Factorizations of Repunit Numbers

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

News

-  Last update: Dec 02, 2021      

-  Found by Kurt Beschorner    
   Dec 02, 2021   n =90653: 214445033709540802180933 * 5692033966......c90003;      ecm: B1 = 5e4; sigma = 0:4329911231673300  
   Dec 02, 2021   n=284651: 4240252934906766053;                                    gr-mfaktc
   Dec 02, 2021   n=284701: 18008501114444788477;                                   gr-mfaktc
   Dec 02, 2021   n=284777: 104729417928757759;                                     gr-mfaktc
   Dec 02, 2021   n=285119: 6692492467510082929;                                    gr-mfaktc
   Dec 02, 2021   n=285161: 962492065640054227;                                     gr-mfaktc
   Dec 02, 2021   n=285179: 2930749435078945231;                                    gr-mfaktc
   Dec 02, 2021   n=285283: 1277006858710167707;                                    gr-mfaktc
   Dec 02, 2021   n=285301: 1282107243103148723;                                    gr-mfaktc
   Dec 02, 2021   n=285457: 171550807909502477;                                     gr-mfaktc
   Dec 02, 2021   n=285539: 2169135586142299837;                                    gr-mfaktc
   Dec 02, 2021   n=285631: 159744990004992947;                                     gr-mfaktc

 
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Dec 02, 2021   R888/c258: SNFS-difficult = 296 
                  727M unique r. relations and 625M unique ideals are collected
                  msieve: filtering is complete
                  msieve linear algebra: currently progress  47 %:    
                  estimated time of arrival: 505 hours (~ 21 days)  
                  msieve-logfile abstract:
                  -> setting target matrix density to 130
                  -> begin with 727778254 relations and 625686486 unique ideals
                  -> found 38132423 cycles, need 37964762
                  -> weight of 37964762 cycles is about 4935432927 (130.00/cycle)
                  -> matrix size: 37.9M x 37.9M 
	

-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Dec 02, 2021   R1340L/c265: SNFS-difficult = 268; degree 8
                  41.5 M unique r. relations and 144 M unique ideals are collected
                  currently progress 6%;   


-  Found by Kurt Beschorner    
   Nov 28, 2021   n=283553: 204697891689599603;                                     gr-mfaktc
   Nov 28, 2021   n=283573: 1039331475589281241;                                    gr-mfaktc 
   Nov 28, 2021   n=283637: 2651405655306075277;                                    gr-mfaktc 
   Nov 28, 2021   n=283669: 15319988841290678803;                                   gr-mfaktc 
   Nov 28, 2021   n=283741: 167253790701960227;                                     gr-mfaktc 
   Nov 28, 2021   n=283741: 1503041387479074991;                                    gr-mfaktc 
   Nov 28, 2021   n=283769: 173802703622009027;                                     gr-mfaktc 
   Nov 28, 2021   n=283859: 3644575238591606471;                                    gr-mfaktc 
   Nov 28, 2021   n=284041: 83614019252912431;                                      gr-mfaktc 
   Nov 28, 2021   n=284131: 17977335384299386289;                                   gr-mfaktc     
   Nov 28, 2021   n=284159: 436766746522505957;                                     gr-mfaktc 
   Nov 28, 2021   n=284159: 481155496229463791;                                     gr-mfaktc 
   Nov 28, 2021   n=284173: 12957657872550097237;                                   gr-mfaktc 
   Nov 28, 2021   n=284201: 1254581461998895721;                                    gr-mfaktc 
   Nov 28, 2021   n=284231: 9471971273019466969;                                    gr-mfaktc 
   Nov 28, 2021   n=284267: 113830695254481449;                                     gr-mfaktc 
   Nov 28. 2021   n=284573: 338389194105733093;                                     gr-mfaktc  


