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


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News

-  Last update: Mar 29, 2020                      

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Mar 29, 2020   R459, c221; SNFS-difficult = 306 
                  726M unique relations and 614M unique ideals are collected
                  unique rels / unique ideals: 1.182 
                  currently progress ~ 97%:                     
                  last msieve-extract: 
                     begin with 726012301 relations and 613941599 unique ideals
                     reduce to 174033584 relations and 170979899 ideals in 5 passes
                     found 50032169 cycles, need 49989416
                     weight of 49989416 cycles is about 6499345056 (130.01/cycle)
                  matrix-size: 49989416; the matrix is still a bit too big
                  

-  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 
                  R1740M, c204, GNFS: the R507-polynom was created by Maksym Voznyy - thanks!
                  5.3M unique relations and 28.8M unique ideals are collected           
                  currently progress ~ 0.7%:    


-  Found by Kurt Beschorner 
   Sep 28, 2019   n =8940M: 2647733864525435357868825323065594021;                 B1= 11e6; sigma = 2165451346
   Oct 14, 2019   n = 1417: 55931448966246130071538810222836707;                   B1= 11e6; sigma = 3780116918
   Dec 03, 2019   n = 9013: 1232659648200408834362715471709133;                    B1= 1e6;  sigma = 0:5076496851656937  
         

-  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 
   Oct 31, 2019   n =93001: 12570832586559636779231 * 8838802867......c92978;      B1=11e3; sigma = 3743076398710936781
   Nov 21, 2019   n =93827: 2544410332113800320497347 * 4366870771......c93802;    B1=11e3; sigma = 4336063350918828 
   Dec 15, 2019   n =52147: 1060978174020566009811787 * 1047251619......c52123;    B1= 5e4; sigma = 329756761546524
   Dec 17, 2019   n =95443: 2110314549471605025311723 * 5265144532......c95418;    B1=11e3; sigma = 5404124221991931
   Dec 24, 2019   n =52223: 5706344809886297017064443 * 2687544852......c52176;    B1= 5e4; sigma = 6672244074087398 
   Dec 31, 2019   n =52321: 37683103967057351697462641 * 2948565787......c52295;   B1= 5e4; sigma = 1086750337276893
   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
        

-  Found by NFS@home 
   Oct 13, 2019   n =  626: 589855742530873303648997100606906463934277315614405401704255573694516882878454393085805024793769310885400567; SNFS 
   
   
-  Found by Alfred Reich 
   Jun 11, 2019   n = 3013: 54801984828194245177182941528875876754999;             ecm
   Jun 11, 2019   n = 3375: 9928227087054120839404714671321001;                    ecm
   Jun 11, 2019   n = 3763: 33819951029015563544261960393215363;                   ecm
   Jun 11, 2019   n = 4005: 1867328658390232232662140183278161;                    ecm
   Jun 11, 2019   n = 4541: 3490250651625330786758706967866961;                    ecm

     
-  Found by YOYO@home 
   YOYO@home/Danny    
   Aug 06, 2019   n =2380M: 55722909386297024938297392343519300689842174503366122181; B1= 26e7; sigma = 0:2377822517027304999     
   
   YOYO@home/Henric   
   Oct 16, 2019   n = 1357: 800551567150597779248843185551955662432161;            B1= 11e6; sigma = 0:13842388686??30632     
   
   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      
                             


ECM efforts
with Rn:      323 < n < 2000 (Mar 27, 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 (Mar 27, 2020)
with Rn:     6999 < n < 8000 (JuL 16, 2019) with Rn:     7999 < n < 9000 (Oct 30, 2019)
with Rn:     8999 < n <10000 (Feb 24, 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
621
working
675
working



Factorizations
Repunits: R1        - R2500 (Feb 23, 2020) Repunits:  R2501 - R5000 (Feb 14, 2020)
Repunits: R5001   - R7500 (Jun 16, 2019) Repunits: R7501 - R10000 (Dec 03, 2019)
Repunits: R10001 - R12500 (Jun 12, 2019) Repunits: R12540LM - R14980LM (Apr 13, 2019)




Rprime project; base 10

last update: Mar 03, 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 4094317     no further probable primes




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