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


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News

-  Last update: Jun 27, 2022    

- Found by Kurt Beschorner   
   Jun 27, 2022   n=123259: 138081669688947203;                                     gr-mfaktc
   Jun 27, 2022   n=123307: 3522389340728868067;                                    gr-mfaktc
   Jun 27, 2022   n=123341: 7611397617926757689;                                    gr-mfaktc
   Jun 27, 2022   n=123407: 77377648499541413;                                      gr-mfaktc
   Jun 27, 2022   n=123601: 117358480984956947;                                     gr-mfaktc
   Jun 27, 2022   n=123677: 105106345750844117;                                     gr-mfaktc
   Jun 27, 2022   n=123701: 1412589819155622493;                                    gr-mfaktc


- Found by Kurt Beschorner   
   Jun 21, 2022   n =4700L: 45356719338814489536408951887817301;                    ecm: B1 =43e6; sigma = 1704111251554519
   Jun 21, 2022   n=122393: 3453423798333215723;                                    gr-mfaktc
   Jun 21, 2022   n=122443: 461044996951660733;                                     gr-mfaktc
   Jun 21, 2022   n=122761: 14178079314053879843;                                   gr-mfaktc
   Jun 21, 2022   n=122827: 92605585260518597;                                      gr-mfaktc   


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Jun 21, 2022   R1340L/c265: SNFS-difficult = 268; degree 8
                  494M unique r. relations and 538M unique ideals are collected
                  currently progress 69 %;       


- Found by Kurt Beschorner   
   Jun 17, 2022   n =12038: 5249732671244525229278815957352881;                     ecm: B1 = 1e6; sigma = 0:7712952776091375 
   Jun 17, 2022   n=122011: 3091937545068030959;                                    gr-mfaktc
   Jun 17, 2022   n=122081: 180567753811428757;                                     gr-mfaktc

-  Found by Alfred Eichhorn 
   Jun 13, 2022   n =46573: 46225394782451108877144597271;                          ecm: B1 = 5e4; sigma = 3273871842688952 
   Jun 13, 2022   n =81359: 591617717027016191003599;                               ecm: B1 = 5e4; sigma = 2233894346486827 
   Jun 13, 2022   n =81421: 273050887479607951819307;                               ecm: B1 = 5e4; sigma = 3740024001393635 
   Jun 13, 2022   n =81509: 24022214710361586369320083;                             ecm: B1 = 5e4; sigma = 5954467701967165
 

- Found by Kurt Beschorner   
   Jun 13, 2022   n =50089: 1123778700521220813695237;                              ecm: B1 =25e4; sigma = 0:7418723949217218 
   Jun 13, 2022   n =50091: 352153516456022723123923;                               ecm: B1 =25e4; sigma = 0:7343133892651212 
   Jun 13, 2022   n=121157: 289963297111654519;                                     gr-mfaktc
   Jun 13, 2022   n=121487: 113266201861047173;                                     gr-mfaktc
   Jun 13, 2022   n=121501: 6817997072029161209;                                    gr-mfaktc
   

- Found by Sam Wagstaff   
   May 27, 2022   n =1780L: 7660395383708237627973789216434577857253936548886784731800803873631881; ecm: B1 =22e8; sigma = 1:532322200 


- Found by Kurt Beschorner   
   Jun 07, 2022   n=119723: 16029261086411541667;                                   gr-mfaktc
   Jun 07, 2022   n=119981: 134659098042339929;                                     gr-mfaktc
   Jun 07, 2022   n=120011: 72235142882804039;                                      gr-mfaktc
   Jun 07, 2022   n=120223: 3593139386032985123;                                    gr-mfaktc
   Jun 07, 2022   n=120349: 1339890396898864387;                                    gr-mfaktc
   Jun 07, 2022   n=120539: 6598223271524054921;                                    gr-mfaktc
   Jun 07, 2022   n=120739: 2864131139469349201;                                    gr-mfaktc


