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


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News

-  Last update: May 28, 2022 

-  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


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   May 28, 2022   R1340L/c265: SNFS-difficult = 268; degree 8
                  452M unique r. relations and 524M unique ideals are collected
                  currently progress 63 %;       


- 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! 


-  Found by Kurt Beschorner    
   Mar 21, 2022   n =60003: 1140424855078343303208889;                              ecm: B1 =25e4; sigma = 2827598131369570 
   Mar 21, 2022   n=108793: 1167704791152468197;                                    gr-mfaktc
   Mar 21, 2022   n=108907: 583880633763310627;                                     gr-mfaktc
   Mar 21, 2022   n=109211: 126937459545462521;                                     gr-mfaktc
 
 
-  Found by Alfred Eichhorn 
   Mar 19, 2022   n =62827: 7777690806649677716267 * 1428587403......c62805;        ecm: B1 = 5e4; sigma = 3473282770034336  
   Mar 19, 2022   n =62921: 4802717418923454899429369 * 2313505072......c62896;     ecm: B1 = 5e4; sigma = 4037487434681691  
 

-  Found by Kurt Beschorner    
   Mar 19, 2022   n =50041: 19199285928625054818523 * 3937978207......c49535;       ecm: B1 =25e4; sigma = 0:7955970943956376 
   Mar 19, 2022   n =50081: 852422867511808915726801 * 3172808326......c49149;      ecm: B1 =25e4; sigma = 5940992916829042
 

 -  Found by Kurt Beschorner    
   Mar 10, 2022   n =10425: 1609108948542966695478682525801;                        ecm: B1 = 1e6; sigma = 0:3379722065397352 
   Mar 10, 2022   n =10425: 14200413472717962745698299857144951;                    ecm: B1 = 1e6; sigma = 0:6314518817386092 
   Mar 10, 2022   n=107209: 4547576407708198481;                                    gr-mfaktc
   Mar 10, 2022   n=107927: 940707248331079717;                                     gr-mfaktc
				  
				  
-  Found by Alfred Eichhorn 
   Mar 04, 2022   n =44971: 15479193868097282334637 * 7178094160......c44948;       ecm: B1 = 5e4; sigma = 7295230555714081  
   Mar 04, 2022   n =62687: 26876428905287020627471867364637707 * 4134147118......c62652; ecm: B1 = 5e4; sigma = 0:5579796336872722  
   Mar 04, 2022   n =80231: 1839645269593249353199 * 1174091285......c80194;        ecm: B1 = 5e4; sigma = 8110353428198051 
 
 
-  Found by Kurt Beschorner    
   Mar 04, 2022   n =11468: 132327211589322363091440449 * 1324553695......c5479;    ecm: B1 = 1e6; sigma = 412850290796073 
   Mar 04, 2022   n =11764: 6137387517793439411384306141 * 1645651341......c5477;   ecm: B1 = 1e6; sigma = 5383335464986607 
   Mar 04, 2022   n =50067: 194200846806842075182991347;                            ecm: B1 =25e4; sigma = 0:5396483357768431  
   Mar 04, 2022   n =50067: 2559698594044837286966360354590201;                     ecm: B1 =25e4; sigma = 0:4038669283018763  
   Mar 04, 2022   n=106783: 503518636524815609;                                     gr-mfaktc



				  
-  Found by Kurt Beschorner    
   Feb 27, 2022   n = 8643: 7154478296260791031971319821631 * 1399590795......c5446; ecm: B1 = 1e6; sigma = 0:3662300498525421 
   Feb 27, 2022   n=105983: 524006488639301231;                                     gr-mfaktc
   Feb 27, 2022   n=106261: 964304556368384557;                                     gr-mfaktc
   Feb 27, 2022   n=106357: 136932795017065511;                                     gr-mfaktc
   Feb 27, 2022   n=106427: 208323587345773747;                                     gr-mfaktc
   Feb 27, 2022   n=106433: 9683864110604702003;                                    gr-mfaktc


