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


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News

-  Last update: Aug 17, 2022    


-  Found by Alfred Eichhorn 
   Aug 17, 2022   n =46997: 113175953490663133273888933 * 9817554673......c46970;   ecm: B1 = 5e4; sigma = 5607928389575783 
   Aug 17, 2022   n =82483: 1795716550338982195640129 * 3060339309......c82436;     ecm: B1 = 5e4; sigma = 8509871448674776 


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Aug 17, 2022   R1340L/c265: SNFS-difficult = 268; degree 8
                  568M unique r. relations and 562M unique ideals are collected
                  currently progress 79 %;        
 

- Found by Kurt Beschorner    
   Aug 13, 2022   n = 5311: 426181508882040099180570908153689;                      ecm: B1 = 1e6; sigma = 4811743559501154 
   Aug 13, 2022   n=130363: 1506139996811359667;                                    gr-mfaktc
   Aug 13, 2022   n=130531: 17208150406300826009;                                   gr-mfaktc
   Aug 13, 2022   n=130873: 6266849542838449667;                                    gr-mfaktc


- Found by Kurt Beschorner    
   Aug 06, 2022   n=129113: 1224181268756132441;                                    gr-mfaktc
   Aug 06, 2022   n=129401: 4010264049806196253;                                    gr-mfaktc
   Aug 06, 2022   n=129497: 14008139847643280267;                                   gr-mfaktc
   Aug 06, 2022   n=129917: 112833716872069013;                                     gr-mfaktc
   Aug 06, 2022   n=130021: 446857943777814827;                                     gr-mfaktc
   Aug 06, 2022   n=130043: 138190955281021609;                                     gr-mfaktc
   Aug 06, 2022   n=130099: 1318521172210868599;                                    gr-mfaktc

- Found by Kurt Beschorner    
   Jul 30, 2022   n = 6279: 11410286542095251356695919014798215209;                 ecm: B1 = 3e6; sigma = 0:3680840401684413 
   Jul 30, 2022   n=128903: 534075966511610693;                                     gr-mfaktc
   Jul 30, 2022   n=128959: 4681928849630741707;                                    gr-mfaktc
   Jul 30, 2022   n=128993: 116129754627041201;                                     gr-mfaktc


- Found by Kurt Beschorner    
   Jul 29, 2022   n = 5473: 1307142018775417051488486551;                           ecm: B1 = 1e6; sigma = 0:6264506291694973 
   Jul 29, 2022   n=128021: 432022553418757013;                                     gr-mfaktc
   Jul 29, 2022   n=128591: 1720450900083150959;                                    gr-mfaktc
   Jul 29, 2022   n=128663: 311963829483302401;                                     gr-mfaktc
   Jul 29, 2022   n=128819: 286102055216622751;                                     gr-mfaktc   


- Found by Makoto Kamada    
   Jul 28, 2022   n=149401: is probable prime; length: 128003 digits

 
- Found by Kurt Beschorner    
   Jul 22, 2022   n = 6195: 545580401705761895030586938911;                         ecm: B1 = 3e6; sigma = 3700842710804836 
   Jul 22, 2022   n =50097: 3623943703785414020081995009;                           ecm: B1 =25e4; sigma = 0:1490915758377029
   Jul 22, 2022   n=127487: 216217623431069563;                                     gr-mfaktc
   Jul 22, 2022   n=127487: 8772072614765426963;                                    gr-mfaktc
   Jul 22, 2022   n=127591: 96284250110795639;                                      gr-mfaktc

  
-  Found by Alfred Eichhorn 
   Jul 21, 2022   n =82219: 3426743053976309972144323 * 3242469871......c82194;     ecm: B1 = 5e4; sigma = 238330239553817 
   Jul 21, 2022   n =82241: 305516594796838230758933 * 3636827360......c82217;      ecm: B1 = 5e4; sigma = 6454317885563619 


