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


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-  Last update: Oct 08, 2024 

- Found by YOYO@home/Defrag      
   Oct 08, 2024  n =  639: 929627442074193448101717553045350224940201718470443276606531700472416289; ecm: B1 = 2.9e9 
 

- Found by Alfred Eichhorn 
   Oct 06, 2024  n =15667: 11426092181973011277118595481581089;                     ecm: B1 = 1e6; sigma = 4278876499549301
   Oct 06, 2024  n =24019: 3856673819590507066880930323;                            ecm: B1 = 1e6; sigma = 4547196708979326
   Oct 06, 2024  n =24179: 67361590008950077783742827;                              ecm: B1 = 1e6; sigma = 2575665522867841
   Oct 06, 2024  n =24197: 37885141066413960891472381643;                           ecm: B1 = 1e6; sigma = 3930153077720417


- Found by Kurt Beschorner  
   Oct 04, 2024  n = 8152: 935691385845929911240971439606855630225681;              P-1: B1 = 1e9 
   Oct 04, 2024  n = 9332: 16747120850646488349464235094757201141;                  ecm: B1 = 1e6; sigma = 0:1748271489658466 
   Oct 04, 2024  n = 9638: 904580087855766619816908424382329;                       ecm: B1 = 1e6; sigma = 0:7953838129020119
   Oct 04, 2024  n = 9778: 10762415990988011981326048333823;                        ecm: B1 = 1e6; sigma = 4883708394567929
   Oct 04, 2024  n =33459: 6886400356423961565667;                                  P-1: B1 = 26e6  
   Oct 04, 2024  n =33460: 19577012143151821;                                       P-1: B1 = 55e6  
   Oct 04, 2024  n=100373: 58853502149943742151;                                    P-1: B1 = 26e6  
   Oct 04, 2024  n=100373: 28534847658501812904277;                                 P-1: B1 = 26e6  
   Oct 04, 2024  n=100375: 15593123793263712247751;                                 P-1: B1 = 26e6  
   Oct 04, 2024  n=100381: 9207186664030681;                                        P-1: B1 = 26e6  
   Oct 04, 2024  n=100384: 7027069454256328270529;                                  P-1: B1 = 55e6  
   Oct 04, 2024  n=100385: 49001033306526376591;                                    P-1: B1 = 26e6  
   Oct 04, 2024  n=100385: 214084067863086357490871;                                P-1: B1 = 26e6  
   Oct 04, 2024  n=100387: 47147676278372987773;                                    P-1: B1 = 26e6  
   Oct 04, 2024  n=100388: 321732821187430257125479349;                             P-1: B1 = 55e6  
   Oct 04, 2024  n=100394: 163453595655334375106811929;                             P-1: B1 = 55e6  
   Oct 04, 2024  n=100397: 9045742621485993523;                                     P-1: B1 = 26e6  
   Oct 04, 2024  n=100398: 10174546359106095367;                                    P-1: B1 = 55e6  
   Oct 04, 2024  n=100398: 34868951341687528358193007;                              P-1: B1 = 55e6  
   Oct 04, 2024  n=166013: 10958014037763604489;                                    gr-mfaktc 
   Oct 04, 2024  n=166151: 7272024960114191083;                                     gr-mfaktc 
   Oct 04, 2024  n=166273: 5530882519588581227;                                     gr-mfaktc 
 
 
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Oct 04, 2024   R2100L/c215: SNFS-difficulty = 280;
                  160M unique raw relations are collected;
                  target: 1450M unique raw relations;  
                  currently progress 11 %;    

 
- Found by Kurt Beschorner  
   Sep 29, 2024  n = 5935: 895577649718240766851420771286431;                       ecm: B1 = 1e6; sigma = 0:2558740426237798
   Sep 29, 2024  n =14008: 7557466138018613887752839718241;                         P-1: B1 = 425e6  
   Sep 29, 2024  n =14025: 494799595468837592912765329951;                          P-1: B1 = 200e6  
   Sep 29, 2024  n =20069: 625888769768322182081;                                   P-1: B1 =  26e6  
   Sep 29, 2024  n =20071: 10717561504971990516345053;                              P-1: B1 =  26e6  
   Sep 29, 2024  n =33445: 1469336791608911;                                        P-1: B1 =  26e6  
   Sep 29, 2024  n =33447: 491608830005525988853;                                   P-1: B1 =  26e6  
   Sep 29, 2024  n =33447: 187416928712199166553464081;                             P-1: B1 =  26e6  
   Sep 29, 2024  n =33448: 1351418898150824104130233;                               P-1: B1 =  55e6  
   Sep 29, 2024  n=100336: 330028917981567723303942673;                             P-1: B1 =  55e6  
   Sep 29, 2024  n=100338: 206912510296423;                                         P-1: B1 =  55e6  
   Sep 29, 2024  n=100339: 54223021923540945759365761;                              P-1: B1 =  26e6  
   Sep 29, 2024  n=100346: 383728351907091520013;                                   P-1: B1 =  55e6  
   Sep 29, 2024  n=100349: 2394463284595550867;                                     P-1: B1 =  25e6  
   Sep 29, 2024  n=100349: 571773078188199797711;                                   P-1: B1 =  25e6  
   Sep 29, 2024  n=100349: 2170923897743298135871;                                  P-1: B1 =  25e6  
   Sep 29, 2024  n=100354: 7017770946180281805900997;                               P-1: B1 =  55e6  
   Sep 29, 2024  n=100367: 437309391825563618085106691353003;                       P-1: B1 =  25e6  
   Sep 29, 2024  n=165059: 1412576064729866441;                                     gr-mfaktc 
   Sep 29, 2024  n=165367: 219042871356182639;                                      gr-mfaktc 
   Sep 29, 2024  n=165559: 3022209644667383591;                                     gr-mfaktc 
   Sep 29, 2024  n=165887: 2103548727932086601;                                     gr-mfaktc 


- Found by Kurt Beschorner  
   Sep 22, 2024  n =8820L: 38472335154641256621987535647777642463066081;            ecm: B1 =  43e6; sigma = 0:1776896642260120 
   Sep 22, 2024  n =13981: 41959916167823776617032638519;                           P-1: B1 = 180e6  
   Sep 22, 2024  n =15010: 2247135913811251472757731281;                            P-1: B1 = 475e6   
   Sep 22, 2024  n =33439: 53111770394178347969857294969;                           P-1: B1 =  26e6  
   Sep 22, 2024  n =33443: 136477096357797438371266784827;                          P-1: B1 =  26e6 
   Sep 22, 2024  n=100310: 1212708762180807686728089786270481;                      P-1: B1 =  55e6 
   Sep 22, 2024  n=100315: 50361950805780701077241;                                 P-1: B1 =  26e6 
   Sep 22, 2024  n=100319: 912888165648139220039;                                   P-1: B1 =  26e6 
   Sep 22, 2024  n=100319: 1057846236716005776317;                                  P-1: B1 =  26e6 
   Sep 22, 2024  n=100322: 8108488733399443679408089;                               P-1: B1 =  55e6 
   Sep 22, 2024  n=100325: 5827663597974964201;                                     P-1: B1 =  26e6 
   Sep 22, 2024  n=100325: 25321797375061892351;                                    P-1: B1 =  26e6 
   Sep 22, 2024  n=100325: 56630897862009020083404551;                              P-1: B1 =  26e6 
   Sep 22, 2024  n=100326: 783039991400508236893;                                   P-1: B1 =  55e6 
   Sep 22, 2024  n=100327: 35281606932001009;                                       P-1: B1 =  26e6 
   Sep 22, 2024  n=100327: 12828554947389278628650883738942364921;                  P-1: B1 =  26e6 
   Sep 22, 2024  n=100331: 21467063211868121;                                       P-1: B1 =  26e6 
   Sep 22, 2024  n=100331: 4862518420072955027;                                     P-1: B1 =  26e6 
   Sep 22, 2024  n=163567: 539641922197237843;                                      gr-mfaktc 
   Sep 22, 2024  n=163643: 8742778098628924369;                                     gr-mfaktc 
   Sep 22, 2024  n=163871: 81434437414508879;                                       gr-mfaktc 
   Sep 22, 2024  n=164363: 318453441593001283;                                      gr-mfaktc 
   Sep 22, 2024  n=164363: 7249093626119332237;                                     gr-mfaktc 
 

- Found by Kurt Beschorner  
   Sep 16, 2024  n = 7714: 674756255553554784010629810684186001;                    P-1: B1 = 55e6   
   Sep 16, 2024  n =13959: 10908706960626889587131773;                              P-1: B1 = 200e6 
   Sep 16, 2024  n =13967: 1546739122898324683549717612079311;                      P-1: B1 = 150e6
   Sep 16, 2024  n =14329: 183712653538982131518024939751;                          P-1: B1 = 26e6 
   Sep 16, 2024  n =20059: 80375529458480386963639;                                 P-1: B1 = 26e6 
   Sep 16, 2024  n =33428: 598073364853609567951344661;                             P-1: B1 = 55e6 
   Sep 16, 2024  n =33430: 1940207172302679533640091;                               P-1: B1 = 55e6 
   Sep 16, 2024  n =33431: 2986536836872837600454184202658521;                      P-1: B1 = 26e6 
   Sep 16, 2024  n =33433: 40818089630691856577333;                                 P-1: B1 = 26e6
   Sep 16, 2024  n =33435: 105983936158364548054452631;                             P-1: B1 = 26e6 
   Sep 16, 2024  n=100281: 1815632202447883;                                        P-1: B1 = 26e6 
   Sep 16, 2024  n=100283: 42379862892338239;                                       P-1: B1 = 26e6 
   Sep 16, 2024  n=100302: 163812185449385920151179;                                P-1: B1 = 55e6
   Sep 16, 2024  n=100307: 821138291293898067154050639683;                          P-1: B1 = 26e6 
   Sep 16, 2024  n=161503: 446701045025113763;                                      gr-mfaktc 
   Sep 16, 2024  n=161831: 3150992875204990759;                                     gr-mfaktc 
   Sep 16, 2024  n=161923: 265409454752698439;                                      gr-mfaktc 
   Sep 16, 2024  n=161983: 3102607059593915561;                                     gr-mfaktc 
   Sep 16, 2024  n=162053: 455764003592207053;                                      gr-mfaktc 
   Sep 16, 2024  n=162263: 16573976462383659653;                                    gr-mfaktc 
   Sep 16, 2024  n=162709: 6151846505317453609;                                     gr-mfaktc 
   Sep 16, 2024  n=162821: 533085113807320037;                                      gr-mfaktc 
   Sep 16, 2024  n=163147: 226382336474367907;                                      gr-mfaktc 
   Sep 16, 2024  n=163243: 450452936170769321;                                      gr-mfaktc 
   Sep 16, 2024  n=163243: 1158816080244718243;                                     gr-mfaktc 
   Sep 16, 2024  n=163351: 655996977828896117;                                      gr-mfaktc 
 