-  Found by Kurt Beschorner    
   Nov 24, 2021   n = 1789: 64056025886889373277419436256019351;                    ecm: B1 =11e6; sigma = 0:2109008035502416 
   Nov 24, 2021   n = 1789: 105700953104805896168083326362115409 * 5823310991......c1656; ecm: B1 =11e6; sigma = 0:1163849328483425 
   Nov 24, 2021   n=282281: 3050254332577171723;                                    gr-mfaktc
   Nov 24, 2021   n=282287: 291027295969725319;                                     gr-mfaktc
   Nov 24, 2021   n=282307: 244936864284490867;                                     gr-mfaktc
   Nov 24, 2021   n=282307: 3410622839598329239;                                    gr-mfaktc
   Nov 24, 2021   n=282407: 8476224149782040747;                                    gr-mfaktc
   Nov 24, 2021   n=282911: 15177282624379078237;                                   gr-mfaktc
   Nov 24, 2021   n=283001: 4476346391068715719;                                    gr-mfaktc
   Nov 24, 2021   n=283051: 279882983394401837;                                     gr-mfaktc
   Nov 24, 2021   n=283193: 11106405609309149599;                                   gr-mfaktc
   Nov 24, 2021   n=283463: 1889138653494504253;                                    gr-mfaktc
			  

-  Found by Kurt Beschorner      
   Nov 19, 2021   n=100045: 920335596580080187321;                                  ecm: B1 = 5e4; sigma = 0:4821021755754696 
   Nov 19, 2021   n=281167: 15075142104267073253;                                   gr-mfaktc
   Nov 19, 2021   n=281717: 1736533992761916239;                                    gr-mfaktc
   Nov 19, 2021   n=281767: 85681058131855679;                                      gr-mfaktc
   Nov 19, 2021   n=281849: 2462446307239244279;                                    gr-mfaktc
   Nov 19, 2021   n=281893: 11723432649062896561;                                   gr-mfaktc
   Nov 19, 2021   n=282229: 855841341434890933;                                     gr-mfaktc
 

-  Found by Kurt Beschorner      
   Nov 15, 2021   n =33347: 2641792682087801512951 * 2019406034......c33315;        ecm: B1 = 5e4; sigma = 3172914214415077
   Nov 15, 2021   n=280249: 412759029324961399;                                     gr-mfaktc
   Nov 15, 2021   n=280339: 271113910304731729;                                     gr-mfaktc
   Nov 15, 2021   n=280373: 7884687960871150523;                                    gr-mfaktc
   Nov 15, 2021   n=280409: 3621994722506168923;                                    gr-mfaktc
   Nov 15, 2021   n=280411: 16881827204335034351;                                   gr-mfaktc
   Nov 15, 2021   n=280487: 3360219665281929397;                                    gr-mfaktc
   Nov 15, 2021   n=280591: 10573330224998013049;                                   gr-mfaktc
   Nov 15, 2021   n=280697: 268238999630183333;                                     gr-mfaktc
   Nov 15, 2021   n=280879: 17627784353036854561;                                   gr-mfaktc
   Nov 15, 2021   n=280883: 3770109102985794973;                                    gr-mfaktc
   Nov 15, 2021   n=280933: 152692103379160841;                                     gr-mfaktc
   Nov 15, 2021   n=280933: 481715365806662431;                                     gr-mfaktc
   Nov 15, 2021   n=280949: 157328530691067893;                                     gr-mfaktc
   Nov 15, 2021   n=280957: 5031235475168347519;                                    gr-mfaktc
   Nov 15, 2021   n=280963: 324614190141936397;                                     gr-mfaktc


-  Found by Kurt Beschorner      
   Nov 14, 2021   n=279119: 183015281953366151;                                     gr-mfaktc
   Nov 14, 2021   n=279137: 75759071518453787;                                      gr-mfaktc
   Nov 14, 2021   n=279413: 12339159996284537693;                                   gr-mfaktc
   Nov 14, 2021   n=279479: 849859790552306683;                                     gr-mfaktc
   Nov 14, 2021   n=279551: 1072989027811536071;                                    gr-mfaktc
   Nov 14, 2021   n=279863: 133935968717202107;                                     gr-mfaktc
   Nov 14, 2021   n=279863: 14606124097373260409;                                   gr-mfaktc
   Nov 14, 2021   n=279967: 230683630728214523;                                     gr-mfaktc
   Nov 14, 2021   n=280129: 1349629409879340173;                                    gr-mfaktc
   Nov 14, 2021   n=280139: 1339989672992673929;                                    gr-mfaktc