- Found by Kurt Beschorner    
   Jul 19, 2022   n=125659: 326562852496180759;                                     gr-mfaktc
   Jul 19, 2022   n=126013: 478958691016429969;                                     gr-mfaktc
   Jul 19, 2022   n=126131: 1370100046835287237;                                    gr-mfaktc
   Jul 19, 2022   n=126227: 438384021980410679;                                     gr-mfaktc
   Jul 19, 2022   n=126457: 2300778768848473787;                                    gr-mfaktc
   

- Found by Kurt Beschorner    
   Jul 11, 2022   n =10042: 913718899145162450473918365995735799984619;             ecm: B1 = 1e6; sigma = 0:5125127886895840

  
-  Found by Alfred Eichhorn 
   Jul 06, 2022   n =63853: 33689024059941909083011747;                             ecm: B1 = 5e4; sigma = 5132833866279460 


- Found by Kurt Beschorner    
   Jul 06, 2022   n=124529: 875365247048271359;                                     gr-mfaktc
   Jul 06, 2022   n=124703: 294551416955713471;                                     gr-mfaktc
   Jul 06, 2022   n=125017: 12281096112324010729;                                   gr-mfaktc
   Jul 06, 2022   n=125029: 1117445127097070489;                                    gr-mfaktc
   Jul 06, 2022   n=125063: 230816510591286437;                                     gr-mfaktc
   Jul 06, 2022   n=125113: 6038014320737169637;                                    gr-mfaktc
 
 
- Found by Kurt Beschorner    
   Jul 01, 2022   n = 9495: 204550078006730391999477563521;                         ecm: B1 = 1e6; sigma = 7692386312127836
   Jul 01, 2022   n=123737: 446760762463449067;                                     gr-mfaktc
   Jul 01, 2022   n=123737: 8134329321836665627;                                    gr-mfaktc
   Jul 01, 2022   n=123979: 177570995573249893;                                     gr-mfaktc
   Jul 01, 2022   n=124171: 6370912188660140399;                                    gr-mfaktc

- 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   


- 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


 - Found by NFS@home  
   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 



ECM efforts
with Rn:           1 < n < 2000 (Aug 13, 2022) with Rn:     1999 < n < 3000 (Jul 19, 2022)
with Rn:     2999 < n < 4000 (Aug 13, 2022) with Rn:     3999 < n < 5000 (Aug 13, 2022)
with Rn:     4999 < n < 6000 (Aug 16, 2022) with Rn:     5999 < n < 7000 (Aug 16, 2022)
with Rn:     6999 < n < 8000 (Aug 13, 2022) with Rn:     7999 < n < 9000 (Aug 13, 2022)
with Rn:     8999 < n <10000 (Jul 11, 2022) with Rn:     9999 < n <11000 (Aug 06, 2022)
with Rn:   10999 < n <12000 (Jul 06, 2022) with Rn:   11999 < n <14980L/M (Aug 13, 2022)



currently ECM-efforts by   yoyo@home:    ecm-curves
B1 = 11e7/17500 curves/
numbers < 751 digits
611
in progress
617
in progress
619
in progress
625
in progress
641
in progress
B1 = 26e7/45000 curves/
numbers < 450 digits
645
in progress
1136
in progress
1160
in progress
1254
in progress
....
in progress
B1 = 85e7/70000 curves/
numbers < 400 digits
573
in progress
645
in progress
1086
in progress
1254
in progress
1386
in progress
B1 = 29e8/nnnn curves/
numbers < 400 digits
567
in progress
609
in progress
1080
in progress
1134
in progress
1290
in progress



Factorizations
Repunits: R1        - R2500 (May 08, 2022) Repunits:  R2501 - R5000 (Jun 21, 2022)
Repunits: R5001   - R7500 (Aug 13, 2022) Repunits: R7501 - R10000 (Jul 01, 2022)
Repunits: R10001 - R12500 (Jul 11, 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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