  
- Found by Torbjörn Granlund
   Sep 15, 2024  n = 1213: 3802200856589814744657128636563499435894999;             ecm: B1 = 1e6; sigma = 0:14488647671416981951
   Sep 15, 2024  n = 1815: 4098441872200433015045042676505414155509641;             ecm: B1 = 1e6; sigma = 0:11990104957816418499
   Sep 15, 2024  n = 2285: 2051498341294060742933143147274846947443401;             P-1: B1 = 1e9; B2 = 6084866733918
   Sep 15, 2024  n = 2391: 103182654083788921684537334713499683;                    ecm: B1 = 1e6; sigma = 0:12020620644682256341
   Sep 15, 2024  n = 2449: 600858453913730403856532541976772589443;                 P-1: B1 = 1e9; B2 = 6084866733918
   Sep 15, 2024  n = 2527: 647353766385319691857417203558887401;                    ecm: B1 = 1e6; sigma = 0:3621277789841061197
   Sep 15, 2024  n = 2535: 156754634687052062764416759087670471;                    ecm: B1 = 1e6; sigma = 1:3393956487
   Sep 15, 2024  n = 2543: 753304164049013002621804486735652843;                    ecm: B1 = 1e6; sigma = 1:1466944611
   Sep 15, 2024  n = 2705: 109195685007337483022299748369716146161;                 ecm: B1 = 1e6; sigma = 0:8906779298094550009
   Sep 15, 2024  n = 2745: 28485167471844891801410276138004175081;                  ecm: B1 = 1e6; sigma = 0:8604497436349318999
   Sep 15, 2024  n = 2829: 16410236115549830906505363137937169;                     ecm: B1 = 1e6; sigma = 0:1951234959635419041
   Sep 15, 2024  n = 2937: 18896097703630454952291685509584942533;                  ecm: B1 = 1e6; sigma = 1:759148817
   Sep 15, 2024  n = 3021: 27330873097344696912154806989332483;                     ecm: B1 = 1e6; sigma = 0:3201172410425856953
   Sep 15, 2024  n = 3569: 11400139053302182410990498057327124417267;               ecm: B1 = 3e6; sigma = 0:10865405958817156427
   Sep 15, 2024  n = 3585: 58085336248307618498777162746561;                        ecm: B1 = 1e6; sigma = 0:15009441137241804824
   Sep 15, 2024  n = 3667: 2080475367504865290478276992253031;                      ecm: B1 = 1e6; sigma = 0:12437885057015613011
   Sep 15, 2024  n = 3757: 33694379761057967269754016089273036507;                  ecm: B1 = 1e6; sigma = 1:273908683
   Sep 15, 2024  n = 3787: 7055345299224159172828355011806649;                      ecm: B1 = 1e6; sigma = 0:2830813724368277207
   Sep 15, 2024  n = 4055: 1948787780852220980547111695444679761;                   ecm: B1 = 1e6; sigma = 0:17455056067453863873
   Sep 15, 2024  n = 4103: 1741547372143431977118494290270117837;                   ecm: B1 = 1e6; sigma = 0:5025907934834844875
   Sep 15, 2024  n = 4165: 14502689303731246267058119792968671;                     ecm: B1 = 1e6; sigma = 0:5727017555073026671
   Sep 15, 2024  n = 4191: 22984383232857352472100689865991849;                     ecm: B1 = 1e6; sigma = 0:12310506994298116883
   Sep 15, 2024  n = 4265: 14287864954281769595031262840766686391;                  ecm: B1 = 1e6; sigma = 0:16892259785869631342 
   Sep 15, 2024  n = 4507: 144033826328835512829127544710780565639;                 ecm: B1 = 1e6; sigma = 0:449790939880095147
   Sep 15, 2024  n = 4509: 2460235364293681340814960094035702961;                   ecm: B1 = 3e6; sigma = 0:15501487315860969557
   Sep 15, 2024  n = 4739: 169909323009560405443119802808507;                       ecm: B1 = 1e6; sigma = 0:5951338009732668807
   Sep 15, 2024  n = 4869: 486782628447541143585231274986757711;                    ecm: B1 = 1e6; sigma = 0:7300925068061572311
   Sep 15, 2024  n = 4919: 6530957056632063748192085275662319;                      ecm: B1 = 1e6; sigma = 0:6603285319019973935
   Sep 15, 2024  n = 5215: 125442818692110058393659177580154599647431;              ecm: B1 = 1e6; sigma = 1:177897093
   Sep 15, 2024  n = 5465: 165659419307517545705863974768344231;                    ecm: B1 = 1e6; sigma = 0:6603285319019973935
   Sep 15, 2024  n = 5593: 30774474478303908730228394315801;                        ecm: B1 = 1e6; sigma = 0:78372119094033
   Sep 15, 2024  n = 5651: 253153202072068480481374624902090462157;                 ecm: B1 = 1e6; sigma = 0:12798764993499092605
   Sep 15, 2024  n = 5711: 1458424360860342794605064778192559441;                   ecm: B1 = 1e6; sigma = 0:5963013522829996799
   Sep 15, 2024  n = 5743: 14811624013463002360724048056372841;                     ecm: B1 = 1e6; sigma = 0:78372119094033
   Sep 15, 2024  n = 5831: 318654001333309317352041936803;                          ecm: B1 = 1e6; sigma = 1:3393956487
   Sep 15, 2024  n = 5917: 62128869315196783538931039009211738481;                  ecm: B1 = 1e6; sigma = 1:1474470163
   Sep 15, 2024  n = 6011: 5656607367075011571023869359496363;                      ecm: B1 = 1e6; sigma = 1:273908683
   Sep 15, 2024  n = 6093: 1336143863663099786889758180375119;                      ecm: B1 = 1e6; sigma = 1:3616795357
  *Sep 15, 2024  n = 6155: 16956196546484050694626455982001;                        ecm: B1 = 1e6; sigma = 0:18296581214409180617
   Sep 15, 2024  n = 6173: 5053071098890826667938286305293;                         ecm: B1 = 1e6; sigma = 0:199762724765272745
   Sep 15, 2024  n = 6237: 14089779120825363590790687940304359;                     ecm: B1 = 1e6; sigma = 0:15637767851225334323
   Sep 15, 2024  n = 6327: 1596489365351468828532617242104403;                      ecm: B1 = 1e6; sigma = 1:759148817
   Sep 15, 2024  n = 6407: 373939098107201919765478843483;                          ecm: B1 = 1e6; sigma = 0:11362242212281988111
   Sep 15, 2024  n = 6417: 294088177038615753783998327225437;                       ecm: B1 = 1e6; sigma = 1:3425686205
   Sep 15, 2024  n = 6465: 221112688029324217201473060951751;                       ecm: B1 = 1e6; sigma = 0:8473284529095742021
   Sep 15, 2024  n = 6509: 100936144535747450211445731409;                          ecm: B1 = 1e6; sigma = 0:1532057093235231923
   Sep 15, 2024  n = 6579: 14928911404373501386802247002821217191;                  ecm: B1 = 1e6; sigma = 0:1532057093235231923
   Sep 15, 2024  n = 6747: 6723829837620032920626623393563;                         ecm: B1 = 1e6; sigma = 0:11914725518606056737
   Sep 15, 2024  n = 6767: 1943538884462222777971431975683519;                      ecm: B1 = 1e6; sigma = 0:11914725518606056737
   Sep 15, 2024  n = 6775: 7651560979032194699667735601;                            ecm: B1 = 1e6; sigma = 0:7938031375900419525
   Sep 15, 2024  n = 6785: 8367957136701535535458360493059871;                      ecm: B1 = 1e6; sigma = 0:8253462866479087135
   Sep 15, 2024  n = 6799: 170625890566634686201590537198169;                       ecm: B1 = 1e6; sigma = 0:189873710409027
   Sep 15, 2024  n = 6827: 605563853021030672629776013561;                          ecm: B1 = 1e6; sigma = 0:15042871998340189925
   Sep 15, 2024  n = 6873: 11732138724635366578685236204921;                        ecm: B1 = 1e6; sigma = 1:77461235
   Sep 15, 2024  n = 6933: 2056666694145181286351906929282494283;                   ecm: B1 = 1e6; sigma = 1:1753592501
   Sep 15, 2024  n = 6955: 4770123797091402986659534165081;                         ecm: B1 = 1e6; sigma = 0:7545309159719229623
   Sep 15, 2024  n = 7011: 40932492158522147916939842503117;                        ecm: B1 = 1e6; sigma = 0:15428700728936867661
   Sep 15, 2024  n = 7047: 2721713105317415253764995487154864151;                   ecm: B1 = 1e6; sigma = 0:14957306403135743853
   Sep 15, 2024  n = 7203: 358477182201157632404210989262323;                       ecm: B1 = 1e6; sigma = 0:1899485105162830283
   Sep 15, 2024  n = 7225: 4302621570884152909003933564616551;                      ecm: B1 = 1e6; sigma = 0:263415883537725
   Sep 15, 2024  n = 7389: 2898661596886202374101295254853;                         ecm: B1 = 1e6; sigma = 0:18401888294117552977
   Sep 15, 2024  n = 7405: 1000777605747316235823378402467201;                      ecm: B1 = 1e6; sigma = 1:182620923
   Sep 15, 2024  n = 7435: 31538057598641330421637379793605858911;                  ecm: B1 = 1e6; sigma = 0:17646512381195540761
   Sep 15, 2024  n = 7453: 519352817483043973396038245141801;                       ecm: B1 = 1e6; sigma = 0:17646512381195540761
   Sep 15, 2024  n = 7455: 491214058175515798301044852544161;                       ecm: B1 = 1e6; sigma = 0:1038547052753189993
   Sep 15, 2024  n = 7481: 4972615427247872817986627484420443;                      ecm: B1 = 1e6; sigma = 0:12798764993499092605
   Sep 15, 2024  n = 7497: 120992296050473892227494196483557;                       ecm: B1 = 1e6; sigma = 0:3207401511136924985
   Sep 15, 2024  n = 7571: 18698117426765456482515727025468521;                     ecm: B1 = 1e6; sigma = 0:8906779298094550009
   Sep 15, 2024  n = 7579: 19746693354511063241762048385799;                        ecm: B1 = 1e6; sigma = 1:2923719129
   Sep 15, 2024  n = 7657: 23156299845678068145104500838792479;                     ecm: B1 = 1e6; sigma = 0:11914725518606056737
   Sep 15, 2024  n = 7707: 10239935254977661685645752476121;                        ecm: B1 = 1e6; sigma = 0:14778809121148116955
   Sep 15, 2024  n = 7709: 3603902959985554170713863151227;                         ecm: B1 = 1e6; sigma = 0:78372119094033
   Sep 15, 2024  n = 7735: 7852631810215021420841043096031;                         ecm: B1 = 1e6; sigma = 1:1664073337
   Sep 15, 2024  n = 7751: 2508815958146815988829093095690279;                      ecm: B1 = 1e6; sigma = 0:10977665072412782587
   Sep 15, 2024  n = 7885: 19715636275865932733299589027883883203241;               ecm: B1 = 1e6; sigma = 1:3605802901
   Sep 15, 2024  n = 8065: 60524026956189845504863462287391241;                     ecm: B1 = 1e6; sigma = 0:13156499177556375355
   Sep 15, 2024  n = 8087: 676176399587129808611509701831277;                       ecm: B1 = 1e6; sigma = 0:7093308573280539123
   Sep 15, 2024  n = 8123: 4814330511191140848342973783129;                         ecm: B1 = 1e6; sigma = 0:10440896923169321451
   Sep 15, 2024  n = 8357: 20176718421494524195035668600213;                        ecm: B1 = 1e6; sigma = 0:12798764993499092605
   Sep 15, 2024  n = 8377: 5687690333174390215382594316043;                         ecm: B1 = 1e6; sigma = 1:1156762131
   Sep 15, 2024  n = 8387: 10938520602149818569869171575609;                        ecm: B1 = 1e6; sigma = 1:1664073337
   Sep 15, 2024  n = 8449: 1866759297062204231700511602262397;                      ecm: B1 = 1e6; sigma = 0:10547514346612664537
   Sep 15, 2024  n = 8527: 243375472861762690397991792264917;                       ecm: B1 = 1e6; sigma = 0:11990104957816418499
   Sep 15, 2024  n = 8549: 15925358773101069259411105353519319;                     ecm: B1 = 1e6; sigma = 0:6603285319019973935
   Sep 15, 2024  n = 8665: 25409864545263329255648473295928871;                     ecm: B1 = 1e6; sigma = 0:9616308672479705735
   Sep 15, 2024  n = 8781: 416828196947164610392504584224599;                       ecm: B1 = 1e6; sigma = 0:17365221873064881403
   Sep 15, 2024  n = 8833: 1063599702251709943979714751587;                         ecm: B1 = 1e6; sigma = 1:1652174903
   Sep 15, 2024  n = 8857: 3112229527773266800727250108835512151;                   ecm: B1 = 1e6; sigma = 0:12466699163099994441
   Sep 15, 2024  n = 8861: 514228458427027657041198238405757;                       ecm: B1 = 1e6; sigma = 0:8906779298094550009
   Sep 15, 2024  n = 9295: 13812317980966297693444361767795561;                     ecm: B1 = 1e6; sigma = 0:5963013522829996799
   Sep 15, 2024  n = 9581: 95233941496960508695109319521;                           ecm: B1 = 1e6; sigma = 1:1751343877
   Sep 15, 2024  n = 9879: 622083644065230480047758412090677;                       ecm: B1 = 1e6; sigma = 0:1038547052753189993
   Sep 15, 2024  n = 9965: 50664542210486897314398938301663311;                     ecm: B1 = 1e6; sigma = 0:17127812835675519603
 **Sep 15, 2024  n = 8655: 127381682260506697042031958031;                          ecm: B1 = 1e6; sigma = 0:9616308672479705735

