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


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News

-  Last update: May 27, 2020                                      

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   May 24, 2020   R459, c221; SNFS-difficult = 306 
                  last msieve-extract: 
                     commencing linear algebra
                     matrix is 49114833 x 49115010 (24803.7 MB) with weight 7031998278 (143.17/col)
                     sparse part has weight 5961868268 (121.39/col)
                     commencing Lanczos iteration (16 threads)
                     linear algebra completed 8200000 of 49.1M dimensions (16.8%, ETA 1445h)
    

-  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 
   May 24, 2020   R1740M, c204, GNFS: the R507-polynom was created by Maksym Voznyy - thanks!
                  160M unique relations and 306M unique ideals are collected           
                  currently progress ~ 22 %:    


-  Found by Kurt Beschorner 
   Dec 03, 2019   n = 9013: 1232659648200408834362715471709133;                    B1= 1e6;  sigma = 0:5076496851656937  
   Apr 15, 2020   n = 9029: 1635319120734576358170774369706363;                    B1= 1e6;  sigma = 0:8793739683518911
   Apr 16, 2020   n=299912: 4280532734261684449;                                   B1= 11e3; sigma = 6007364260174254
   Apr 24, 2020   n=299927: 141209565729862067;                                    B1= 11e3; sigma = 6202532062032653
   May 26, 2020   n = 9089: 30418264146162968969429117;                            B1= 1e6;  sigma = 4274930699985848 
   

-  Found by Bo Chen
   Jul 03, 2019   n = 2029: 245013714487726159144720326081715348604363;            B1= 11e6; sigma = 0:12332245062534318460
      

-  Found by ECMNET/Sam Wagstaff
   Oct 03, 2019   n =1420M: 101956533794009284800765131459172391943780858147641273764890861; ecm 
   Feb 21, 2020   n =  337: 906533749251005245151122204670351312590267105760052002862150546121; ecm 
 
  
-  Found by Alfred Eichhorn 
   Jan 15, 2020   n =97177: 124424728162215845811053 * 8929986245......c97153;     B1=11e3; sigma = 0:6685918159451668  
   Jan 17, 2020   n =29833:  128655998212688048074613 * 8636294665......c29809;    B1= 5e4; sigma = 0:446141662229075
   Jan 17, 2020   n =97259:  29785997862163373826283 * 3730313539......c97236;     B1=11e3; sigma = 6073594763329655 
   Jan 25, 2020   n =29921:  7944266590085209407558043 * 1398632710......c29896;   B1= 5e4; sigma = 0:6295422506612517
   Jan 25, 2020   n =97441:  23531831922463159019363 * 4721736559......c97418;     B1=11e3; sigma = 0:572757438078828  
   Jan 25, 2020   n =97499:  909976776008901087671 * 1221032382......c97478;       B1=11e3; sigma = 0:6268074457992331   
   Feb 07, 2020   n =52571:  559529051889727653062093;                             B1= 5e4; sigma = 7455767888265547
   Feb 07, 2020   n =52571:  20517054941520442699702643 * 9678762390......c52521;  B1= 5e4; sigma = 4740502804702800   
   Feb 07, 2020   n =52639:  15711934104819221807719 * 7071765345......c52616;     B1= 5e4; sigma = 6804711781004988
   Feb 18, 2020   n =52901:  123916442620826244778132831 * 8966615629......c52874; B1= 5e4; sigma = 3330132924706343    
   Mar 11, 2020   n =30557:  488739274086097811461190161 * 2273423009......c30530; B1= 5e4; sigma = 2893196195929023
   Apr 24, 2020   n =90187:  5511973860992747650969729 * 2015813461......c90162;   B1= 5e4; sigma = 0:3080777569154888 
   Apr 28, 2020   n =31489:  1075970182610939077766201 * 1032659760......c31465;   B1= 5e4; sigma = 2795030700556035
   Apr 28, 2020   n =31567:  89467776154704014686769 * 4570952559......c31523;     B1= 5e4; sigma = 867681213623428
   Apr 28, 2020   n =31601:  8700549863923556796754027 * 1277058494......c31576;   B1= 5e4; sigma = 0:8761566935674878  
   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
   

-  Correction: find out by Makoto Kamada
   Apr 22, 2020  false:         n = 6881: ......c5840  
   Apr 22, 2020  correct:       n = 6881: ......prp5840  
- 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 NFS@home Oct 13, 2019 n = 626: 589855742530873303648997100606906463934277315614405401704255573694516882878454393085805024793769310885400567; SNFS - Found by YOYO@home YOYO@home/[P3D] Crashtest Feb 14, 2020 n =2580L: 3209681398615442534074101309775547494759396015886801499169945861; B1= 85e7; sigma = 0:1524063036262106663 YOYO@home/Beyond Feb 23, 2020 n = 1233: 82953452943096961359732993332153506983079; B1= 43e6; sigma = 0:10297922851821278427 YOYO@home/cellman May 19, 2020 n = 1233: 2071133703625587214227323104568507030381670852043; B1= 43e6; sigma = 0:12155937095413581933


ECM efforts
with Rn:      323 < n < 2000 (May 19, 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 (Oct 30, 2019)
with Rn:     8999 < n <10000 (May 26, 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 (May 19, 2020) Repunits:  R2501 - R5000 (Feb 14, 2020)
Repunits: R5001   - R7500 (Apr 22, 2020) Repunits: R7501 - R10000 (May 26, 2020)
Repunits: R10001 - R12500 (Jun 12, 2019) Repunits: R12540LM - R14980LM (Apr 13, 2019)




Rprime project; base 10

last update: May 04, 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 4148813     no further probable primes




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