 
-  Found by Kurt Beschorner      
   Nov 10, 2021   n =10005: 106466200135338392760555275314323121;                   ecm: B1 = 1e6; sigma = 0:79662971413339
   Nov 10, 2021   n=278087: 832695079285413997;                                     gr-mfaktc
   Nov 10, 2021   n=278111: 158699393861705533;                                     gr-mfaktc
   Nov 10, 2021   n=278149: 2600222459551020929;                                    gr-mfaktc
   Nov 10, 2021   n=278209: 772619624115800893;                                     gr-mfaktc
   Nov 10, 2021   n=278353: 366059049732818597;                                     gr-mfaktc
   Nov 10, 2021   n=278363: 724050790388717317;                                     gr-mfaktc
   Nov 10, 2021   n=278363: 923445773550766693;                                     gr-mfaktc
   Nov 10, 2021   n=278563: 2981688291870585643;                                    gr-mfaktc
   Nov 10, 2021   n=278639: 2405297960535330163;                                    gr-mfaktc
   Nov 10, 2021   n=278743: 216257133370458437;                                     gr-mfaktc
   Nov 10, 2021   n=278807: 16777830825056234281;                                   gr-mfaktc


-  Found by Alfred Eichhorn 
   Nov 08, 2021   n =43159: 107627158513823342902276631 * 1032370571......c43133;   ecm: B1 = 5e4; sigma = 6610380898161236
   Nov 08, 2021   n =43441:  21863165346803581172782412899187 * 5963110296......c43390; ecm: B1 = 5e4; sigma = 0:1076509070355461

 
-  Found by Kurt Beschorner      
   Nov 08, 2021   n=277169: 2945515857196650079;                                    gr-mfaktc
   Nov 08, 2021   n=277213: 179855909576457241;                                     gr-mfaktc
   Nov 08, 2021   n=277223: 923039938796116517;                                     gr-mfaktc
   Nov 08, 2021   n=277279: 306445601101882511;                                     gr-mfaktc
   Nov 08, 2021   n=277373: 1794865047075142199;                                    gr-mfaktc
   Nov 08, 2021   n=277421: 3156155659154544853;                                    gr-mfaktc
   Nov 08, 2021   n=277643: 109662240378523369;                                     gr-mfaktc
   Nov 08, 2021   n=277813: 2180668751386916639;                                    gr-mfaktc

 
-  Found by Kurt Beschorner      
   Nov 04, 2021   n=275447: 153568897128263117;                                     gr-mfaktc
   Nov 04, 2021   n=275599: 397019001193845757;                                     gr-mfaktc
   Nov 04, 2021   n=275599: 684291815664420281;                                     gr-mfaktc
   Nov 04, 2021   n=275837: 1155521103554867671;                                    gr-mfaktc
   Nov 04, 2021   n=275897: 5273063976457957951;                                    gr-mfaktc
   Nov 04, 2021   n=275999: 104208163019863961;                                     gr-mfaktc
   Nov 04, 2021   n=276091: 591978143590426471;                                     gr-mfaktc
   Nov 04, 2021   n=276229: 597911048809116551;                                     gr-mfaktc
   Nov 04, 2021   n=276247: 157861112443352239;                                     gr-mfaktc
   Nov 04, 2021   n=276373: 303006931219018679;                                     gr-mfaktc
   Nov 04, 2021   n=276443: 18047219416217894603;                                   gr-mfaktc
   Nov 04, 2021   n=276487: 315672792457099613;                                     gr-mfaktc
   Nov 04, 2021   n=276499: 18025562134926136289;                                   gr-mfaktc
   Nov 04, 2021   n=276557: 4167386829459126043;                                    gr-mfaktc
   Nov 04, 2021   n=276779: 2556484381202822849;                                    gr-mfaktc
   Nov 04, 2021   n=276821: 340353739184684689;                                     gr-mfaktc
   Nov 04, 2021   n=276901: 157794345445410283;                                     gr-mfaktc
   Nov 04, 2021   n=276929: 647857877286605203;                                     gr-mfaktc 
   Nov 04, 2021   n=276949: 249083398407160721;                                     gr-mfaktc 

 
-  Found by Kurt Beschorner      
   Nov 03, 2021   n = 3277: 1659625482312684867571670109201289  * 6274352273......c3058; ecm: B1 = 3e6; sigma = 4033646941598850
   Nov 03, 2021   n = 5002: 9257979664211852962861062975013161250901383 * 2274667807...... c2322; ecm: B1 =11e6; sigma = 0:1183374437285197
 