*  this factor is included in other factor collections, but is missing in my list so far
** this factor was also found by Kurt Beschorner mit B1=1e6, sigma=0:2925821086176721


-  Found by Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Oliver Kruse, Kurt Beschorner 
   Sep 09, 2024  n =  471: 1640259175221723797786233348156700513564345502781851447654042775375772294825108377125627674387206196531834389323135517030822828838413 ;SNFS 
   A big thank to Oliver Kruse for carrying out Filtering-, Linear Algebra- and Square Root-Step

   Details:
   - R471: SNFS-difficulty = 314 
   - Compile remdups with the necessary lpb size
     the relations need to be aggregated and cleaned. Run remdups on the total file.
   - use CADO-NFS to perform singleton and clique removal, since msieve was giving weird results with  
     that many relations
     -   compile CADO-NFS from GIT using FLAGS_SIZE='-DSIZEOF_P_R_VALUES=8'.
     -   use dup1 to make sure all relations are in a format that CADO-NFS does understand (and 
	     to split the relations file for dup2). (also see Note A.)
     -   execute freerel to get a renumber table (necessary for dup2 and later to convert relations 
	     back to msieve format).
     -   use check_rels to make sure all relations are not only syntactically, but also semantically 
	     correct. This needs to be compiled half-manually. (also see Note A here, too.)
     -   count the exact number of relations per output file of dup2. It is a required input for purge.
     -   execute dup2.
     -   execute purge with -keep 0. (Also see Note B.)
     -   convert all relations back to msieve format using convert_rels, which must be compiled 
	     half-manually. (also see Note C.)
    Use msieve to build a matrix. Target density must be set such that the resulting matrix is 
	indicated to take up less than (around) 40 % of the available VRAM of the GPU that should be 
	used to solve it.
    Compress the matrix and upload it to the GPU system while preparing msieve-GPU.
    Perform LA on a GPU.
    Only move back the .dep file.
    Use it to perform the square root with msieve.

    General notes:
    In most cases, zstd was used to compress intermediate data instead of gz. The main advantage 
	for this project was a much better compression and also decompression speed.
    All msieve invocations can be done using a normal msieve executable without CUDA. 
	Only step 7 requires CUDA. VBITS must be the same for all, though.
    
	Note A: It looks like we were using a suboptimal version of remdups. It was creating Windows-like 
	line breaks (\r\n) after each relation, which CADO does not like at all. It took some time to 
	figure out that this was the reason CADO rejected the input files. It had not helped that I used 
	the wrong input file at least twice for dup1. At first, we had multiple problems with the 
	relations going into dup2, too. Unlike msieve, CADO will not tolerate malformed or otherwise 
	invalid relations at all and will exit immediately upon coming across such a relation. So, 
	it was necessary to run all relations through CADOs check_rels.
    
    Note B: CADOs purge can be really memory hungry. Combined with running it in WSL instead 
	natively in Linux, it required moving to a 256 GB machine. You can reduce memory usage by 
	increasing the minimum ideal that is taken into account, but this will lead to a bigger matrix. 
	Interestingly, using a single input file here uses less memory than using multiple ones.

    Note C: Because purge puts a header into the output file, convert_rels was unable to read it. 
	This was only obvious after it already ran for around half an hour. The workaround was to rewrite 
	the file completely, since using named pipes (which is officially supported by CADO) did not work. 
	Additionally, since last time around, I forgot to inform the CADO team of another important bug 
	in convert_rels, which lead to a crash multiple times such that I needed to resume this step from 
	the beginning.
    
     Msieve v. 1.54 (SVN Unversioned directory)
     random seeds: 22542d19 700fd33a
     Using 24 OpenMP threads
     factoring 1965855492352837291404845479654790137388296457407020488269903568174723758784689544879875331228364955840869702567549967104798287157041292434187430297308705569214878772495168471094461040429176109825875894905836601377280929371811156517642415988656250783860548270986479505416039357494202079267278420861079 (301 digits)
     no P-1/P+1/ECM available, skipping
     commencing number field sieve (301-digit input)
     R0: -10000000000000000000000000000000000000000000000000000
     R1: 1
     A0: 1
     A1: 0
     A2: 0
     A3: 10
     A4: 0
     A5: 0
     A6: 100
     skew 0.64, size 2.684e-15, alpha -0.127, combined = 1.160e-15 rroots = 0
     commencing relation filtering
     setting target matrix density to 110.0
     estimated available RAM is 130983.0 MB
     commencing duplicate removal, pass 1
     skipped 195759 relations with b > 2^32
     found 14183037 hash collisions in 256635802 relations
     added 812721 free relations
     commencing duplicate removal, pass 2
     found 0 duplicates and 257448523 unique relations
     memory use: 852.8 MB
     reading ideals above 720000
     commencing singleton removal, initial pass
     memory use: 6024.0 MB
     reading all ideals from disk
     memory use: 13898.6 MB
     keeping 255321547 ideals with weight <= 200, target excess is 1416068
     commencing in-memory singleton removal
     begin with 257448523 relations and 255321547 unique ideals
     reduce to 255910332 relations and 253781718 ideals in 10 passes
     max relations containing the same ideal: 200
     removing 2120221 relations and 1877233 ideals in 242988 cliques
     commencing in-memory singleton removal
     begin with 253790111 relations and 253781718 unique ideals
     reduce to 253783216 relations and 251897583 ideals in 6 passes
     max relations containing the same ideal: 200
     removing 1774348 relations and 1531360 ideals in 242988 cliques
     commencing in-memory singleton removal
     begin with 252008868 relations and 251897583 unique ideals
     reduce to 252003594 relations and 250360945 ideals in 6 passes
     max relations containing the same ideal: 200
     relations with 0 large ideals: 35079
     relations with 1 large ideals: 3674
     relations with 2 large ideals: 59481
     relations with 3 large ideals: 659291
     relations with 4 large ideals: 4064521
     relations with 5 large ideals: 15366490
     relations with 6 large ideals: 37495822
     relations with 7+ large ideals: 194319236
     commencing 2-way merge
     reduce to 144312791 relation sets and 142670142 unique ideals
     commencing full merge
     memory use: 20048.0 MB
     found 70134540 cycles, need 70072342
     weight of 70072342 cycles is about 8409316266 (120.01/cycle)
     distribution of cycle lengths:
     1 relations: 4697219
     2 relations: 5089969
     3 relations: 5433471
     4 relations: 5432869
     5 relations: 5495154
     6 relations: 5428351
     7 relations: 5211829
     8 relations: 4928798
     9 relations: 4532377
     10+ relations: 23822305
     heaviest cycle: 28 relations
     commencing cycle optimization
     start with 560882223 relations
     pruned 19098959 relations
     memory use: 16245.5 MB
     distribution of cycle lengths:
     1 relations: 4697219
     2 relations: 5208416
     3 relations: 5636060
     4 relations: 5617967
     5 relations: 5717993
     6 relations: 5624587
     7 relations: 5413703
     8 relations: 5076769
     9 relations: 4648077
     10+ relations: 22431551
     heaviest cycle: 28 relations
     RelProcTime: 4571
     elapsed time 01:16:23	 

     Msieve v. 1.54 (SVN 03e8738)
     random seeds: 95b0afac d58c1bc1
     Using 32 OpenMP threads
     factoring 1965855492352837291404845479654790137388296457407020488269903568174723758784689544879875331228364955840869702567549967104798287157041292434187430297308705569214878772495168471094461040429176109825875894905836601377280929371811156517642415988656250783860548270986479505416039357494202079267278420861079 (301 digits)
     no P-1/P+1/ECM available, skipping
     commencing number field sieve (301-digit input)
     R0: -10000000000000000000000000000000000000000000000000000
     R1: 1
     A0: 1
     A1: 0
     A2: 0
     A3: 10
     A4: 0
     A5: 0
     A6: 100
     skew 0.64, size 2.684e-15, alpha -0.127, combined = 1.160e-15 rroots = 0
     commencing linear algebra
     using VBITS=256
     read 70072342 cycles
     cycles contain 250842437 unique relations
     read 250842437 relations
     using 20 quadratic characters above 4294917295
     building initial matrix
     memory use: 33524.4 MB
     read 70072342 cycles
     matrix is 70072165 x 70072342 (33432.7 MB) with weight 9689382635 (138.28/col)
     sparse part has weight 7993393340 (114.07/col)
     filtering completed in 2 passes
     matrix is 70071650 x 70071825 (33432.7 MB) with weight 9689366449 (138.28/col)
     sparse part has weight 7993389930 (114.07/col)
     matrix starts at (0, 0)
     matrix is 70071650 x 70071825 (33432.7 MB) with weight 9689366449 (138.28/col)
     sparse part has weight 7993389930 (114.07/col)
     saving the first 240 matrix rows for later
     matrix includes 256 packed rows
     matrix is 70071410 x 70071825 (31241.0 MB) with weight 7385816689 (105.40/col)
     sparse part has weight 7068490644 (100.87/col)
	 
     Msieve v. 1.54 (SVN unknown)
     random seeds: 251b2ce5 114b0fd1
     Using 32 OpenMP threads
     factoring 1965855492352837291404845479654790137388296457407020488269903568174723758784689544879875331228364955840869702567549967104798287157041292434187430297308705569214878772495168471094461040429176109825875894905836601377280929371811156517642415988656250783860548270986479505416039357494202079267278420861079 (301 digits)
     no P-1/P+1/ECM available, skipping
     commencing number field sieve (301-digit input)
     R0: -10000000000000000000000000000000000000000000000000000
     R1: 1
     A0: 1
     A1: 0
     A2: 0
     A3: 10
     A4: 0
     A5: 0
     A6: 100
     skew 0.64, size 2.684e-15, alpha -0.127, combined = 1.160e-15 rroots = 0
     commencing linear algebra
     using VBITS=256
     skipping matrix build
     matrix starts at (0, 0)
     matrix is 70071650 x 70071825 (33432.7 MB) with weight 9689366449 (138.28/col)
     sparse part has weight 7993389930 (114.07/col)
     saving the first 240 matrix rows for later
     matrix includes 256 packed rows
     matrix is 70071410 x 70071825 (31241.0 MB) with weight 7385816689 (105.40/col)
     sparse part has weight 7068490644 (100.87/col)
     using GPU 0 (NVIDIA H100 PCIe)
     selected card has CUDA arch 9.0
     commencing Lanczos iteration
     memory use: 73708.7 MB
     linear algebra at 0.0%, ETA 75h36m
     checking every 10000 dimensions, checkpointing every 930000 dimensions
     lanczos halted after 274538 iterations (dim = 70071410)
     recovered 40 nontrivial dependencies
     BLanczosTime: 276117
     elapsed time 76:41:59
	 
     Msieve v. 1.54 (SVN 03e8738)
     random seeds: d6ea5a4e 0e0c5aab
     Using 32 OpenMP threads
     factoring 1965855492352837291404845479654790137388296457407020488269903568174723758784689544879875331228364955840869702567549967104798287157041292434187430297308705569214878772495168471094461040429176109825875894905836601377280929371811156517642415988656250783860548270986479505416039357494202079267278420861079 (301 digits)
     no P-1/P+1/ECM available, skipping
     commencing number field sieve (301-digit input)
     R0: -10000000000000000000000000000000000000000000000000000
     R1: 1
     A0: 1
     A1: 0
     A2: 0
     A3: 10
     A4: 0
     A5: 0
     A6: 100
     skew 0.64, size 2.684e-15, alpha -0.127, combined = 1.160e-15 rroots = 0
     commencing square root phase
     reading relations for dependency 1
     read 35037193 cycles
     cycles contain 125421358 unique relations
     read 125421358 relations
     multiplying 125421358 relations
     multiply complete, coefficients have about 4308.20 million bits
     initial square root is modulo 67829
     sqrtTime: 2268
     p133 factor: 1640259175221723797786233348156700513564345502781851447654042775375772294825108377125627674387206196531834389323135517030822828838413
     p169 factor: 1198502969560954086012481725168695397135830513406164199283390644836971622395777548502750249372319768692484414977114966914781995864448420397015346304418294720261680325683
     elapsed time 00:37:49


