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


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News

-  Last update: Nov 25, 2020                                                         


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Nov 25, 2020   R337, c202, GNFS: the R337-polynom was created by Gimarel and Maksym Voznyy - thanks!
                  643M unique relations and 598M unique ideals are collected           
                  currently progress ~ 87 %:    
                  msieve-logfile abstract:
                  -> setting target matrix density to 80.0
                  -> begin with 642529014 relations and 597810038 unique ideals
                  -> found 62571840 cycles, need 62271113
                  -> matrix is 62270934 x 62271113 (21283.2 MB) with weight 6581974200 (105.70/col)
                  -> linear algebra at 0.0%, ETA 6213h38m  
                  the matrix is still too big

-  Found by Alfred Eichhorn 
   Nov 24, 2020   n =57059 77130293380876050034724747 * 5404583504......c57011;     ecm: B1= 5e4;  sigma = 8530835383246204


-  Found by Kurt Beschorner 
   Nov 24, 2020   n=299417: 15041932191962002693;                                   gr-mfaktc  
   Nov 24, 2020   n=299539: 8800946114082291853;                                    gr-mfaktc  


-  Found by Kurt Beschorner 
   Nov 21, 2020   n=299063: 2670533975255739641;                                    gr-mfaktc  
   Nov 21, 2020   n=299213: 34092711578653731803;                                   gr-mfaktc  
   Nov 21, 2020   n=299603: 415573210364120867;                                     gr-mfaktc  
   Nov 21, 2020   n=299623: 21655715883573614533;                                   gr-mfaktc

-  Found by Kurt Beschorner 
   Nov 16, 2020   n=299701: 6051293487116048203;                                    gr-mfaktc  
   Nov 16, 2020   n=299771: 1124881636397646871;                                    gr-mfaktc  
   Nov 16, 2020   n=299881: 238686970172792923;                                     gr-mfaktc  


-  Found by Alfred Eichhorn 
   Nov 11, 2020   n =35899: 903057269392419295345649 * 1230388313......c35875;      ecm: B1= 5e4;  sigma = 8689394078808867

-  Found by Sam Wagstaff 
   Nov 08, 2020   n =  371: 8443278213142643683880850952929502264137832292889910297487445526484776400899484558952278931894560501953983650020256591767199; SNFS 


-  Found by Kurt Beschorner 
   Nov 01, 2020   n = 9215: 328425918977197803434420450586471871;                   ecm: B1= 1e6;  sigma = 0:2058359928220220 


-  Found by Kurt Beschorner 
   Oct 26, 2020   n = 9139: 102323103870499479272499972352456883;                   ecm: B1= 1e6;  sigma = 0:32605637501090 


-  Found by Sam Wagstaff 
   Oct 21, 2020   n =  742: 2548171182130492354464113595833821781588064140986874348075459263402328971040215243200625902015381883224397137647; SNFS 
    

-  Found by Alfred Eichhorn 
   Oct 13, 2020   n =35251: 119046480308568500886427 * 9333422611......c35227;      ecm: B1= 5e4;  sigma = 0:620255578917684
   Oct 13, 2020   n =35363: 2931190842118437948895849 * 3790647456......c35338;     ecm: B1= 5e4;  sigma = 0:3356793723748038
   Oct 13, 2020   n =56671: 17327625606417916093196681 * 3881606412......c56626;    ecm: B1= 5e4;  sigma = 0:8039459931350690

      
-  Found by Kurt Beschorner 
   Oct 11, 2020   n=299912: 26483555133285114793;                                   ecm: B1=11e3;  sigma = 0:2255661832190991 
   Oct 11, 2020   n=299912: 107911061915460883817;                                  ecm: B1=11e3;  sigma = 0:1224499426851938


-  Found by Kurt Beschorner 
   Oct 05, 2020   n = 9097: 55502243290677967041853006539414761;                    ecm: B1= 1e6;  sigma = 0:3429806618658913 


-  Found by YOYO@home 
   James C. Owens       
   Oct 04, 2020   n =  469: 6958997628875965569003769582314963273475677604340583053; ecm: B1=26e7      


-  Found by Alfred Eichhorn 
   Oct 03, 2020   n =35227: 61546699056988639875393323 * 1805313896......c35201;    ecm: B1= 5e4;  sigma = 0:4422238530267184 
   Oct 03, 2020   n =56501: 833735079549139025506013 * 9484523591......c56454;      ecm: B1= 5e4;  sigma = 0:8776110477941862 

 
-  Found by Alfred Eichhorn 
   Sep 30, 2020   n =56267: 1835991125691172513172823643 * 6051832688......c56239;  ecm: B1= 5e4;  sigma = 0:6886219702756561
   Sep 30, 2020   n =92353: 9936534644772715742414803 * 1118207856......c92328;     ecm: B1= 5e4;  sigma = 0:7757038471345416


