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


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News

-  Last update: Oct 11, 2022/2nd  

- Found by Kurt Beschorner   
   Oct 11, 2022   n=12180L: 2750865191314983385202411742967911795988441;            ecm: B1 =11e6; sigma = 0:3511433398072626 

 
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Oct 11, 2022   R1340L/c265: SNFS-difficult = 268; degree 8
                  633M unique r. relations and 580M unique ideals are collected
                  matrix is 91.5M x 91.5M 
                  the matrix is still too big 
                  currently progress 89 %;        


- Found by Kurt Beschorner   
   Oct 09, 2022   n = 8613: 36357990161285007949864483;                             ecm: B1 = 1e6; sigma = 3516630546511552 
   Oct 09, 2022   n =10414: 161529899335536848415319865023163477;                   ecm: B1 = 1e6; sigma = 6236160411899970 
   Oct 09, 2022   n=137597: 139698058612259729;                                     gr-mfaktc
   Oct 09, 2022   n=137597: 3554455399781350373;                                    gr-mfaktc


- Found by Kurt Beschorner   
   Oct 03, 2022   n = 7593: 112887580911050204414751529;                            ecm: B1 = 1e6; sigma = 0:7734327110386253 
   Oct 03, 2022   n=136373: 5918722751609848889;                                    gr-mfaktc
   Oct 03, 2022   n=136537: 987858503096180231;                                     gr-mfaktc
   Oct 03, 2022   n=136651: 1146491861927584649;                                    gr-mfaktc
   Oct 03, 2022   n=136733: 107300944919547803;                                     gr-mfaktc

 
- YOYO@home/Boone    
   Oct 01, 2022   n =2580M: 5450116210658743893234594584043237507827598349697948371796539141; ecm: B1 = 29e8; sigma = 0:10511886308721671557 


- Found by Kurt Beschorner   
   Sep 25, 2022   n = 6555: 42140277738214794289054869972841;                       ecm: B1 = 3e6; sigma = 0:4590123871373091
   Sep 25, 2022   n=135077: 121039782337620529;                                     gr-mfaktc
   Sep 25, 2022   n=135101: 1279566313721112199;                                    gr-mfaktc
   Sep 25, 2022   n=135403: 1650544604703421013;                                    gr-mfaktc
   Sep 25, 2022   n=135607: 91960517273658083;                                      gr-mfaktc
   Sep 25, 2022   n=135613: 11597825762132593721;                                   gr-mfaktc
   Sep 25, 2022   n=135727: 194775127927361213;                                     gr-mfaktc
   Sep 25, 2022   n=135829: 14363297250027008159;                                   gr-mfaktc
   Sep 25, 2022   n=135859: 1812264618772038373;                                    gr-mfaktc
   Sep 25, 2022   n=136069: 16826617683300406043;                                   gr-mfaktc
   Sep 25, 2022   n=136207: 354088341024477281;                                     gr-mfaktc
   Sep 25, 2022   n=136327: 6515905459906372403;                                    gr-mfaktc
  
   
-  Found by Sam Wagstaff 
   Sep 19, 2022   n =  878: 3127889058329352843751138723028784195008863188510913210373 * 3758889450......P303 


-  Found by Alfred Eichhorn 
   Sep 13, 2022   n =64499: 19863776914146324936308159 * 5593654801......c64473;    ecm: B1 = 5e4; sigma = 8249463174429580 


- Found by Kurt Beschorner    
   Sep 12, 2022   n = 6555: 7704748191989680635586430551;                           ecm: B1 = 3e6; sigma = 1974080013846066
   Sep 12, 2022   n = 8841: 594464132403304317895457070078890067883;                ecm: B1 = 1e6; sigma = 0:2101783093505696
   Sep 12, 2022   n=133723: 5804457150257817787;                                    gr-mfaktc
   Sep 12, 2022   n=134047: 2215727822061991957;                                    gr-mfaktc


 -  Found by Yousuke Koide    
   Sep 10, 2022   n =  892: 6159486985016013075067913427429040588111855293215481915322769; ecm: B1 = 3e8; sigma = 2:10607718275885008793