- Found by Alfred Eichhorn 
   Sep 09, 2024  n =15091: 14845413823789711008287828293;                           ecm: B1 = 1e6; sigma = 2136717002765025
   Sep 09, 2024  n =15149: 12301910027669319512906185199;                           ecm: B1 = 1e6; sigma = 8122641535983119

 
- Found by Kurt Beschorner  
   Sep 06, 2024  n = 6655: 47002315541332120475432927835118351;                     ecm: B1 = 1e6; sigma = 0:3671949798087517
   Sep 06, 2024  n =13908: 4796645886147946366365200759449;                         P-1: B1 = 500e6 
   Sep 06, 2024  n =13917: 1946882395844921741959;                                  P-1: B1 =150e6 
   Sep 06, 2024  n =13917: 479634834466543489354729;                                P-1: B1 =150e6 
   Sep 06, 2024  n =33423: 1431696564802773760921;                                  P-1: B1 = 23e6 
   Sep 06, 2024  n=100256: 2129531546192902994273;                                  P-1: B1 = 55e6 
   Sep 06, 2024  n=100259: 7373367128510290221763;                                  P-1: B1 = 23e6 
   Sep 06, 2024  n=100261: 2578509001157321;                                        P-1: B1 = 23e6 
   Sep 06, 2024  n=100265: 1081414204698376192537440361;                            P-1: B1 = 23e6 
   Sep 06, 2024  n=100268: 510114955101536530235729;                                P-1: B1 = 55e6 
   Sep 06, 2024  n=100270: 92110972364038616356834631775642121;                     P-1: B1 = 55e6 
   Sep 06, 2024  n=100271: 22605675903598064150949502733;                           P-1: B1 = 23e6 
   Sep 06, 2024  n=159977: 16055910264628866119;                                    gr-mfaktc 
   Sep 06, 2024  n=160481: 3061777772635910203;                                     gr-mfaktc 
   Sep 06, 2024  n=160619: 12625299179729486347;                                    gr-mfaktc 
   Sep 06, 2024  n=160637: 6622464926200147133;                                     gr-mfaktc 
   Sep 06, 2024  n=160687: 14217364466292133721;                                    gr-mfaktc 
   Sep 06, 2024  n=160723: 1053461002320903707;                                     gr-mfaktc 
   Sep 06, 2024  n=160781: 10091891125422883573;                                    gr-mfaktc 
   Sep 06, 2024  n=160879: 1363625823793966609;                                     gr-mfaktc 


- Found by Kurt Beschorner  
   Aug 30, 2024  n = 9382: 9300968916181881256379682557271761;                      ecm: B1 = 1e6; sigma = 0:5919480135446658   
   Aug 30, 2024  n = 9388: 6367464694402438045010892622442009;                      ecm: B1 = 1e6; sigma = 0:7946659145174239  
   Aug 30, 2024  n = 9404: 22051978558725308479114046671949;                        ecm: B1 = 1e6; sigma = 0:5927629009860808    
   Aug 30, 2024  n =13891: 3783946127200973031121;                                  P-1: B1 = 150e6 
   Aug 30, 2024  n=100243: 2801869717572335479993639;                               P-1: B1 = 23e6 
   Aug 30, 2024  n=100247: 2270707106604318898415803;                               P-1: B1 = 23e6 
   Aug 30, 2024  n=100248: 137328742232380242793;                                   P-1: B1 = 55e6 
   Aug 30, 2024  n=100249: 3589469193300853;                                        P-1: B1 = 23e6 
   Aug 30, 2024  n=100251: 57734074812011041;                                       P-1: B1 = 23e6 
   Aug 30, 2024  n=100252: 288219713789126385282941;                                P-1: B1 = 55e6 
   Aug 30, 2024  n=158761: 672701845713258917;                                      gr-mfaktc 
   Aug 30, 2024  n=158849: 1725374401029737483;                                     gr-mfaktc 
   Aug 30, 2024  n=159233: 529647323937549359;                                      gr-mfaktc 
   Aug 30, 2024  n=159589: 5519361762904215599;                                     gr-mfaktc 
   Aug 30, 2024  n=159673: 86101299875254837;                                       gr-mfaktc 
   Aug 30, 2024  n=159673: 4106033786290026523;                                     gr-mfaktc 
 

- Refound by Torbjörn Granlund
  These factors are included in other factor collections, but were missing in my list so far
   Aug 25, 2024  n = 6021: 23308378966227762884772440482213;                        ecm: B1 = 5e5; sigma = 1:2763443333  
   Aug 25, 2024  n = 6039: 618705572139372055392845874667;                          ecm  
   Aug 25, 2024  n = 6077: 131250203872602296917762907;                             ecm  
   Aug 25, 2024  n = 6109: 572304669039890040281668915751;                          ecm: B1 = 5e5; sigma = 1:2790569943  
   Aug 25, 2024  n = 6129: 82258264783630847326576167169759;                        ecm: B1 = 5e5; sigma = 1:1157681981 
   Aug 25, 2024  n = 6141: 7674353218561984441674367003;                            ecm: B1 = 1e6; sigma = 9291063370823 
   Aug 25, 2024  n = 6511: 29364035473504104631839304799;                           ecm: B1 = 5e5; sigma = 1:4134148097  
   Aug 25, 2024  n = 6585: 9708257864061709876965357361;                            ecm: B1 = 5e5; sigma = 1:1421757241  
   Aug 25, 2024  n = 6699: 63215543447578696429538053;                              ecm: B1 = 5e5; sigma = 1:4106642173 
   Aug 25, 2024  n = 8343: 454691884393831469612926843;                             ecm  

  
- Found by Anonymous  
   Jul 31, 2024  n = 1322: 32428891213264191224745951834819424405467767 * 4620246399......P608;                     

- Found by Anonymous  
   Aug 22, 2024  n = 2342: 1277793770824393367115298917352334092381609;                     
   Aug 22, 2024  n = 2966: 95981284857953712560599708643474527;                     
   Aug 22, 2024  n=110158: 745282464034481898056474303437;                     
   Aug 22, 2024  n=111854: 177644219562011245398893;                     


- Found by Kurt Beschorner  
   Aug 21, 2024  n = 5681: 107401683479315589206835972735096277;                    ecm: B1 = 1e6; sigma = 0:4319425451299188 
   Aug 21, 2024  n = 9374: 106678980116741885690755417326646783;                    ecm: B1 = 1e6; sigma = 0:5204325677688199 
   Aug 21, 2024  n =13855: 456647776571096966682457032601;                          P-1: B1 = 200e6
   Aug 21, 2024  n =13865: 18952458289368990140570605351;                           P-1: B1 = 175e6
   Aug 21, 2024  n =13875: 20231400133345763391573474001;                           P-1: B1 = 175e6 
   Aug 21, 2024  n =13877: 2665599110827931151219887243864069553535617569;          P-1: B1 = 175e6 
   Aug 21, 2024  n =13881: 613342693696505872009;                                   P-1: B1 = 175e6 
   Aug 21, 2024  n =14319: 10344827787841879150524132169;                           P-1: B1 = 23e6 
   Aug 21, 2024  n =33411: 3967059885436254664099519;                               P-1: B1 = 23e6 
   Aug 21, 2024  n=157561: 5998484463028396333;                                     gr-mfaktc 
   Aug 21, 2024  n=157889: 6489787974242716681;                                     gr-mfaktc 
   Aug 21, 2024  n=157999: 98725868644107347;                                       gr-mfaktc 
   Aug 21, 2024  n=158591: 1270898937718055791;                                     gr-mfaktc 
   Aug 21, 2024  n=158731: 2774590512897177347;                                     gr-mfaktc 