-  Found by Kurt Beschorner    
   Feb 22, 2022   n = 8643: 1231918927102657144077740449 * 1001334197......c5477;  ecm: B1 = 1e6; sigma = 8806613616603264
   Feb 22, 2022   n =12013: 1536385834522876929141100643711 * 1249213510......c11628; ecm: B1 = 1e6; sigma = 7457107054039909 


-  Found by Kurt Beschorner    
   Feb 17, 2022   n =50063: 9757380713636228609 * 9223786858......c46181;           ecm: B1 = 25e4; sigma = 1809386948907866
   Feb 17, 2022   n=104743: 5126997492618438959;                                    gr-mfaktc
   Feb 17, 2022   n=104827: 72376172739448439;                                      gr-mfaktc
   Feb 17, 2022   n=105167: 398082563045247551;                                     gr-mfaktc
   Feb 17, 2022   n=105253: 6193072086727682041;                                    gr-mfaktc
   Feb 17, 2022   n=105277: 148845517588448453;                                     gr-mfaktc



-  Found by Kurt Beschorner    
   Feb 11, 2022   n =12861: 774486397053952386409 * 3986073345......c8531;          ecm: B1 =25e4; sigma = 0:2573481897062944
   Feb 11, 2022   n =50059: 260852930083785338623772801;                            ecm: B1 =25e4; sigma = 7059562592557702
   Feb 11, 2022   n=103993: 6667088762912202871;                                    gr-mfaktc
   Feb 11, 2022   n=104239: 8331613232480529479;                                    gr-mfaktc
   Feb 11, 2022   n=104297: 1080325254039937483;                                    gr-mfaktc
   Feb 11, 2022   n=104327: 106524334433958997;                                     gr-mfaktc
   Feb 11, 2022   n=104399: 7527312047006451523;                                    gr-mfaktc

				  
-  Found by Alfred Eichhorn 
   Feb 05, 2022   n =44417: 23644045417857121244959 * 4699327426......c44394;       ecm: B1 = 5e4; sigma = 1404055939903579     


-  Found by Kurt Beschorner    
   Feb 04, 2022   n = 6019: 64934896628523533951892511453819871 * 1328324372...c5500; ecm: B1 = 1e6; sigma = 0:580414165519015 
   Feb 04, 2022   n=103171: 2457902326114895239;                                    gr-mfaktc 
   Feb 04, 2022   n=103217: 326880279049463801;                                     gr-mfaktc 
   Feb 04, 2022   n=103387: 486679672657017643;                                     gr-mfaktc 
   Feb 04, 2022   n=103391: 83982211551443267;                                      gr-mfaktc 
   Feb 04, 2022   n=103613: 1950601507045220591;                                    gr-mfaktc 




ECM efforts
with Rn:           1 < n < 2000 (May 19, 2022) with Rn:     1999 < n < 3000 (May 19, 2022)
with Rn:     2999 < n < 4000 (Apr 24, 2022) with Rn:     3999 < n < 5000 (May 06, 2022)
with Rn:     4999 < n < 6000 (Apr 30, 2022) with Rn:     5999 < n < 7000 (May 19, 2022)
with Rn:     6999 < n < 8000 (May 28, 2022) with Rn:     7999 < n < 9000 (Apr 25, 2022)
with Rn:     8999 < n <10000 (May 06, 2022) with Rn:     9999 < n <11000 (May 14, 2022)
with Rn:   10999 < n <12000 (May 19, 2022) with Rn:   11999 < n <14980L/M (Apr 25, 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 07, 2022) Repunits:  R2501 - R5000 (Mar 29, 2022)
Repunits: R5001   - R7500 (Apr 04, 2022) Repunits: R7501 - R10000 (Feb 27, 2022)
Repunits: R10001 - R12500 (May 19, 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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