 
-  Found by Kurt Beschorner      
   Oct 31, 2021   n=274301: 3851879422687577443;                                    gr-mfaktc
   Oct 31, 2021   n=274583: 120900352917058357;                                     gr-mfaktc
   Oct 31, 2021   n=274679: 120483721806251569;                                     gr-mfaktc
   Oct 31, 2021   n=274777: 123789627686850883;                                     gr-mfaktc
   Oct 31, 2021   n=274831: 515049728169895147;                                     gr-mfaktc
   Oct 31, 2021   n=274871: 14771607848042739791;                                   gr-mfaktc
   Oct 31, 2021   n=274951: 14491370422833073921;                                   gr-mfaktc
   Oct 31, 2021   n=274993: 259693845059197951;                                     gr-mfaktc
   Oct 31, 2021   n=275039: 110455776013660199;                                     gr-mfaktc
   Oct 31, 2021   n=275131: 1566250580971879427;                                    gr-mfaktc
   Oct 31, 2021   n=275251: 12749574876292742561;                                   gr-mfaktc
  

-  Found by Kurt Beschorner      
   Oct 28, 2021   n = 5002: 522346250245015592799109827193626997 * 2105882830......c2365; ecm: B1 =11e6; sigma = 0:7715223337182973
   Oct 28, 2021   n=273061: 163178372176225213;                                     gr-mfaktc
   Oct 28, 2021   n=273073: 5399179797132721351;                                    gr-mfaktc
   Oct 28, 2021   n=273157: 403936707494102357;                                     gr-mfaktc
   Oct 28, 2021   n=273181: 2938631864980648523;                                    gr-mfaktc
   Oct 28, 2021   n=273269: 329485867200504277;                                     gr-mfaktc
   Oct 28, 2021   n=273281: 1983156493168103969;                                    gr-mfaktc
   Oct 28, 2021   n=273313: 3445094047802837249;                                    gr-mfaktc
   Oct 28, 2021   n=273857: 2056692014344053311;                                    gr-mfaktc
   Oct 28, 2021   n=273899: 3471448001176655329;                                    gr-mfaktc
   Oct 28, 2021   n=273899: 13222436172540061003;                                   gr-mfaktc
   Oct 28, 2021   n=273941: 262661501043042481;                                     gr-mfaktc
   Oct 28, 2021   n=274069: 399721169562503813;                                     gr-mfaktc
   Oct 28, 2021   n=274081: 1273619675192014079;                                    gr-mfaktc
   Oct 28, 2021   n=274093: 1518923273700025079;                                    gr-mfaktc


-  Found by Kurt Beschorner      
   Oct 26, 2021   n =40019: 61620387150019925819822231;                             ecm: B1 =25e4; sigma = 0:7925212246147850 
   Oct 26, 2021   n =40019: 66459048737033637939135822043619279 * 4132251231......c34186; ecm: B1 =25e4; sigma = 0:3980336408708090 
 
 
-  Found by Alfred Eichhorn 
   Oct 25, 2021   n =97927: 4330628433327671445689 * 2565704096......c97905;        ecm: B1 = 5e4; sigma = 2444771095148551