- Found by Torbjörn Granlund
   Aug 20, 2024  n = 1651: 275217017911139624191776255507977127851519;              ecm: B1 = 1e6; sigma = 1:2194818103 
   Aug 20, 2024  n = 1841: 13025697981837238885482617576986077347;                  ecm: B1 = 2e6; sigma = 1:2177576267 
   Aug 20, 2024  n = 1891: 25728430999471065289640031125872987;                     ecm: B1 = 5e5; sigma = 1:3646079215 
   Aug 20, 2024  n = 2099: 904895108749261583158479086319155797;                    ecm: B1 = 1e6; sigma = 120529647102471 
   Aug 20, 2024  n = 2305: 216435273116164865199941012008081;                       ecm: B1 = 1e6; sigma = 1:2792610879 
   Aug 20, 2024  n = 2321: 7819586608885407861280912213052933;                      ecm: B1 = 2e6; sigma = 144531525929635 
   Aug 20, 2024  n = 2361: 15093661730388660744164111101395889;                     ecm                        
   Aug 20, 2024  n = 2413: 945153149166264948533842733420136547;                    ecm: B1 = 1e6; sigma = 30278076774429 
   Aug 20, 2024  n = 2453: 805882633277252112088879931097297947;                    ecm: B1 = 2e6; sigma = 116639200445373 
   Aug 20, 2024  n = 2495: 14339967467738136676523658916529111;                     ecm: B1 = 1e6; sigma = 1:3516144215 
   Aug 20, 2024  n = 2817: 19763398523108376154207863498493214803;                  ecm: B1 = 2e6; sigma = 1:1298358369 
   Aug 20, 2024  n = 2849: 1066161704325642263898000395207191477;                   P-1: B1 = 1e8  
   Aug 20, 2024  n = 2921: 2318555267727405835742851813721;                         ecm: B1 = 5e5; sigma = 1:4248825949 
   Aug 20, 2024  n = 2995: 284277203341019855415851097076878001;                    ecm: B1 = 2e6; sigma = 53292640982751 
   Aug 20, 2024  n = 3303: 17001394447702258475801953896133;                        ecm: B1 = 1e6; sigma = 1:164161343 
   Aug 20, 2024  n = 3403: 7709805385433232909996248569396122289;                   ecm: B1 = 1e6; sigma = 756340299292 
   Aug 20, 2024  n = 3613: 791933522809774878033488285297044583803;                 ecm: B1 = 5e5; sigma = 1:799608949 
   Aug 20, 2024  n = 3811: 29858372234782008133506150260148517;                     ecm: B1 = 1e6; sigma = 1:2792610879 
   Aug 20, 2024  n = 3911: 18918639432157448162617460631131878973;                  ecm: B1 = 5e5; sigma = 1:443161973 
   Aug 20, 2024  n = 3923: 44626167058457804083500990661961;                        ecm: B1 = 5e5; sigma = 1:2340622139 
   Aug 20, 2024  n = 3941: 156231445687689775996693860568271;                       ecm: B1 = 1e6; sigma = 1:121282519 
   Aug 20, 2024  n = 3977: 2354312200678631452069214594821314015641;                ecm: B1 = 1e6; sigma = 756340299292 
   Aug 20, 2024  n = 4125: 86059536640000496045815898721001;                        ecm: B1 = 1e6; sigma = 1:2200366123 
   Aug 20, 2024  n = 4319: 9422301660512506090795954466290799;                      ecm: B1 = 3e6; sigma = 1:177065869 
   Aug 20, 2024  n = 4393: 865255910975605274092556312523773;                       ecm: B1 = 3e6; sigma = 1:173734405 
   Aug 20, 2024  n = 4543: 588604060502740427330089290043351;                       ecm: B1 = 1e6; sigma = 1:2991743399 
   Aug 20, 2024  n = 4673: 4345443283056620687247864599302382797;                   ecm: B1 = 1e6; sigma = 1:3966327997 
   Aug 20, 2024  n = 4757: 2801002227013271452145195299558637776841;                ecm: B1 = 1e6; sigma = 192084558329613 
   Aug 20, 2024  n = 4805: 110892774637887477659990433599099441;                    ecm: B1 = 5e5; sigma = 1:3281332265 
   Aug 20, 2024  n = 5239: 48210422609883103613072789653231729;                     ecm: B1 = 1e6; sigma = 80482442127625 
   Aug 20, 2024  n = 5331: 2816300997574793172646729775188850191;                   ecm: B1 = 5e5; sigma = 1:1564726371 
   Aug 20, 2024  n = 5699: 64766941561181774734373002834423813;                     ecm: B1 = 5e5; sigma = 1:1274567173 
   Aug 20, 2024  n = 5785: 39654135024926477843166872734614906521;                  ecm: B1 = 5e5; sigma = 1:1199392889 
   Aug 20, 2024  n = 5871: 65942014250649795606197848118521;                        ecm: B1 = 1e6; sigma = 52967061287689 
   Aug 20, 2024  n = 5935: 712210020588854919195548201211311;                       ecm: B1 = 5e5; sigma = 1:3855436389 
   Aug 20, 2024  n = 5989: 36923066507963101716971022287147;                        ecm: B1 = 1e6; sigma = 52967061287689 
   Aug 20, 2024  n = 6001: 695816812023656477562394175892797;                       ecm: B1 = 5e5; sigma = 1:1088594985 
   Aug 20, 2024  n = 6323: 315438813996319438031657566306729;                       ecm: B1 = 25e4; sigma = 1:1373130007 
   Aug 20, 2024  n = 6367: 21345380483323818968803525877502810443;                  ecm: B1 = 5e5; sigma = 1:1564726371 
   Aug 20, 2024  n = 6413: 69615667805021500294627143908293;                        ecm: B1 = 5e5; sigma = 1:1064874425 
   Aug 20, 2024  n = 6425: 27345173228035282739638463755096201;                     ecm: B1 = 5e5; sigma = 1:916047441 
   Aug 20, 2024  n = 6459: 4627697372220068903113651202699449;                      ecm  
   Aug 20, 2024  n = 6463: 33976933348129210891637803696471;                        ecm: B1 = 5e5; sigma = 1:1064874425 
   Aug 20, 2024  n = 6505: 771799133272450765286793118681;                          ecm  
   Aug 20, 2024  n = 6531: 20515216490975134970589492865957;                        ecm: B1 = 5e5; sigma = 1:3134844861 
   Aug 20, 2024  n = 6547: 26082784537768285040784962616203;                        ecm: B1 = 5e5; sigma = 1:3186806677 
   Aug 20, 2024  n = 6579: 30501891916761369005083200765507831649;                  P-1: B1 = 1e8  
   Aug 20, 2024  n = 6627: 207229602677110354999505334024037;                       ecm: B1 = 1e6; sigma = 1:3318069251 
   Aug 20, 2024  n = 6633: 59925833228400736755484667890693;                        ecm: B1 = 5e5; sigma = 1:4049122495
   Aug 20, 2024  n = 6635: 496404891911358902350041179362831;                       ecm: B1 = 5e5; sigma = 1:1293962689
   Aug 20, 2024  n = 6711: 7144586569612918208700259798639;                         ecm: B1 = 1e6; sigma = 1:1318957861
   Aug 20, 2024  n = 6749: 10793463478838927967624074051197;                        ecm: B1 = 1e6; sigma = 0:180146487010777
   Aug 20, 2024  n = 6827: 50807343997336659532852562053547;                        ecm: B1 = 1e6; sigma = 1:4261948433
   Aug 20, 2024  n = 6853: 4407897845005598926599049755323;                         ecm: B1 = 1e6; sigma = 1:105806636643035
   Aug 20, 2024  n = 6855: 813532341364371691666368330069631;                       ecm: B1 = 5e5; sigma = 1:3404967785
   Aug 20, 2024  n = 6863: 45576442660261405454027843005099279363;                  ecm: B1 = 5e5; sigma = 1:4017018739
   Aug 20, 2024  n = 6885: 1199045447656509408148014511681;                         ecm: B1 = 1e6; sigma = 0:105806636643035
   Aug 20, 2024  n = 6895: 345254099442479690466807243161;                          ecm: B1 = 5e5; sigma = 1:3951530911
   Aug 20, 2024  n = 6983: 1016624078655033790209211909154053;                      ecm: B1 = 5e5; sigma = 1:562663719
   Aug 20, 2024  n = 7011: 308573070164753259193607112742747;                       ecm: B1 = 5e5; sigma = 1:3092943329
   Aug 20, 2024  n = 7027: 3270662421470064751270391979111641;                      ecm: B1 = 25e4; sigma = 1:1767257015
   Aug 20, 2024  n = 7041: 350676874085293214078098349707;                          ecm: B1 = 1e6; sigma = 0:145129032457365
   Aug 20, 2024  n = 7077: 13016598920031794002941702559;                           ecm: B1 = 5e5; sigma = 1:2078807511
   Aug 20, 2024  n = 7079: 211936457265809995565760245520973;                       ecm: B1 = 5e5; sigma = 1:262151673
   Aug 20, 2024  n = 7115: 69481578807619036204623270154076561;                     ecm: B1 = 5e5; sigma = 1:1051968875
   Aug 20, 2024  n = 7155: 2363421643121012840509778918901271;                      ecm: B1 = 5e5; sigma = 1:3855436389
   Aug 20, 2024  n = 7259: 8189484816570707340091163330635453;                      ecm: B1 = 5e5; sigma = 1:3485439623
   Aug 20, 2024  n = 7371: 7595905095301842399593540737711;                         ecm: B1 = 5e5; sigma = 1:3087225587
   Aug 20, 2024  n = 7403: 102810485748819791639879926615169;                       ecm: B1 = 5e5; sigma = 1:714400689
   Aug 20, 2024  n = 7451: 1258746002886628455412882180639;                         ecm: B1 = 5e5; sigma = 1:1210794309 
   Aug 20, 2024  n = 7505: 1744960597338433533447362115952081;                      ecm: B1 = 1e6; sigma = 1:1393014461 
   Aug 20, 2024  n = 7627: 10280281551935956005167840871450787;                     ecm: B1 = 5e5; sigma = 1:1559371313 
   Aug 20, 2024  n = 7751: 147104989244161239270656842614006284071;                 ecm: B1 = 5e5; sigma = 1:4130667131 
   Aug 20, 2024  n = 7773: 624701770395169312585090935732649;                       ecm: B1 = 5e5; sigma = 1:1157681981 
   Aug 20, 2024  n = 7827: 7293854796500084099657229729157;                         ecm: B1 = 1e6; sigma = 1:1156762131 
   Aug 20, 2024  n = 7847: 99557767070717924371208413000293881;                     ecm 
   Aug 20, 2024  n = 7861: 898119705955942710848729642627;                          ecm: B1 = 5e5; sigma = 1:2790569943 
   Aug 20, 2024  n = 7889: 215231103155467706279277026425453;                       ecm: B1 = 5e5; sigma = 1:202868745 
   Aug 20, 2024  n = 7897: 385449578021310700390256413787;                          ecm  
   Aug 20, 2024  n = 7987: 8883682708391634937679236698173;                         ecm: B1 = 5e5; sigma = 1:2489921303 
   Aug 20, 2024  n = 8041: 15477413700845533672594920389159;                        ecm: B1 = 5e5; sigma = 1:3116732165 
   Aug 20, 2024  n = 8053: 41902595593620392086855271026079;                        ecm: B1 = 1e6; sigma = 1:1368566913 
   Aug 20, 2024  n = 8115: 1769701865578466450153518679881;                         ecm: B1 = 5e5; sigma = 1:3003735203 
   Aug 20, 2024  n = 8201: 17770709819243095708975667749958463949643;               ecm: B1 = 5e5; sigma = 1:3446626047 
   Aug 20, 2024  n = 8237: 219464278700937029463657983203;                          ecm: B1 = 5e5; sigma = 1:2790569943 
   Aug 20, 2024  n = 8245: 4595241096933927040005468109324991;                      ecm: B1 = 5e5; sigma = 1:4134148097 
   Aug 20, 2024  n = 8257: 29619972904892450273922341588641;                        ecm: B1 = 1e6; sigma = 80482442127625 
   Aug 20, 2024  n = 8421: 891574094727581152824232840516519;                       ecm: B1 = 5e5; sigma = 1:1903005545 
   Aug 20, 2024  n = 8457: 16591431242812670951237114925751;                        ecm: B1 = 1e6; sigma = 9291063370823 
   Aug 20, 2024  n = 8477: 13155977065160004722127813180227;                        ecm: B1 = 5e5; sigma = 1:1088594985 
   Aug 20, 2024  n = 8537: 7068078234757599410245923277;                            ecm: B1 = 5e5; sigma = 1:1428254743 
   Aug 20, 2024  n = 8545: 101646283310197475908829512121;                          ecm: B1 = 5e5; sigma = 1:3087225587 
   Aug 20, 2024  n = 8575: 5293740271005338383592716601;                            ecm: B1 = 5e5; sigma = 1:190540483 
   Aug 20, 2024  n = 8577: 634815482288444139636540572011003;                       ecm: B1 = 5e5; sigma = 1:149514197612885 
   Aug 20, 2024  n = 8639: 818877774370128142691864096231;                          ecm: B1 = 5e5; sigma = 1:2043845067 
   Aug 20, 2024  n = 8735: 12192865776540531965438812912547431;                     ecm: B1 = 5e5; sigma = 1:2256808913 
   Aug 20, 2024  n = 8737: 13361685887895082160085395228039;                        ecm: B1 = 5e5; sigma = 1:3738655573 
   Aug 20, 2024  n = 8745: 2272528654159007646526616145391;                         ecm: B1 = 1e6; sigma = 1:2923719129 
   Aug 20, 2024  n = 8829: 1513085581534586859396871232498095957759;                ecm: B1 = 5e5; sigma = 1:2044862669 
   Aug 20, 2024  n = 8869: 1628099806387144273085256658529;                         ecm: B1 = 5e5; sigma = 1:1772750603 
   Aug 20, 2024  n = 8959: 749539463454661849173837786563;                          ecm: B1 = 1e6; sigma = 1:2780467357 
   Aug 20, 2024  n = 9283: 8013308143108550298429503948087441;                      ecm: B1 = 5e5; sigma = 1:562663719 
   Aug 20, 2024  n = 9419: 5684469744053776020964152035591;                         ecm: B1 = 5e5; sigma = 1:121282519 
   Aug 20, 2024  n = 9437: 1624851391389487899053479556237;                         ecm: B1 = 5e5; sigma = 1:799608949 
   Aug 20, 2024  n = 9473: 136213632400294112039787697679;                          ecm: B1 = 1e6; sigma = 113918028976573 
   Aug 20, 2024  n = 9485: 308062384945102512389982980881;                          ecm: B1 = 25e4; sigma = 1:3226404411 
   Aug 20, 2024  n = 9655: 304548237530189995568241284486281;                       ecm: B1 = 5e5; sigma = 1:4248825949 
   Aug 20, 2024  n = 9725: 6266679657139037831692848478951;                         ecm: B1 = 5e5; sigma = 1:153953135 
   Aug 20, 2024  n = 9777: 1707913452762899722866250746001;                         ecm: B1 = 1e6; sigma = 1:1368566913 
   Aug 20, 2024  n = 9885: 1373181471814143351694865705521;                         ecm: B1 = 5e5; sigma = 1:2610241785 
   Aug 20, 2024  n = 9935: 7881330031472834202922901774150160151;                   ecm: B1 = 5e5; sigma = 1:153953135  


- Found by Kurt Beschorner   
   Aug 12, 2024  n = 9442: 4052157023046612121139511209683398529;                   ecm: B1 = 1e6; sigma = 0:3565740379605301457
   Aug 12, 2024  n = 9448: 7338135276821871674079344603010953;                      ecm: B1 = 1e6; sigma = 0:11602320950923801947 
   Aug 12, 2024  n =14317: 6244588599937216531003831;                               P-1: B1 = 23e6 
   Aug 12, 2024  n=100217: 177461650174240446229859314688317;                       P-1: B1 = 23e6 
   Aug 12, 2024  n=100219: 1267861060221281;                                        P-1: B1 = 23e6 
   Aug 12, 2024  n=100219: 1312970789851169;                                        P-1: B1 = 23e6 
   Aug 12, 2024  n=100221: 13832902008141117617827;                                 P-1: B1 = 23e6 