- Found by Kurt Beschorner   
   May 30, 2022   n=118081: 409924485675218119;                                     gr-mfaktc
   May 30, 2022   n=118787: 1453558106158132679;                                    gr-mfaktc
   May 30, 2022   n=119099: 1484474627262151277;                                    gr-mfaktc
   May 30, 2022   n=119363: 8618449548915348929;                                    gr-mfaktc
   May 30, 2022   n=119419: 73384391452754867;                                      gr-mfaktc
   May 30, 2022   n=119447: 230571158344992599;                                     gr-mfaktc
   May 30, 2022   n=119549: 6726593772867620467;                                    gr-mfaktc
   May 30, 2022   n=119633: 2375307680670946631;                                    gr-mfaktc
   

-  Found by Alfred Eichhorn 
   May 28, 2022   n =46153: 53823681238932630531997;                                ecm: B1 = 5e4; sigma = 2774199055649663
   May 28, 2022   n =81173: 4544854780120414167656597;                              ecm: B1 = 5e4; sigma = 6484780220008802


- Found by Kurt Beschorner   
   May 19, 2022   n =11176: 8864340352444583393805312185281;                        ecm: B1 = 1e6; sigma = 0:7739221409077085
   May 19, 2022   n=117373: 15970680274980387493;                                   gr-mfaktc
   May 19, 2022   n=117503: 6815122939922071721;                                    gr-mfaktc
   May 19, 2022   n=117911: 74946032021733809;                                      gr-mfaktc
   May 19, 2022   n=117911: 178224635229444787;                                     gr-mfaktc


- Found by Kurt Beschorner   
   May 14, 2022   n =10102: 2264134357087878518383067539;                           ecm: B1 = 1e6; sigma = 0:6192617428100729
   May 14, 2022   n =50075: 2245485278512778686151;                                 ecm: B1 =25e4; sigma = 6790109589502313
   May 14, 2022   n =50089: 2187447775344942718973;                                 ecm: B1 =25e4; sigma = 1521200596419729
   May 14, 2022   n=116359: 1219389300710971471;                                    gr-mfaktc
   May 14, 2022   n=116483: 229410768832595569;                                     gr-mfaktc
   May 14, 2022   n=116639: 336584201879544209;                                     gr-mfaktc
   May 14, 2022   n=117133: 2360667724552247359;                                    gr-mfaktc


   May 06, 2022   n =  646: 298705372736554351789156294144090138390916509553983003911433879637774413; SNFS
                  - SNFS-difficult = 324
                  - SNFS-degree = 6
                  - skew 1.47, size 7.314e-16, alpha 1.507, combined = 4.122e-16 rroots = 0
                  - 1478071230 relations and 1224198207 unique ideals
                  - matrix: 89374447 x 89374624 (45160.2 MB) with weight 12899020426 (144.33/col)
                  - details: https://escatter11.fullerton.edu/nfs/numbers.php
                  congratulations!


- Found by Kurt Beschorner   
   May 06, 2022   n =60547: 409896670397756192083;                                  ecm: B1 = 5e4; sigma = 8502195504310877 
   May 06, 2022   n=115631: 5485705253601321907;                                    gr-mfaktc
   May 06, 2022   n=115861: 268547348251027987;                                     gr-mfaktc
   May 06, 2022   n=116041: 527472710527941599;                                     gr-mfaktc


- Found by Kurt Beschorner   
   Apr 30, 2022   n = 1441: 1314434306697830924275628881502710792058563;            ecm: B1 =11e6; sigma = 0:281840436550688 
   Apr 30, 2022   n =50063: 4102384153439750219081587;                              ecm: B1 =25e4; sigma = 0:6244918942670668 


-  Found by Alfred Eichhorn 
   Apr 29, 2022   n =45989: 660056492305443457540399 * 1683357597......c45965;      ecm: B1 = 5e4; sigma = 7793369107252965
   Apr 29, 2022   n =80911: 4885219645269106864075111 * 2274434297......c80886;     ecm: B1 = 5e4; sigma = 4865999027539681