-  Found by Kurt Beschorner      
   Oct 25, 2021   n=299942: 83308428885922445773 * 4290142473......c149938;         ecm: B1 = 5e4; sigma = 0:4620972490834684 
   Oct 25, 2021   n=269419: 3837362385443044747;                                    gr-mfaktc
   Oct 25, 2021   n=269623: 681453187781247719;                                     gr-mfaktc
   Oct 25, 2021   n=269701: 5579295029130449839;                                    gr-mfaktc
   Oct 25, 2021   n=269719: 2886377680293296911;                                    gr-mfaktc
   Oct 25, 2021   n=269741: 11675297161904717573;                                   gr-mfaktc
   Oct 25, 2021   n=269987: 277121759041303769;                                     gr-mfaktc
   Oct 25, 2021   n=270143: 1894594335335258639;                                    gr-mfaktc
   Oct 25, 2021   n=270209: 1717400393284335049;                                    gr-mfaktc
   Oct 25, 2021   n=270229: 638669513432603843;                                     gr-mfaktc
   Oct 25, 2021   n=270241: 3388439674484420639;                                    gr-mfaktc
   Oct 25, 2021   n=270337: 182404284786229199;                                     gr-mfaktc
   Oct 25, 2021   n=270443: 137810051322210277;                                     gr-mfaktc
   Oct 25, 2021   n=270539: 185842886908151849;                                     gr-mfaktc
   Oct 25, 2021   n=270563: 3593513077600618253;                                    gr-mfaktc
   Oct 25, 2021   n=270679: 14444676718953266363;                                   gr-mfaktc
   Oct 25, 2021   n=270961: 15361056971310340837;                                   gr-mfaktc
   Oct 25, 2021   n=271097: 3972766603758758867;                                    gr-mfaktc
   Oct 25, 2021   n=271129: 1089875032935185467;                                    gr-mfaktc
   Oct 25, 2021   n=271181: 148159834013863481;                                     gr-mfaktc
   Oct 25, 2021   n=271853: 1926532437419318507;                                    gr-mfaktc
   Oct 25, 2021   n=271867: 9328792920686308637;                                    gr-mfaktc
   Oct 25, 2021   n=271919: 10985887740839237267;                                   gr-mfaktc
   Oct 25, 2021   n=272053: 696341486872476043;                                     gr-mfaktc
   Oct 25, 2021   n=272141: 426183958859602157;                                     gr-mfaktc
   Oct 25, 2021   n=272287: 1619530646276307529;                                    gr-mfaktc
   Oct 25, 2021   n=272477: 9274305694214503643;                                    gr-mfaktc
   Oct 25, 2021   n=272563: 227112773475062281;                                     gr-mfaktc
   Oct 25, 2021   n=272693: 87399873105059639;                                      gr-mfaktc
   Oct 25, 2021   n=272737: 826631267715988919;                                     gr-mfaktc
   Oct 25, 2021   n=272971: 4611753488915525159;                                    gr-mfaktc


-  Found by Kurt Beschorner      
   Oct 24, 2021   n =13051: 289792400507496591746951639;                            ecm: B1 =25e4; sigma = 0:916112482751869
   Oct 24, 2021   n =13051: 1336449884279254346334474191 * 2967578754......c12542;  ecm: B1 =25e4; sigma = 0:7320727441128006
   Oct 24, 2021   n =40019: 4464415870915646717 * 1692252876......c34247;           ecm: B1 =25e4; sigma = 0:4019875591801662


-  Found by Yousuke Koide      
   Oct 18, 2021   n =  846: 8147270298945964118744634040617462692098679807835492529 * 2987454923......P194; SNFS  

 
-  Found by Kurt Beschorner      
   Oct 13, 2021   n=267227: 5802699966039622757;                                    gr-mfaktc
   Oct 13, 2021   n=267497: 75110974071743443;                                      gr-mfaktc
   Oct 13, 2021   n=267647: 6591528654040759453;                                    gr-mfaktc
   Oct 13, 2021   n=267677: 1272126774560122973;                                    gr-mfaktc
   Oct 13, 2021   n=267763: 5795140650529128809;                                    gr-mfaktc
   Oct 13, 2021   n=267811: 2051527349761559963;                                    gr-mfaktc
   Oct 13, 2021   n=267893: 176993151402036511;                                     gr-mfaktc
   Oct 13, 2021   n=268013: 11125077469663849283;                                   gr-mfaktc
   Oct 13, 2021   n=268123: 196858632027395321;                                     gr-mfaktc
   Oct 13, 2021   n=268237: 107502744926918951;                                     gr-mfaktc
   Oct 13, 2021   n=268271: 1627397530950607111;                                    gr-mfaktc
   Oct 13, 2021   n=268487: 14908781637327253009;                                   gr-mfaktc
   Oct 13, 2021   n=268519: 941578665312035329;                                     gr-mfaktc
   Oct 13, 2021   n=268607: 2292233533421438521;                                    gr-mfaktc
   Oct 13, 2021   n=268613: 5792304796588693853;                                    gr-mfaktc
   Oct 13, 2021   n=268643: 1087082814733148329;                                    gr-mfaktc
   Oct 13, 2021   n=268729: 1495003159231853881;                                    gr-mfaktc
   Oct 13, 2021   n=268841: 3779903927160364093;                                    gr-mfaktc
   Oct 13, 2021   n=268937: 100367602797034733;                                     gr-mfaktc
   Oct 13, 2021   n=268979: 900899209332127963;                                     gr-mfaktc
   Oct 13, 2021   n=269117: 178225823410173031;                                     gr-mfaktc