- Found by Alfred Eichhorn 
   Aug 11, 2024  n =14369: 6252123219579321033213298399;                            ecm: B1 = 1e6; sigma = 2508837445113559
   Aug 11, 2024  n =20963: 679855362627476703188888563288481;                       ecm: B1 = 1e6; sigma = 2476641858178927
   Aug 11, 2024  n =21929: 1442656925526309675517766997677;                         ecm: B1 = 1e6; sigma = 8039991546359893
   Aug 11, 2024  n =21937: 8472869234992293321112289;                               ecm: B1 = 1e6; sigma = 4102916080405166


- Found by Kurt Beschorner  
   Aug 05, 2024  n =14316: 57346926970351862773268747899315323798217129;            P-1: B1 = 55e6 
   Aug 05, 2024  n =33404: 2842302772256147755172610821669;                         P-1: B1 = 55e6 
   Aug 05, 2024  n=100216: 4723351119100314857559865270748770769;                   P-1: B1 = 55e6 
   Aug 05, 2024  n=156817: 108632521422322241;                                      gr-mfaktc 
   Aug 05, 2024  n=156913: 5023303367908589107;                                     gr-mfaktc 


- Found by Kurt Beschorner  
   Aug 03, 2024  n = 9428: 2370468745271779901326864609926829;                      ecm: B1 = 1e6; sigma = 0:1560246379640767270 
   Aug 03, 2024  n = 9705: 76753429826310638321101265149201;                        ecm: B1 = 1e6; sigma = 0:861848002098196
   Aug 03, 2024  n = 9795: 40441561262801004062488422962196368791;                  ecm: B1 = 1e6; sigma = 0:4001697049805009211
   Aug 03, 2024  n =13799: 225884482231168124105632363243;                          P-1: B1 = 150e6 
   Aug 03, 2024  n =13809: 254549964727519328742841;                                P-1: B1 = 150e6 
   Aug 03, 2024  n =13837: 4585227773759256410020228867;                            P-1: B1 = 150e6 
   Aug 03, 2024  n =33402: 42216466210272128093191353979;                           P-1: B1 = 55e6 
   Aug 03, 2024  n=100191: 255101965378397273674357;                                P-1: B1 = 23e6 
   Aug 03, 2024  n=100194: 426230986986026617893247;                                P-1: B1 = 55e6 
   Aug 03, 2024  n=155579: 9514397111067708403;                                     gr-mfaktc 
   Aug 03, 2024  n=156059: 635634025160003827;                                      gr-mfaktc 
   Aug 03, 2024  n=156227: 8590295976939445399;                                     gr-mfaktc 
   Aug 03, 2024  n=156347: 13071673667955473161;                                    gr-mfaktc 
   Aug 03, 2024  n=156539: 6844820953215681911;                                     gr-mfaktc 
   Aug 03, 2024  n=156619: 12648044075298729563;                                    gr-mfaktc 
   Aug 03, 2024  n=156679: 13136467037721548159;                                    gr-mfaktc 
   Aug 03, 2024  n=156733: 791344277329055227;                                      gr-mfaktc 
 

- Found by NFS@Home
   Jul 28, 2024  n =  730: 209567419815575088893039502374017044565180465719504614143239653652312239618655809712098924957353042723741728874079596356118568603287093812371; SNFS 
   

- Found by Alfred Eichhorn 
   Jul 21, 2024  n =13613: 15262282368599483015998894649;                           ecm: B1 = 1e6; sigma = 5210964136833681  


- Found by Kurt Beschorner  
   Jul 21, 2024  n =13733: 11066901234321643251415990246667;                        P-1: B1 = 150e6
   Jul 21, 2024  n =13739: 815051569821918488835533038711;                          P-1: B1 = 150e6 
   Jul 21, 2024  n =13751: 30084129960755867761834373333372723;                     P-1: B1 = 150e6
   Jul 21, 2024  n =13756: 3070906950345823080010940982444870941;                   P-1: B1 = 400e6 
   Jul 21, 2024  n =13769: 238899466227509549998368631;                             P-1: B1 = 175e6 
   Jul 21, 2024  n=100187: 4212448211184003403;                                     P-1: B1 = 23e6
   Jul 21, 2024  n=154459: 654674838797941477;                                      gr-mfaktc     
   Jul 21, 2024  n=154897: 288575490359805653;                                      gr-mfaktc 
   Jul 21, 2024  n=154981: 659143481425129271;                                      gr-mfaktc 
   Jul 21, 2024  n=154981: 725117156196649187;                                      gr-mfaktc 
   Jul 21, 2024  n=155017: 1537923485747759557;                                     gr-mfaktc 
   Jul 21, 2024  n=155137: 6213654742199632163;                                     gr-mfaktc 


- Found by Alfred Eichhorn 
   Jun 29, 2024  n =13523: 13387751970993012362901079637;                           ecm: B1 = 1e6; sigma = 5381565215536551  
   Jun 29, 2024  n =20411: 8856502355660511775523407391;                            ecm: B1 = 1e6; sigma = 7929625471060670  
   Jun 29, 2024  n =20431: 18699538092936415160078201691271;                        ecm: B1 = 1e6; sigma = 1168082089032586  
   Jun 29, 2024  n =20483: 41932266046649700904863383587;                           ecm: B1 = 1e6; sigma = 3257560573251327  
   Jun 29, 2024  n =20641: 84562062985268488366611846511;                           ecm: B1 = 1e6; sigma = 7612567426602960  
   Jun 29, 2024  n =20717: 466634734466535006245712555307;                          ecm: B1 = 1e6; sigma = 146688564762787  


- Found by Torbjörn Granlund
   Jul 16, 2024  n =  731: 1847429475936181681973479760912708743358821710551;       ecm: B1 =11e6; sigma = 1:3939899409  


- Found by Torbjörn Granlund
   Jul 14, 2024  n =3900M: 44612114135261049915172448202991314405938701;            ecm: B1 =11e6; sigma = 1:2348484157  
  

- Found by Torbjörn Granlund
   Jul 13, 2024  n = 1556: 1355157068675915381446032476103133130496209;             ecm: B1 =11e6; sigma = 1:3330891095	  


- Found by Torbjörn Granlund
   Jul 12, 2024  n = 1408: 106110538711611081989682173453117312268289;              ecm: B1 =11e6; sigma = 1:423379121   


- Found by Kurt Beschorner  
   Jul 11, 2024  n = 1525: 315847098431407555514016207329179201;                    P-1: B1 = 200e6
   Jul 11, 2024  n =13721: 1864073211647238592948736905104361;                      P-1: B1 = 150e6 
   Jul 11, 2024  n =33395: 1523915962744198013287961;                               P-1: B1 = 23e6
   Jul 11, 2024  n=100175: 290759670245407201;                                      P-1: B1 = 23e6
   Jul 11, 2024  n=153701: 1440092232895724267;                                     gr-mfaktc 
   Jul 11, 2024  n=154211: 17523178529846097809;                                    gr-mfaktc 


- Found by NFS@home   
   Jul 08, 2024  n =  365: 1304946319836672523549871511207656785231498701576036930724645238399101906921; SNFS 
   Jul 08, 2024  n =  365: 5528825275894858698684129584828307231241005568273768148118728392440732070424671; SNFS 

 
- Found by Anonymous  
   Jul 08, 2024  n = 8026: 11092134801718675055606994656545513411                    
   Jul 08, 2024  n = 9034: 2112314427024188715300943526715275533                    
 

- Found by Torbjörn Granlund
   Jul 07, 2024  n =3740M: 813728620031462038871992677376718544646779541;           ecm: B1 =11e6; sigma = 1:2213254673   
 
 
- Found by Torbjörn Granlund
   Jul 05, 2024  n = 1538: 9287243504302734314292246493018665305411;                ecm: B1 =11e6; sigma = 1:2599237159  
 

- Found by Kurt Beschorner  
   Jul 04, 2024  n =13687: 3352869000001257408071704371187;                         P-1: B1 = 150e6
   Jul 04, 2024  n =13692: 448790289019202435089828835874995221;                    P-1: B1 = 550e6


- Found by Anonymous  
   Jul 04, 2024  n = 3646: 7249609412129031102349676213675320028207                    
   Jul 04, 2024  n = 5426: 421794296629383911904809584049                    
   Jul 04, 2024  n = 5878: 1293862103310971228813269265251889                     
   Jul 04, 2024  n = 9806: 6856501055738088117609720236405115757649                     
   Jul 04, 2024  n = 9874: 116769305954826569316770086211501521                     
 

- Found by YOYO@home/philwire    
   Jul 04, 2024  n =  639: 108404283009093688449943940269189804724790189486660307;  ecm: B1 = 2.9e9; sigma = 10714174124914808047

 
- Found by Torbjörn Granlund
   Jul 04, 2024  n = 1484: 12934325238528583194928423610286679740731789;            ecm: B1 =11e6; sigma = 1:85680977    
   Jul 04, 2024  n = 1654: 2014736089669888940425352477546278092192268265858033129; ecm: B1 =11e6; sigma = 1:1681499511 


- Found by Kurt Beschorner  
   Jul 04, 2024  n = 7599: 4944885332403182509417069471681;                         ecm: B1 = 1e6; sigma = 3792909555228110
   Jul 04, 2024  n =13664: 17782554637005831866125656641;                           P-1: B1 = 450e6 
   Jul 04, 2024  n =13667: 5032044810625021177332187;                               P-1: B1 = 158e6
   Jul 04, 2024  n=100172: 340257492271303914975039056389;                          P-1: B1 = 55e6
   Jul 04, 2024  n=153077: 116991563943187237;                                      gr-mfaktc 
   Jul 04, 2024  n=153277: 283051850735220719;                                      gr-mfaktc 
 

- Found by Alfred Eichhorn 
   Jun 29, 2024  n =20143: 195336622099383139974192234034547;                       ecm: B1 = 1e6; sigma = 3729048310073734 
   

- Found by Kurt Beschorner  
   Jun 29, 2024  n = 6565: 967455252377753723469264601;                             ecm: B1 = 1e6; sigma = 5085665109651225
   Jun 29, 2024  n = 7209: 245876032391282720514670601435797;                       ecm: B1 = 1e6; sigma = 7176496071620092 
   Jun 29, 2024  n =13651: 63685984885065209582819476115071;                        P-1: 1e6 = 165e6
   Jun 29, 2024  n=152249: 667640256156011561;                                      gr-mfaktc 
   Jun 29, 2024  n=152407: 3863061623316166853;                                     gr-mfaktc 
   Jun 29, 2024  n=152417: 4384597323140904347;                                     gr-mfaktc 


- Found by Alfred Eichhorn 
   Jun 27, 2024  n =12611: 151596145122775505868566782271 * 7329415337......P12581  ecm: B1 = 1e6; sigma = 1891578441988465
 

- Found by Alfred Eichhorn 
   Jun 24, 2024  n =73847: 7891144115301619472022803497889;                         ecm: B1 = 5e4; sigma = 430692243951430
   Jun 24, 2024  n =74507: 1096611993139741046923;                                  ecm: B1 = 5e4; sigma = 6502661398168781
   Jun 24, 2024  n =74507: 144576321485621311976359;                                ecm: B1 = 5e4; sigma = 5710557500718102
   Jun 24, 2024  n =74527: 18472086123310264797552077;                              ecm: B1 = 5e4; sigma = 5012480456469592
   Jun 24, 2024  n =74587: 12585888766454654778477001;                              ecm: B1 = 5e4; sigma = 5787057121355163
   Jun 24, 2024  n =74707: 2246495418530976647385485111;                            ecm: B1 = 5e4; sigma = 4865186604072078
   Jun 24, 2024  n =74929: 23613576233446350795077641;                              ecm: B1 = 5e4; sigma = 3815193115992148
   
 
- Found by Torbjörn Granlund
   Jun 21, 2024  n = 1870: 30981838801127734361302339269066902886001;               ecm: B1 =11e6; sigma = 1:3306279234


- Found by Torbjörn Granlund
   Jun 18, 2024  n =3540M: 154364888033739260172380158583232052475743273261;        ecm: B1 =11e6; sigma = 1:1431821900 

  
- Found by Torbjörn Granlund
   Jun 17, 2024  n =  891: 5768352029220733367366868921292458501408214165423363;    ecm: B1 =11e7; sigma = 1:333812611