-  Found by YOYO@home 
   Possix      
   Sep 27, 2020   n =6580M: 5226300854932192952818901175186968159161;               ecm: B1=11e6;  sigma = 0:6986030302957500225         

   
-  Found by YOYO@home 
   Domstang68    
   Sep 26, 2020   n =7980L: 7852530157762803085617492355913151301;                  ecm: B1=43e6;  sigma = 0:6858431455024526459         

   
-  Found by Kurt Beschorner 
   Sep 21, 2020   n = 9155: 7616089497844942161161351656201;                        ecm: B1= 1e6;  sigma = 0:6590737663680927 


-  Found by Kurt Beschorner 
   Sep 19, 2020   n =12501: 6535104588045721;                                       ecm: B1= 1e6;  sigma = 1760487021690192 

 
-  Found by Alfred Eichhorn 
   Sep 17, 2020   n =56041: 102321462089518541403732043 * 1085902300......c56015;  ecm: B1= 5e4;  sigma = 3303935810774227


-  Found by Alfred Eichhorn 
   Sep 11, 2020   n =34613: 1120910859943369124449753067 * 9912573343......c34585;  ecm: B1= 5e4; sigma = 0:3124205414575670 
   Sep 11, 2020   n =34631: 1865442867892204591011209 * 5956285932......c34606;     ecm: B1= 5e4; sigma = 1303306403291282 
   Sep 11, 2020   n =55949: 763128123673032584695757159 * 1455995496......c55922;   ecm: B1= 5e4; sigma = 0:756659182058430 
   Sep 11, 2020   n =92237: 13137107473702256458541917 * 8457806357......c92211;    ecm: B1= 5e4; sigma = 1934092352120563 


-  Found by Alfred Eichhorn 
   Sep 03, 2020   n =55717: 32755939171857795635814010711 * 3392090531......c55688; ecm:B1= 5e4; sigma = 0:4984892550861418 


-  Found by YOYO@home 
   Barrie   
   Aug 30, 2020   n = 1465: 4124958033208387919306004986222829222160703448431;      ecm: B1= 11e6;        
 
      
-  Found by Alfred Eichhorn 
   Aug 22, 2020   n =34213: 1447483603198972631826271 * 7676156805......c34188;     ecm: B1= 5e4; sigma = 2299520442601417
   Aug 22, 2020   n =91823: 150710591896116987435871 * 7372481901......c91799;      ecm: B1= 5e4; sigma = 5727404210433105
   Aug 22, 2020   n =91943: 4423729066459701825541397 * 2511706965......c91918;     ecm: B1= 5e4; sigma = 4538722838662089


-  Found by Kurt Beschorner 
   Aug 10, 2020   n = 9125: 731542295610070635675114751;                            ecm: B1= 1e6;  sigma = 8234450462098695 


-  Found by Kurt Beschorner 
   Aug 03, 2020   n = 9051: 25812255150720206620915150429891843;                    ecm: B1= 3e6;  sigma = 0:4029561786297060

    
-  Found by Kurt Beschorner 
   Aug 02, 2020   n = 9113: 17245749127283658743551012523;                          ecm: B1= 1e6;  sigma = 1521521902935765
         


ECM efforts
with Rn:      323 < n < 2000 (Nov 24, 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 (Sep 28, 2020)
with Rn:     6999 < n < 8000 (Sep 27, 2020) with Rn:     7999 < n < 9000 (Aug 22, 2020)
with Rn:     8999 < n <10000 (Nov 24, 2020) with Rn:     9999 < n <11000 (Jun 12, 2019)
with Rn:   10999 < n <12000 (Jun 12, 2019) with Rn:   11999 < n <12500L/M (Oct 31, 2020)



currently ECM-efforts by   yoyo@home:    ecm-curves
B1 = 43e6/8600 curves/
numbers < 1001 digits
1117
working
1255
working
1257
working
1465
working
1475
working
B1 = 11e7/18400 curves/
numbers < 701 digits
593
working
599
working
607
working
611
working
617
working
B1 = 26e7/46000 curves/
numbers < 450 digits
467
working
469
working
521
working
1136
working
1160
working
B1 = 85e7/75000 curves/
numbers < 250 digits
609
working
675
working
1008
working
1188
working
1200
working



Factorizations
Repunits: R1        - R2500 (Nov 08, 2020) Repunits:  R2501 - R5000 (Feb 14, 2020)
Repunits: R5001   - R7500 (Sep 28, 2020) Repunits: R7501 - R10000 (Nov 01, 2020)
Repunits: R10001 - R12500 (Jun 12, 2019) Repunits: R12501 - R14980L/M (Sep 19, 2020)




Rprime project; base 10

last update: Nov 11, 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, Paul Bourdelais , Benjamin Chaffin, Edo Rajh, Kurt Beschorner

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)
    - 10ˆ 4300447     no further probable primes




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