- Found by Kurt Beschorner   
   Apr 26, 2022   n =50061: 20631292838324832743226551317;                          ecm: B1 =25e4; sigma = 0:6326572938999362 
   Apr 26, 2022   n=113489: 6294021289926306917;                                    gr-mfaktc
   Apr 26, 2022   n=113779: 104544335152862999;                                     gr-mfaktc
   Apr 26, 2022   n=113963: 6129976650930936107;                                    gr-mfaktc
   Apr 26, 2022   n=114193: 447099731123899643;                                     gr-mfaktc
   Apr 26, 2022   n=114547: 896705230860005471;                                     gr-mfaktc
   Apr 26, 2022   n=114641: 5661704334072995053;                                    gr-mfaktc

 
-  Found by Samuel Wagstaff 
   Apr 24, 2022   n =  718: 2731764846587782091546914066524656594612608438032609803989298453; ecm 


 - Found by NFS@home  
   Apr 19, 2022   n =  323: 1000889286725563474405662045911093540900908710082344227506919162972107; SNFS
   Apr 19, 2022   n =  323: 2024740873938190513425266673474911634048354422503451267887726938473483; SNFS
                  - SNFS-degree = 6
                  - skew 1.47, size 8.887e-16, alpha 1.180, combined = 4.681e-16 rroots = 2
                  - 1558078549 r. relations and 1233362732 unique ideals
                  - matrix: 82609756 x 82609935 (41687.6 MB) with weight 11917189430 (144.26/col)
                  - details: https://escatter11.fullerton.edu/nfs/numbers.php
                  congratulations!
   

 - Found by Kurt Beschorner   
   Apr 18, 2022   n=112913: 651336694612007893;                                     gr-mfaktc
   Apr 18, 2022   n=112919: 10013202845099079641;                                   gr-mfaktc
   Apr 18, 2022   n=113039: 800729930567911831;                                     gr-mfaktc
   Apr 18, 2022   n=113363: 611462127682645093;                                     gr-mfaktc
   Apr 18, 2022   n=113453: 1666342390868100431;                                    gr-mfaktc

 
-  Found by Alfred Eichhorn 
   Apr 15, 2022   n= 45691: 116408718433083077382079 * 9544913182......c45667;      ecm: B1 = 5e4; sigma = 1929643248636331 
   Apr 15, 2022   n= 63097: 1182703041481644252705761 * 9394675350......c63072;     ecm: B1 = 5e4; sigma = 8537965496336827 
   Apr 15, 2022   n= 80761: 10954906902597028057655279 * 1014258834......c80736;    ecm: B1 = 5e4; sigma = 3090792250112772 


 -  Yousuke Koide    
   Apr 12, 2022   n =  852: 791145568078856137872408096636314622331869565265096415358925771275309; SNFS 
   Apr 12, 2022   n =  852: 843407644889588409015473024758866665298118138956929263554289382634028509255935457469; SNFS 


 -  Found by Kurt Beschorner   
   Apr 12, 2022   n=111949: 2904985885984274921;                                    gr-mfaktc
   Apr 12, 2022   n=112061: 94854068032024601;                                      gr-mfaktc
   Apr 12, 2022   n=112139: 15710755567820525071;                                   gr-mfaktc
   Apr 12, 2022   n=112213: 165002069869703387;                                     gr-mfaktc
   Apr 12, 2022   n=112237: 8861377526042820587;                                    gr-mfaktc
   Apr 12, 2022   n=112583: 952635577911225563;                                     gr-mfaktc


 -  Found by Kurt Beschorner   
   Apr 04, 2022   n = 1293: 81462499223765124189973519762431164923148551627;        ecm: B1 =43e6; sigma = 0:5078991612991630 
   Apr 04, 2022   n = 6435: 804151036122815034947264401;                            ecm: B1 = 3e6; sigma = 2862599954684006 
   Apr 04, 2022   n =50045: 77188137237745562881 * 1004465726...c39971;             ecm: B1 =25e4; sigma = 3490032384743785 
   Apr 04, 2022   n=110569: 790019899718817049;                                     gr-mfaktc
   Apr 04, 2022   n=111337: 13491324392167301893;                                   gr-mfaktc