- Found by Torbjörn Granlund
   Jun 16, 2024  n = 1672: 545358172357012292201336067885308067971306777;           ecm 


- Found by Torbjörn Granlund
   Jun 15, 2024  n = 1392: 10825430995573655349911905703088339464977;               ecm 

 
- Found by Torbjörn Granlund
   Jun 14, 2024  n = 1792: 4560897401317754430626820629544566062629889;             ecm 
 
 
- Found by Kurt Beschorner
   Jun 14, 2024  n = 7821: 10391751287135966688011512453;                           ecm  B1 = 1e6; sigma = 409243078866167
   Jun 14, 2024  n =13548: 12997605280355035463166531521403529;                     P-1: B1 = 500e6
   Jun 14, 2024  n =13562: 15353741655549410028804307084051;                        P-1: B1 = 325e6
   Jun 14, 2024  n =13563: 77411955285810787348651626991;                           P-1: B1 = 165e6
   Jun 14, 2024  n =13593: 177925771645928134641547027;                             P-1: B1 = 150e6
   Jun 14, 2024  n =13612: 17167210449977525602398480599175117101;                  P-1: B1 = 375e6
   Jun 14, 2024  n =20032: 2505607329459631611641153;                               P-1: B1 = 55e6
   Jun 14, 2024  n =33385: 747826005686416007231;                                   P-1: B1 = 55e6
   Jun 14, 2024  n =33387: 106504353311117769139519;                                P-1: B1 = 20e6
   Jun 14, 2024  n=150883: 97118496609892523;                                       gr-mfaktc      
   Jun 14, 2024  n=150901: 563456271424457431;                                      gr-mfaktc      
   Jun 14, 2024  n=150919: 2079148442457322799;                                     gr-mfaktc      
   Jun 14, 2024  n=151171: 608634030260192639;                                      gr-mfaktc      
   Jun 14, 2024  n=151247: 113196576201967147;                                      gr-mfaktc      
   Jun 14, 2024  n=151429: 147222954843343733;                                      gr-mfaktc      
   Jun 14, 2024  n=151499: 146383186511736689;                                      gr-mfaktc      
                                               
 
- Found by Torbjörn Granlund
   Jun 12, 2024  n = 1496: 28330881496644957570065523400505204114494529;            ecm 
 

- Found by Torbjörn Granlund
   Jun 09, 2024  n = 1430: 82419252546478457878215964924871918728196281;            ecm 
 

- Found by Yousuke Koide 
   Jun 03, 2024  n =  938: 11562710405302740261753778982810543629872202227744910916651 * 6120646518......P312; ecm: B1 =3e8; sigma = 2:4970505043646219549 


- Found by Kurt Beschorner
   Jun 03, 2024  n =13475: 14034822309195006833617951;                              P-1: B1 = 150e6
   Jun 03, 2024  n =13501: 204470063667253089494397679362163;                       P-1: B1 = 150e6
   Jun 03, 2024  n =13505: 447230547521550428905961;                                P-1: B1 = 160e6
   Jun 03, 2024  n =33384: 7821295128811946507432484961;                            P-1: B1 = 55e6
   Jun 03, 2024  n=100145: 668544845427588593671;                                   P-1: B1 = 20e6
   Jun 03, 2024  n=100152: 2015344433453833;                                        P-1: B1 = 55e6
   Jun 03, 2024  n=149341: 337426151183136437;                                      gr-mfaktc      
   Jun 03, 2024  n=149729: 522185468610743293;                                      gr-mfaktc      
   Jun 03, 2024  n=149893: 234739865552796839;                                      gr-mfaktc 
   Jun 03, 2024  n=149911: 641276195249134517;                                      gr-mfaktc 
   Jun 03, 2024  n=149953: 3666251351417794037;                                     gr-mfaktc 
   Jun 03, 2024  n=150211: 4128566210846845711;                                     gr-mfaktc 
   Jun 03, 2024  n=150517: 1452830539950831049;                                     gr-mfaktc 
				

- Found by Alfred Eichhorn 
   May 29, 2024  n =73693: 200046209932683892220519 * 8236393422......c73650;       ecm  B1 = 5e4; sigma = 7063252640234059
   May 29, 2024  n =74279: 1643398485800760569800597963 * 6761057167......c74251;   ecm  B1 = 5e4; sigma = 0:3190123306072765


- Found by Sam Wagstaff    
   May 28, 2024  n =  433: 8824028723798902981997215284751342520751929886344438185486188157; ecm 


- Found by Kurt Beschorner
   May 20, 2024  n =13391: 1793492413423312326764415268439;                         P-1: B1 = 400e6
   May 20, 2024  n =13403: 1273543812643453522963599991;                            P-1: B1 = 150e6
   May 20, 2024  n =13405: 369025298556704617267721;                                P-1: B1 = 160e6
   May 20, 2024  n =13409: 194192011616958540654680651965361;                       P-1: B1 = 150e6
   May 20, 2024  n =13410: 152178270161972061588566451931;                          P-1: B1 = 650e6
   May 20, 2024  n=100135: 815970507695643165200161;                                P-1: B1 = 22e6
   May 20, 2024  n=100136: 1546658379143032144324057;                               P-1: B1 = 22e6
   May 20, 2024  n=100136: 29303671942968558470094241;                              P-1: B1 = 22e6
   May 20, 2024  n=149099: 191666476417472557;                                      gr-mfaktc 
   May 20, 2024  n=149197: 6018787351196629987;                                     gr-mfaktc 


- Found by Kurt Beschorner
   May 14, 2024  n =13310: 358431625219151747847359198249482811;                    P-1: B1 = 375e6
   May 14, 2024  n =13317: 310201028691515049948813827173;                          P-1: B1 = 150e6
   May 14, 2024  n =13335: 57025106614551649638121;                                 P-1: B1 = 160e6
   May 14, 2024  n =13383: 210951149080654081665994312063747;                       P-1: B1 = 160e6
   May 14, 2024  n =13387: 10821004067230761918288895517;                           P-1: B1 = 150e6
   May 14, 2024  n=100128: 12965255566706017;                                       P-1: B1 = 55e6
   May 14, 2024  n=100133: 1904718174391121;                                        P-1: B1 = 18e6
   May 14, 2024  n=148249: 5763577084308138631;                                     P-1: B1 = 17e6
   May 14, 2024  n=148853: 3201872038854169067;                                     gr-mfaktc 


- Found by Alfred Reich      
   Dec 30, 2023  n =11694: 25265936178377677271923695277;                           ecm  
 

- Found by Kurt Beschorner
   Apr 30, 2024  n = 1407: 1642802515245357383912944034418987319;                   ecm  B1 = 110e6; sigma = 2951090968820559
   Apr 30, 2024  n = 2564: 27189275929548127954581257800366864533484049;            ecm  B1 = 110e6; sigma = 2371963344321011
   Apr 30, 2024  n =13303: 70942071240313959608007929622671;                        P-1: B1 = 140e6
   Apr 30, 2024  n =13304: 57181546620162299318379978328716132443977;               P-1: B1 = 275e6


- Found by Alfred Eichhorn 
   Apr 29, 2024  n =73361: 1721423059346637677879;                                  ecm  B1 = 5e4; sigma = 1582421447520844
   Apr 29, 2024  n =73361: 408219527355823133818759;                                ecm  B1 = 5e4; sigma = 3826123512129081
   Apr 29, 2024  n =73433: 1480290724528512092611333441;                            ecm  B1 = 5e4; sigma = 7994314783584498
   Apr 29, 2024  n =79691: 10288546796776484035092067;                              ecm  B1 = 5e4; sigma = 5445195526405636


- Found by John Lee          
   Apr 29, 2024  n =12841: 4522160233632425161342305395203;                         ecm  B1 = 3e6; sigma = 851351432404823
   Apr 29, 2024  n =17573: 47231703533723987783810453;                              ecm  B1 = 1e6; sigma = 775071180902912
   Apr 29, 2024  n =35537: 330417476836465920785432053;                             ecm  B1 = 1e6; sigma = 7926625206541607


- Found by Kurt Beschorner
   Apr 20, 2024  n =13265: 1290668262735890884325761;                               P-1: B1 = 160e6
   Apr 20, 2024  n =13269: 2427709598953063772750559319;                            P-1: B1 = 140e6
   Apr 20, 2024  n =13282: 7480441362289212211418170076851;                         P-1: B1 = 275e6
   Apr 20, 2024  n=100118: 2213092040998752430410504041;                            P-1: B1 = 55e6
   Apr 20, 2024  n=100119: 135903373927930060098307;                                P-1: B1 = 16e6
 

- Found by YOYO@home/Gouik    
   Apr 14, 2024  n =  651: 18761726160436368465384904039916752385257524435903404839 * 1876172616......P298; ecm: B1 = 2.9e9; sigma = 0:15913088270609817167


- Found by Kurt Beschorner
   Apr 14, 2024  n =  659: 149909896971539560984652057797566890100299359259837 * 2846412051......P570; ecm  B1 =11e7; sigma = 0:4226535905387705
   Apr 14, 2024  n =13251: 12296428612923146794052172531037;                        P-1: B1 = 160e6
   Apr 14, 2024  n=100098: 17325552919871634468049;                                 P-1: B1 = 35e6
   Apr 14, 2024  n=100105: 144493170813628346471;                                   P-1: B1 = 17e6


- Found by Kurt Beschorner
   Apr 07, 2024  n =12771: 314224898531750364984013;                                P-1: B1 = 160e6
   Apr 07, 2024  n =12771: 238824929913673638997582363;                             P-1: B1 = 160e6 
   Apr 07, 2024  n =13158: 68581509075838066581670099156849;                        P-1: B1 = 140e6 
   Apr 07, 2024  n=100079: 6068994380637463834185467;                               P-1: B1 = 10e6 
   Apr 07, 2024  n=100363: 1016391456544433853547;                                  P-1: B1 = 15e6           
   Apr 07, 2024  n=100379: 66388841093949454147;                                    P-1: B1 = 15e6   
   Apr 07, 2024  n=100417: 286825064305738012150961;                                P-1: B1 = 15e6  
   Apr 07, 2024  n=100459: 22782665966376356329;                                    P-1: B1 = 15e6
   Apr 07, 2024  n=100517: 17361707890852059740855929;                              P-1: B1 = 16e6 
   Apr 07, 2024  n=100519: 101147426853941494945049;                                P-1: B1 = 16e6    
   Apr 07, 2024  n=100559: 95610786074378976307;                                    P-1: B1 = 16e6    
   Apr 07, 2024  n=100591: 1291405529277231477460435169;                            P-1: B1 = 16e6    
   Apr 07, 2024  n=100669: 2806386502390207284249241483;                            P-1: B1 = 16e6    
   Apr 07, 2024  n=100811: 281860909823518349338601;                                P-1: B1 = 16e6    
   Apr 07, 2024  n=100817: 507962247211408289;                                      P-1: B1 = 16e6    
   Apr 07, 2024  n=147941: 37558743005776041839 ***                                 P-1: B1 = 8.8e6  
   *** 37558743005776041839 = composite and all small factors are known 
   Apr 07, 2024  n=147977: 114084230812902508795841;                                P-1: B1 = 8.8e6    


- Found by Alfred Eichhorn 
   Apr 01, 2024  n =79337: 9145312312862925909640977721;                            ecm  B1 = 5e4; sigma = 7464158329682606
   Apr 01, 2024  n =79427: 1284283667245483471417172921;                            ecm  B1 = 5e4; sigma = 5590089294394130


- Found by Kurt Beschorner
   Apr 01, 2024  n =14549: 4005021584963302209471746401;                            P-1: B1 = 14e7
   Apr 01, 2024  n =14747: 252632181388341912925629401;                             P-1: B1 = 14e7           
   Apr 01, 2024  n=147799: 24724127378034035880566249;                              P-1: B1 = 8.8e6    


- Found by Kurt Beschorner
   Mar 29, 2024  n =  713: 31070861795268450321139284436817844468068239;            ecm: B1 = 11e7; sigma = 4800378595879534
   Mar 29, 2024  n =13175: 422686483673200816801;                                   P-1: B1 = 56e6           
   Mar 29, 2024  n =13187: 2072300747670825285092510827;                            P-1: B1 = 35e6     


