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


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News

-  Last update: Dec 04, 2022 

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Dec 04, 2022  - R1340L/c265: SNFS-difficult = 268; degree 8
                 - 691.4M unique r. relations and 610.3unique ideals are collected
                 - msieve filtering: well done
                 - matrix is 65.7M x 65.7M with weight 7818384770 (118.98/col)  
                 - linear algebra completed 23500 dimensions of 65.7M dim. (0.0%, ETA 3208h 0m

			  
-  Found by Alfred Eichhorn 
   Dec 02, 2022   n = 65257: 29021845406574177689182183471831;                      ecm: B1 = 5e4; sigma = 8827912087270031
   Dec 02, 2022   n = 65267: 196872763596771607155929;                              ecm: B1 = 5e4; sigma = 5907651863350580
   Dec 02, 2022   n = 65419: 77658403478600955160498507;                            ecm: B1 = 5e4; sigma = 5773479858856831
   Dec 02, 2022   n = 83903: 1072388632041797323856413;                             ecm: B1 = 5e4; sigma = 3013216190367338
   Dec 02, 2022   n = 83921: 935916352185237988152529;                              ecm: B1 = 5e4; sigma = 2096569748642875
   Dec 02, 2022   n = 83987: 971921165004064866353773;                              ecm: B1 = 5e4; sigma = 2917559887380640


- Found by Kurt Beschorner   
   Dec 02, 2022   n = 5167: 58534812511619307791582990857213930867;                 ecm: B1 = 1e6; sigma = 0:8576584531991617 
   Dec 02, 2022   n=141551: 683294806297822001;                                     gr-mfaktc

 
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Nov 30, 2022   R942/c209: SNFS-difficulty = 314 
                  11M unique r. relations from 1250M are collected
                  currently progress 0.9 %;       
 
 
- Found by Kurt Beschorner   
   Nov 20, 2022   n = 5087: 855696576819526114321368468241;                         ecm: B1 = 1e6; sigma = 0:2338557618126682 
   Nov 20, 2022   n=140779: 1886531517329207467;                                    gr-mfaktc
   Nov 20, 2022   n=141067: 3019266738055160111;                                    gr-mfaktc


- Found by YOYO@home/Lars_Seidel   
   Nov 24, 2022   n =  497: 4247178976042868082665679915673747026882614569 * 1712111424......P321; ecm: B1 = 85e7; sigma = 0:17252997664838270985 


- Found by Kurt Beschorner   
   Nov 20, 2022   n = 9525: 246411272719873911988478401;                            ecm: B1 = 1e6; sigma = 0:1153280773493264
   Nov 20, 2022   n=140443: 3420910228546247551;                                    gr-mfaktc
   Nov 20, 2022   n=140587: 11931743520497439239;                                   gr-mfaktc

			  
-  Found by Alfred Eichhorn 
   Nov 18, 2022   n = 47857: 267862652398859882975627;                              ecm: B1 = 5e4; sigma = 8846267970344855
   Nov 18, 2022   n = 47857: 5814050299123021647722194082747;                       ecm: B1 = 5e4; sigma = 8795177300895013


- Found by Kurt Beschorner   
    Nov 18, 2022   n=139921: 121435939069357037;                                    gr-mfaktc
    Nov 18, 2022   n=139987: 5328475787572005311;                                   gr-mfaktc
    Nov 18, 2022   n=140227: 439337271274130849;                                    gr-mfaktc


- Found by Kurt Beschorner   
   Nov 05, 2022   n = 5999: 30098469727206035303519014883;                          ecm: B1 = 1e6; sigma = 5200900600359875 
   Nov 05, 2022   n=139703: 268697501287103723;                                     gr-mfaktc


- Found by Kurt Beschorner   
   Nov 01, 2022   n = 1389: 39307144309365706756279849773434495203 * 9193907609......P840;  ecm: B1 =43e6; sigma = 1509003123809924 
   Nov 01, 2022   n=139343: 1506620826908739203;                                    gr-mfaktc
   Nov 01, 2022   n=139387: 76653039033857987;                                      gr-mfaktc
   Nov 01, 2022   n=139387: 4376783573901975947;                                    gr-mfaktc
   Nov 01, 2022   n=139457: 88280371885189489;                                      gr-mfaktc


- Found by Kurt Beschorner   
   Oct 27, 2022   n =7380L: 18083439727099436159112817133086310461;                 ecm: B1 =43e6; sigma = 2954795763367013 
   Oct 27, 2022   n=138587: 13456808017227013951;                                   gr-mfaktc
   Oct 27, 2022   n=138599: 4336913339749953827;                                    gr-mfaktc
   Oct 27, 2022   n=138661: 4253629350519214951;                                    gr-mfaktc
   Oct 27, 2022   n=138661: 11518943054098475483;                                   gr-mfaktc

				  
-  Found by Alfred Eichhorn 
   Oct 21, 2022   n =64877: 58307945412705205493;                                   ecm: B1 = 5e4; sigma = 4058862805750220


- Found by Kurt Beschorner   
   Oct 20, 2022   n = 7595: 53301899984916861489592976390111;                       ecm: B1 = 1e6; sigma = 2862452422412262 
   Oct 20, 2022   n=138511: 16639782600533415413;                                   gr-mfaktc


- Found by YOYO@home/Scottie McKinley   
   Oct 19, 2022   n = 1290: 46918389192417684252494192977798983971157315180037905073531; ecm: B1 =2.9e9; sigma = 0:15756483711164029501 
   
 
- Found by Kurt Beschorner   
   Oct 18, 2022   n=138181: 260118541625705071;                                     gr-mfaktc
   Oct 18, 2022   n=138251: 128617317085653479;                                     gr-mfaktc
   Oct 18, 2022   n=138389: 377328885591268151;                                     gr-mfaktc


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


- 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



ECM efforts
with Rn:           1 < n < 2000 (Nov 24, 2022) with Rn:     1999 < n < 3000 (Nov 01, 2022)
with Rn:     2999 < n < 4000 (Nov 05, 2022) with Rn:     3999 < n < 5000 (Nov 17, 2022)
with Rn:     4999 < n < 6000 (Dec 04, 2022) with Rn:     5999 < n < 7000 (Dec 01, 2022)
with Rn:     6999 < n < 8000 (Nov 20, 2022) with Rn:     7999 < n < 9000 (Oct 20, 2022)
with Rn:     8999 < n <10000 (Nov 20, 2022) with Rn:     9999 < n <11000 (Oct 11, 2022)
with Rn:   10999 < n <12000 (Sep 08, 2022) with Rn:   11999 < n <14980L/M (Nov 05, 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 (Nov 25, 2022) Repunits:  R2501 - R5000 (Oct 01, 2022)
Repunits: R5001   - R7500 (Dec 04, 2022) Repunits: R7501 - R10000 (Nov 20, 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)




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