-  Found by Alfred Eichhorn 
   Mar 31, 2022   n =80537: 98997936620816701558631 * 1122357848......c80514;       ecm: B1 = 5e4; sigma = 3459219771074912  
   Mar 31, 2022   n =80567: 237614342335310020762441 * 4676111299......c80543;      ecm: B1 = 5e4; sigma = 6517012485133803 


 -  Found by Kurt Beschorner    
   Mar 29, 2022   n = 2773: 399155678597075993642585721855751;                      ecm: B1 = 3e6; sigma =  0:1761429257841097 
   Mar 29, 2022   n = 2773: 619324111616350475702975927728595284601;                ecm: B1 = 3e6; sigma =  0:8238301661507597  
   Mar 29, 2022   n=110221: 5850281131860729997;                                    gr-mfaktc
   Mar 29, 2022   n=110563: 198916074227483203;                                     gr-mfaktc

 -  Found by Kurt Beschorner    
   Mar 24, 2022   n = 2773: 1954284136265233470908751563083;                        ecm: B1 = 3e6; sigma = 8275802607864457 
   Mar 24, 2022   n=109859: 13188872879181827987;                                   gr-mfaktc


-  Found by Paul Underwood    
   Mar 21, 2022   n =49081 is definitely prime 
   see: Mersenneforum.org/Math Stuff/Computer Science/Computational Number Theory/new ECPP record/post #35
   congratulations! 



ECM efforts
with Rn:           1 < n < 2000 (Jun 08, 2022) with Rn:     1999 < n < 3000 (Jun 13, 2022)
with Rn:     2999 < n < 4000 (Apr 24, 2022) with Rn:     3999 < n < 5000 (Jun 21, 2022)
with Rn:     4999 < n < 6000 (Jun 13, 2022) with Rn:     5999 < n < 7000 (May 19, 2022)
with Rn:     6999 < n < 8000 (May 28, 2022) with Rn:     7999 < n < 9000 (Jun 17, 2022)
with Rn:     8999 < n <10000 (May 06, 2022) with Rn:     9999 < n <11000 (Jun 21, 2022)
with Rn:   10999 < n <12000 (Jun 13, 2022) with Rn:   11999 < n <14980L/M (Jun 17, 2022)



currently ECM-efforts by   yoyo@home:    ecm-curves
B1 = 11e7/17500 curves/
numbers < 751 digits
611
working
617
working
619
working
625
working
641
working
B1 = 26e7/45000 curves/
numbers < 450 digits
475
working
567
working
645
working
1136
working
1160
working
B1 = 85e7/70000 curves/
numbers < 400 digits
609
working
1080
working
1176
working
1470
working
....
....
B1 = 29e8/nnnn curves/
numbers < 400 digits
1134
working
1155
working
1320
working
2460M
working
2820M
working



Factorizations
Repunits: R1        - R2500 (May 08, 2022) Repunits:  R2501 - R5000 (Jun 21, 2022)
Repunits: R5001   - R7500 (Apr 04, 2022) Repunits: R7501 - R10000 (Feb 27, 2022)
Repunits: R10001 - R12500 (Jun 17, 2022) Repunits: R12501 - R14980L/M (Sep 19, 2020)




Rprime project; base 10

last update: Mar 21, 2022

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, Kurt Beschorner

all contributors:   Danilo Nitsche, Serge Batalov, Paul Bourdelais, Benjamin Chaffin, Charles, Bo Chen, Alfred Eichhorn, FactorDB.com, Giovanni Di Maria,
                              Fan Ming, Phil, Richard Kapek, kkmrkkblmbrbk (aka GP2), Pavlos, Ryan Propper, 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 = prime               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)




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