- Found by Alfred Reich
   Mar 24, 2024  n = 8914: 1680862037183886151986766096284943;                      ecm

  
- Found by Anonymous   
   Mar 24, 2024  n =  695: 8397548714483238063663389786354175256018831              ecm: B1 = 3e6 
   Mar 24, 2024  n = 3019: 3139259690159845335135979206644089969  
   Mar 24, 2024  n = 3023: 107018760919046918330490860941009  
   Mar 24, 2024  n = 3097: 57179667256536688029715193166703488359641 
 


- Found by Kurt Beschorner
   Mar 22, 2024  n =  655: 2603347672124284040229582413722681735668626862241;       ecm: B1 =11e7; sigma = 0:3963412036452067 
   Mar 22, 2024  n =13108: 44331551068710498173013783881;                           P-1: B1 = 94e6           
   Mar 22, 2024  n =13131: 276600609054191780298991;                                P-1: B1 = 60e6     


- Found by Alfred Eichhorn 
   Mar 18, 2024  n =73019: 1323020047051919660237;                                  ecm  B1 = 5e4; sigma = 1341369107631264


- Found by NFS@home     
   Mar 17, 2024  n =1420L: 247950328172294050136754481538951409190364075674960071233394038784474817867352415168199452660754962688866321901; SNFS 
        		

- Found by NFS@home     
   Mar 13, 2024  n =1420M: 150068993718936038588227244574366404285884513639444374982663085901463237698274075317154251769989823397761; GNFS 


-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Oliver Kruse, Kurt Beschorner 
   Feb 10, 2024  n =  942: 9755872853901756680890615403191792297388117293582105055568357694889056982187114874692197915708047; SNFS  
   Details:
   - R942: SNFS-difficulty = 314 
     Sat Nov 11 11:17:54 2023  Msieve v. 1.54 (SVN r1044)
     Sat Nov 11 11:17:54 2023  random seeds: 60253a75 007cd855
     Sat Nov 11 11:17:54 2023  factoring 30862083832190969399642448329237079281358998786734541342232902569072683505580523380381489228423400116527554057338104357145657543175005161681489015756307835902130639405231933246244136812560041424780296737530889 (209 digits)
     Sat Nov 11 11:17:55 2023  no P-1/P+1/ECM available, skipping
     Sat Nov 11 11:17:55 2023  commencing number field sieve (209-digit input)
     Sat Nov 11 11:17:55 2023  R0: -10000000000000000000000000000000000000000000000000000
     Sat Nov 11 11:17:55 2023  R1: 1
     Sat Nov 11 11:17:55 2023  A0: 1
     Sat Nov 11 11:17:55 2023  A1: 0
     Sat Nov 11 11:17:55 2023  A2: 0
     Sat Nov 11 11:17:55 2023  A3: -10
     Sat Nov 11 11:17:55 2023  A4: 0
     Sat Nov 11 11:17:55 2023  A5: 0
     Sat Nov 11 11:17:55 2023  A6: 100
     Sat Nov 11 11:17:55 2023  skew 0.64, size 2.684e-15, alpha -0.127, combined = 1.160e-15 rroots = 0
     Sat Nov 11 11:17:55 2023  commencing relation filtering
     Sat Nov 11 11:17:55 2023  setting target matrix density to 130.0
     Sat Nov 11 11:17:55 2023  estimated available RAM is 130983.0 MB
     Sat Nov 11 11:17:55 2023  commencing duplicate removal, pass 1
     Sat Nov 11 11:52:23 2023  error -15 reading relation 196874611
     ...
     Sat Nov 11 15:51:51 2023  skipped 1120644 relations with b > 2^32
     Sat Nov 11 15:51:51 2023  skipped 2634 relations with composite factors
     Sat Nov 11 15:52:00 2023  found 325844461 hash collisions in 1439959899 relations
     Sat Nov 11 15:52:28 2023  commencing duplicate removal, pass 2
     Sat Nov 11 17:18:01 2023  found 8457401 duplicates and 1431502498 unique relations
     Sat Nov 11 17:18:01 2023  memory use: 16280.0 MB
     Sat Nov 11 17:18:03 2023  reading ideals above 812974080
     Sat Nov 11 17:18:03 2023  commencing singleton removal, initial pass
     Sat Nov 11 22:20:10 2023  memory use: 21024.0 MB
     Sat Nov 11 22:20:15 2023  reading all ideals from disk
     Sat Nov 11 22:22:13 2023  memory use: 26910.1 MB
     Sat Nov 11 22:25:23 2023  commencing in-memory singleton removal
     Sat Nov 11 22:28:29 2023  begin with 1431502498 relations and 1210425856 unique ideals
     Sat Nov 11 23:38:05 2023  reduce to 962297124 relations and 696430793 ideals in 15 passes
     Sat Nov 11 23:38:05 2023  max relations containing the same ideal: 53
     Sat Nov 11 23:42:10 2023  reading ideals above 720000
     Sat Nov 11 23:42:14 2023  commencing singleton removal, initial pass
     Sun Nov 12 03:28:50 2023  memory use: 21024.0 MB
     Sun Nov 12 03:28:54 2023  reading all ideals from disk
     Sun Nov 12 03:31:44 2023  memory use: 44648.7 MB
     ... 
     Tue Nov 14 08:39:49 2023  commencing in-memory singleton removal
     Tue Nov 14 08:40:17 2023  begin with 236428517 relations and 235660066 unique ideals
     Tue Nov 14 08:47:03 2023  reduce to 236285362 relations and 230413441 ideals in 6 passes
     Tue Nov 14 08:47:03 2023  max relations containing the same ideal: 85
     Tue Nov 14 08:51:28 2023  relations with 0 large ideals: 127875
     Tue Nov 14 08:51:28 2023  relations with 1 large ideals: 95486
     Tue Nov 14 08:51:28 2023  relations with 2 large ideals: 1301900
     Tue Nov 14 08:51:28 2023  relations with 3 large ideals: 7741623
     Tue Nov 14 08:51:28 2023  relations with 4 large ideals: 25166632
     Tue Nov 14 08:51:28 2023  relations with 5 large ideals: 49597077
     Tue Nov 14 08:51:28 2023  relations with 6 large ideals: 62285102
     Tue Nov 14 08:51:28 2023  relations with 7+ large ideals: 89969667
     Tue Nov 14 08:51:28 2023  commencing 2-way merge
     Tue Nov 14 08:56:46 2023  reduce to 150480987 relation sets and 144609066 unique ideals
     Tue Nov 14 08:56:47 2023  commencing full merge
     Tue Nov 14 10:39:21 2023  memory use: 18337.9 MB
     Tue Nov 14 10:39:51 2023  found 67501310 cycles, need 66981266
     Tue Nov 14 10:39:56 2023  weight of 66981266 cycles is about 8707922449 (130.01/cycle)
     Tue Nov 14 10:39:56 2023  distribution of cycle lengths:
     Tue Nov 14 10:39:56 2023  1 relations: 3801061
     Tue Nov 14 10:39:56 2023  2 relations: 4306316
     Tue Nov 14 10:39:56 2023  3 relations: 4711699
     Tue Nov 14 10:39:56 2023  4 relations: 4725778
     Tue Nov 14 10:39:56 2023  5 relations: 4836562
     Tue Nov 14 10:39:56 2023  6 relations: 4738034
     Tue Nov 14 10:39:56 2023  7 relations: 4697005
     Tue Nov 14 10:39:56 2023  8 relations: 4502168
     Tue Nov 14 10:39:56 2023  9 relations: 4303068
     Tue Nov 14 10:39:56 2023  10+ relations: 26359575
     Tue Nov 14 10:39:56 2023  heaviest cycle: 28 relations
     Tue Nov 14 10:40:32 2023  commencing cycle optimization
     Tue Nov 14 10:44:49 2023  start with 578109023 relations
     Tue Nov 14 11:23:20 2023  pruned 25164870 relations
     Tue Nov 14 11:23:21 2023  memory use: 15674.6 MB
     Tue Nov 14 11:23:21 2023  distribution of cycle lengths:
     Tue Nov 14 11:23:21 2023  1 relations: 3801061
     Tue Nov 14 11:23:21 2023  2 relations: 4418872
     Tue Nov 14 11:23:21 2023  3 relations: 4910588
     Tue Nov 14 11:23:21 2023  4 relations: 4919179
     Tue Nov 14 11:23:21 2023  5 relations: 5064834
     Tue Nov 14 11:23:21 2023  6 relations: 4959291
     Tue Nov 14 11:23:21 2023  7 relations: 4926516
     Tue Nov 14 11:23:21 2023  8 relations: 4712847
     Tue Nov 14 11:23:21 2023  9 relations: 4494751
     Tue Nov 14 11:23:21 2023  10+ relations: 24773327
     Tue Nov 14 11:23:21 2023  heaviest cycle: 28 relations
     Tue Nov 14 11:26:57 2023  RelProcTime: 259742
     Tue Nov 14 11:26:57 2023  elapsed time 72:09:03
 
   - Linear Algebra was performed by Oliver Kruse using CADO and MSIEVE-GPU
     - remove duplicates with CADO                                             
       - compile CADO with FLAGS_SIZE='-DSIZEOF_P_R_VALUES=8'.
       - run dup1.
       - run freerel to get the renumber table.
       - count the number of relations exactly (!).
       - run dup2.
       - run purge, making sure that -col-min-index is not too small and that -keep is set to 0.
       - convert all relations back to msieve format using convert_rels. 
       - the version used is not yet officially available; the currently used CADO version is not
         error-free	
       - build a matrix with the desired target density using msieve 
       - upload the matrix file to LambdaLabs, while building Greg Childers msieve-GPU on the target system
       - execute the LA (without root step) on a rented 80-GB-VRAM ( H100); time: about 73hours! 
       - get the dependency file (.dep) back to the local system
       - execute the root step (msieve -nc3) locally



ECM efforts
with Rn:         1 < n < 2000 (Oct 08, 2024) with Rn:     1999 < n < 3000 (Sep 17, 2024)
with Rn:     2999 < n < 4000 (Sep 17, 2024) with Rn:     3999 < n < 5000 (Oct 06, 2024)
with Rn:     4999 < n < 6000 (Oct 06, 2024) with Rn:     5999 < n < 7000 (Sep 17, 2024)
with Rn:     6999 < n < 8000 (Sep 17, 2024) with Rn:     7999 < n < 9000 (Oct 08, 2024)
with Rn:     8999 < n <10000 (Oct 08, 2024) with Rn:     9999 < n <11000 (Oct 08, 2024)
with Rn:   10999 < n <12000 (Oct 04, 2024) with Rn:   11999 < n <14980L/M (Oct 08, 2024)



currently ECM-efforts by   yoyo@home:    ecm-curves
B1 = 11e7/17500 curves/
numbers < 951 digits
643
in progress
....
in progress
....
in progress
....
in progress
....
in progress
B1 = 26e7/45000 curves/
numbers < 600 digits
557
in progress
617
in progress
619
in progress
625
in progress
629
in progress
B1 = 85e7/70000 curves/
numbers < 400 digits
539
in progress
1146
in progress
....
in progress
....
in progress
....
in progress
B1 = 29e8/nnnn curves/
numbers < 400 digits
1036
in progress
1040
in progress
....
in progress
....
in progress
....
in progress



Factorizations
Repunits: R1      - R2500 (Oct 08, 2024) Repunits:  R2501 - R5000 (Sep 17, 2024)
Repunits: R5001   - R7500 (Sep 29, 2024) Repunits: R7501 - R10000 (Oct 04, 2024)
Repunits: R10001 - R12500 (May 03, 2024) Repunits: R12501 - R14980L/M (Feb 27, 2024)




Rprime project; base 10

last update: Dec 19, 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 ...
    - 10ˆ10     R2 = prime
    - 10ˆ20     R19 = prime
    - 10ˆ100     R23 = prime
    - 10ˆ1000     R317 = prime
    - 10ˆ10000     R1031 = prime                 WD (Dec 1985)
    - 10ˆ50000     R49081 = prime               Paul Underwood (Mar 2022)
    - 10ˆ100000     R86453 = prime               Andreas Enge (May 15, 2023)
    - 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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