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


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News

-  Last update: Jan 24, 2020                      

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jan 22, 2020   R459, c221; SNFS-difficult = 306 
                  588M unique relations and 581M unique ideals are collected
                  unique rels / unique ideals: 1.01  
                  currently progress ~ 78%:                     
                  last msieve-extract: begin with 587319129 relations and 580906502 unique ideals
                                       reduce to 276731886 relations and 228350190 ideals in 28 passes
                                       keeping 280587931 ideals with weight <= 200, target excess is 1470342
                                       begin with 276731886 relations and 280587931 unique ideals
                                       reduce to 276563664 relations and 280419690 ideals in 18 passes
                                       max relations containing the same ideal: 200
                                       filtering wants 1000000 more relations
                  

-  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!
                  # lognorm 64.69, E 56.25, alpha -8.43 (proj -2.29), 3 real roots
                  # MurphyE(Bf=1.000e+07,Bg=5.000e+06,area=1.000e+16)=2.47e-15
                  status: ready for sieving  


-  Found by Kurt Beschorner 
   Jun 16, 2019   n =6140M: 42633651269057784211262036586055241;                   B1= 11e6; sigma = 456257847 
   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 
 
  
-  Found by Alfred Eichhorn 
   Aug 11, 2019   n =51673: 8143414287233592839653231187 * 1364429061......c51645; B1= 5e4; sigma = 7054969580827199057 
   Sep 22, 2019   n =51679: 1247742855201912541954231 * 8904968731......c51654;    B1= 5e4; sigma = 1894864779293655113               
   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 
   

-  Found by NFS@home 
   Jul 29, 2019   n =  728: 146922836547557380904624883811070801579636649582426027039761; SNFS
   Jul 29, 2019   n =  728: 1236386443286416000845205982296310762602996796920706630693450425385353425494707969; SNFS
   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 = 0:13842388622860530632     
                            


ECM efforts
with Rn:      323 < n < 2000 (Jan 06, 2020) with Rn:     1999 < n < 3000 (Dec 13, 2019)
with Rn:     2999 < n < 4000 (Jun 12, 2019) with Rn:     3999 < n < 5000 (Jun 12, 2019)
with Rn:     4999 < n < 6000 (Apr 04, 2019) with Rn:     5999 < n < 7000 (Oct 17, 2019)
with Rn:     6999 < n < 8000 (JuL 16, 2019) with Rn:     7999 < n < 9000 (Oct 30, 2019)
with Rn:     8999 < n <10000 (Jan 06, 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
997
working
1233
working
1235
working
1251
working
1255
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 (Nov 20, 2019) Repunits:  R2501 - R5000 (Jun 12, 2019)
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: Jan 24, 2020

project page   Status: 3 - 2.5M     Status: 2.5M - 5.0M     Details: 3 - 1.5M     Details: 1.5M - 3M     Details: 3M - 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)
    - 10ˆ4069771     no further probable primes




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