 2021   n=213713: 620749908442090159;                                     gr-mfaktc
   Mar 03, 2021   n=213833: 87340218115042163;                                      gr-mfaktc
   Mar 03, 2021   n=213833: 168807630196434121;                                     gr-mfaktc
   Mar 03, 2021   n=213881: 2396838986481378227;                                    gr-mfaktc
   Mar 03, 2021   n=214043: 2080270622974631239;                                    gr-mfaktc
   Mar 03, 2021   n=214063: 280958440224711311;                                     gr-mfaktc
   Mar 03, 2021   n=214309: 5310312998658512521;                                    gr-mfaktc
   Mar 03, 2021   n=214373: 458195196789972427;                                     gr-mfaktc 


-  Found by Alfred Eichhorn 
   Mar 01, 2021   n =58411: 2539839131939281205390129 * 4374730262......c58386;     ecm: B1 = 5e4; sigma = 8976113873031808  
   Mar 01, 2021   n =94597: 2042773772655964269063455569 * 5439227417......c94569;  ecm: B1 = 5e4; sigma = 4044242220692006  
 

-  Found by Kurt Beschorner 
   Feb 28, 2021   n=100012: 780912188539783080137667658349 * 1293359246......c45411; Prime95: B1=25e4; sigma = 3175381230230104     
   Feb 28, 2021   n=100026: 1871059796165538019;                                     Prime95: B1=25e4; sigma = 2651544150559178 


-  Found by Kurt Beschorner 
   Feb 24, 2021   n=100023: 476278158633764719; ***                                 Prime95      
   *** the factor  476278158633764719 already divides n=33341;  
   Feb 24, 2021   n=211007: 16108072373966534359;                                   gr-mfaktc
   Feb 24, 2021   n=211039: 121358142140355173;                                     gr-mfaktc
   Feb 24, 2021   n=211039: 568243849419069917;                                     gr-mfaktc
   Feb 24, 2021   n=211051: 4515755453965056043;                                    gr-mfaktc
   Feb 24, 2021   n=211151: 6162081300878026519;                                    gr-mfaktc
   Feb 24, 2021   n=211153: 3668324944244154347;                                    gr-mfaktc
   Feb 24, 2021   n=211199: 313896846525745009;                                     gr-mfaktc
   Feb 24, 2021   n=211217: 5477131534499966797;                                    gr-mfaktc
   Feb 24, 2021   n=211241: 2568458580598604671;                                    gr-mfaktc
   Feb 24, 2021   n=211271: 793229446948073413;                                     gr-mfaktc
   Feb 24, 2021   n=211283: 81848684329912037;                                      gr-mfaktc
   Feb 24, 2021   n=211349: 6189509756660822797;                                    gr-mfaktc
   Feb 24, 2021   n=211711: 1336912743372801877;                                    gr-mfaktc
   Feb 24, 2021   n=211741: 2241427174247365999;                                    gr-mfaktc
   Feb 24, 2021   n=211747: 134457860930495077;                                     gr-mfaktc
   Feb 24, 2021   n=211789: 75078663858018773;                                      gr-mfaktc
   Feb 24, 2021   n=211949: 136224213331104083;                                     gr-mfaktc
   Feb 24, 2021   n=212243: 82633507966860679;                                      gr-mfaktc
   Feb 24, 2021   n=212243: 125531464465765159;                                     gr-mfaktc
   Feb 24, 2021   n=212243: 4070069162918934431;                                    gr-mfaktc


-  Found by Kurt Beschorner 
   Feb 18, 2021   n= 33338: 26473748122148971459 * 4155059551......c16361;          Prime95: B1 = 25e4; sigma = 3721822416092411  
   Feb 18, 2021   n=100006: 131222263455836422852729 * 3208425163......c48316;      Prime95: B1 = 25e4; sigma = 877451076478088 
   Feb 18, 2021   n=100008: 9738110213269872780083329;                              ecm:     B1 = 25e4; sigma = 0:921283191225905 
   Feb 18, 2021   n=210019: 294916672661938277;                                     gr-mfaktc
   Feb 18, 2021   n=210139: 8016608178255878321;                                    gr-mfaktc
   Feb 18, 2021   n=210359: 15449896569520745963;                                   gr-mfaktc
   Feb 18, 2021   n=210527: 772445233470428801;                                     gr-mfaktc
   Feb 18, 2021   n=210907: 10480618899828921959;                                   gr-mfaktc
   Feb 18, 2021   n=210961: 720606730320035333;                                     gr-mfaktc
   Feb 18, 2021   n=210967: 263914086493298321;                                     gr-mfaktc


-  Found by Alfred Eichhorn 
   Feb 16, 2021   n =58061: 18335318772409337757493627 * 6059949788......c58035;    ecm: B1 = 5e4; sigma = 4013194110374496

ECM efforts
with Rn: 323 < n < 2000 (Apr 29, 2021)	with Rn: 1999 < n < 3000 (Mar 24, 2021)
with Rn: 2999 < n < 4000 (Jun 12, 2019)	with Rn: 3999 < n < 5000 (Jun 12, 2019)
with Rn: 4999 < n < 6000 (May 10, 2021)	with Rn: 5999 < n < 7000 (May 10, 2021)
with Rn: 6999 < n < 8000 (Sep 27, 2020)	with Rn: 7999 < n < 9000 (Aug 22, 2020)
with Rn: 8999 < n <10000 (Apr 21, 2021)	with Rn: 9999 < n <11000 (Jun 12, 2019)
with Rn: 10999 < n <12000 (May 07, 2021)	with Rn: 11999 < n <12500L/M (Mar 19, 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	599 working	611 working	617 working	619 working	625 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 (Apr 26, 2021)	Repunits: R2501 - R5000 (Feb 14, 2020)
Repunits: R5001 - R7500 (May 12, 2021)	Repunits: R7501 - R10000 (Mar 26, 2021)
Repunits: R10001 - R12500 (May 07, 2021)	Repunits: R12501 - R14980L/M (Sep 19, 2020)

Rprime project; base 10

last update: May 13, 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: May 13, 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: May 13, 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