- Found by Kurt Beschorner    
   Sep 08, 2022   n=132409: 1024647272668872173;                                    gr-mfaktc
   Sep 08, 2022   n=132971: 10322025968955497639;                                   gr-mfaktc
   Sep 08, 2022   n=133153: 136805032698890161;                                     gr-mfaktc
   Sep 08, 2022   n=133153: 4747388624163033049;                                    gr-mfaktc
   Sep 08, 2022   n=133387: 5705798022619207883;                                    gr-mfaktc
   Sep 08, 2022   n=133543: 665876485045228627;                                     gr-mfaktc

 
- Found by Kurt Beschorner    
   Aug 30, 2022   n = 6149: 132349404800470430780608308039133;                      ecm: B1 = 1e6; sigma = 0:3971808653409445 


-  Found by Alfred Eichhorn 
   Aug 30, 2022   n =47093: 647087756300331974529153667 * 1717094938......c47066;   ecm: B1 =50e3; sigma = 2950912849634400 
   Aug 30, 2022   n =64333: 63744434450435977540369 * 1743071564......c64310;       ecm: B1 =50e3; sigma = 3325153410398689
   Aug 30, 2022   n =64403: 2881682076249630649213;                                 ecm: B1 =50e3; sigma = 911997270172798
   Aug 30, 2022   n =64403: 7972768836948372230717;                                 ecm: B1 =50e3; sigma = 1700074645962328 
   Aug 30, 2022   n =82699: 2004682871864185885027933;                              ecm: B1 =50e3 
   Aug 30, 2022   n =82699: 3012388610562637844173403 * 1187646351......c82631;     ecm: B1 =50e3; sigma = 4361301083726803 


- Found by Kurt Beschorner    
   Aug 28, 2022   n=131777: 83906405241521557;                                      gr-mfaktc
   Aug 28, 2022   n=131779: 15591013644840274001;                                   gr-mfaktc
   Aug 28, 2022   n=131837: 76443943224424157;                                      gr-mfaktc
   Aug 28, 2022   n=131837: 5389702364983905559;                                    gr-mfaktc
   Aug 28, 2022   n=131939: 1954518640414612399;                                    gr-mfaktc
   Aug 28, 2022   n=132113: 2343810386196887093;                                    gr-mfaktc
   Aug 28, 2022   n=132367: 2284280356448387879;                                    gr-mfaktc
   Aug 28, 2022   n=132367: 9641080956367411519;                                    gr-mfaktc


- Found by Kurt Beschorner    
   Aug 21, 2022   n=131251: 2639045016257840083;                                    gr-mfaktc
   Aug 21, 2022   n=131317: 583371725193187871;                                     gr-mfaktc
   Aug 21, 2022   n=131441: 2059342053850217827;                                    gr-mfaktc
   Aug 21, 2022   n=131447: 2049972906241478693;                                    gr-mfaktc
   Aug 21, 2022   n=131447: 2642767595636420201;                                    gr-mfaktc
   Aug 21, 2022   n=131501: 188173674865986209;                                     gr-mfaktc
   Aug 21, 2022   n=131713: 7165398003348396293;                                    gr-mfaktc


-  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 



- 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


ECM efforts
with Rn:           1 < n < 2000 (Oct 11, 2022) with Rn:     1999 < n < 3000 (Oct 11, 2022)
with Rn:     2999 < n < 4000 (Aug 13, 2022) with Rn:     3999 < n < 5000 (Sep 08, 2022)
with Rn:     4999 < n < 6000 (Aug 21, 2022) with Rn:     5999 < n < 7000 (Sep 25, 2022)
with Rn:     6999 < n < 8000 (Oct 03, 2022) with Rn:     7999 < n < 9000 (Oct 09, 2022)
with Rn:     8999 < n <10000 (Jul 11, 2022) with Rn:     9999 < n <11000 (Oct 11, 2022)
with Rn:   10999 < n <12000 (Sep 08, 2022) with Rn:   11999 < n <14980L/M (Oct 11, 2022)



currently ECM-efforts by   yoyo@home:    ecm-curves
B1 = 11e7/17500 curves/
numbers < 751 digits		 617
in progress		 619
in progress		 625
in progress		 629
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		 1290
in progress		 ....
...........



Factorizations
Repunits: R1        - R2500 (Sep 25, 2022) Repunits:  R2501 - R5000 (Oct 01, 2022)
Repunits: R5001   - R7500 (Sep 25, 2022) Repunits: R7501 - R10000 (Oct 09, 2022)
Repunits: R10001 - R12500 (Oct 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)




Visitors since Oct 27, 2020:

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