-  Found by Alfred Eichhorn 
   Oct 11, 2021   n =42943: 12040267178027196292637 * 9228292816......c42920;       ecm: B1 = 5e4; sigma = 3097410500777759
   Oct 11, 2021   n =61091: 22591912851401440910039 * 4918180759......c61068;       ecm: B1 = 5e4; sigma = 2067528895893704
   Oct 11, 2021   n =97787: 1755655860865731936416422009 * 6328752324......c97759;  ecm: B1 = 5e4; sigma = 7614901593777729

-  Found by Kurt Beschorner      
   Oct 07, 2021   n=264791: 251458761234405001;                                     gr-mfaktc
   Oct 07, 2021   n=264931: 86117538170944363;                                      gr-mfaktc
   Oct 07, 2021   n=264931: 2087554989301673401;                                    gr-mfaktc
   Oct 07, 2021   n=265021: 9715832824398626587;                                    gr-mfaktc
   Oct 07, 2021   n=265273: 554723902290299681;                                     gr-mfaktc
   Oct 07, 2021   n=265399: 962467233355684267;                                     gr-mfaktc
   Oct 07, 2021   n=265451: 3085748498439365173;                                    gr-mfaktc
   Oct 07, 2021   n=265459: 9315853036831073479;                                    gr-mfaktc
   Oct 07, 2021   n=265807: 11956857517308323881;                                   gr-mfaktc
   Oct 07, 2021   n=265873: 124022916936114563;                                     gr-mfaktc
   Oct 07, 2021   n=265873: 5623725838371026801;                                    gr-mfaktc
   Oct 07, 2021   n=266047: 7088188830646864013;                                    gr-mfaktc
   Oct 07, 2021   n=266293: 195734817274382761;                                     gr-mfaktc
   Oct 07, 2021   n=266411: 8987281812303016921;                                    gr-mfaktc
   Oct 07, 2021   n=266587: 1153223175691599839;                                    gr-mfaktc
   Oct 07, 2021   n=266603: 3755034721566797957;                                    gr-mfaktc
   Oct 07, 2021   n=266641: 539030633745274523;                                     gr-mfaktc
   Oct 07, 2021   n=266681: 2527803409042646521;                                    gr-mfaktc
   Oct 07, 2021   n=266719: 3098749672732718843;                                    gr-mfaktc
   Oct 07, 2021   n=266759: 1451633476156381351;                                    gr-mfaktc
   Oct 07, 2021   n=266897: 1525828751668404839;                                    gr-mfaktc
   Oct 07, 2021   n=267017: 3943279215994780253;                                    gr-mfaktc
   Oct 07, 2021   n=267049: 626738994607284907;                                     gr-mfaktc


-  Found by Kurt Beschorner      
   Oct 01, 2021   n =12017: 4242772710733294354040968914239 * 1058426045......c11705; ecm: B1 = 1e6; sigma = 0:130400900789959  
 

-  Found by Kurt Beschorner      
   Sep 30, 2021   n=262901: 170442763746975721;                                     gr-mfaktc
   Sep 30, 2021   n=262909: 718743767790293369;                                     gr-mfaktc
   Sep 30, 2021   n=263023: 96609298079530283;                                      gr-mfaktc
   Sep 30, 2021   n=263267: 4275127429787038387;                                    gr-mfaktc
   Sep 30, 2021   n=263273: 115615698838996121;                                     gr-mfaktc
   Sep 30, 2021   n=263491: 137784085615951003;                                     gr-mfaktc
   Sep 30, 2021   n=263591: 189165903860274947;                                     gr-mfaktc
   Sep 30, 2021   n=264029: 12176997096050828009;                                   gr-mfaktc
   Sep 30, 2021   n=264071: 13014827146259212003;                                   gr-mfaktc
   Sep 30, 2021   n=264167: 7520351785430128163;                                    gr-mfaktc 
   Sep 30, 2021   n=264169: 390940513330122293;                                     gr-mfaktc 
   Sep 30, 2021   n=264169: 1742522548445577401;                                    gr-mfaktc 
   Sep 30, 2021   n=264353: 166446091036058959;                                     gr-mfaktc 
   Sep 30, 2021   n=264437: 470728911924073477;                                     gr-mfaktc 
   Sep 30, 2021   n=264527: 153371096807703839;                                     gr-mfaktc 
   Sep 30, 2021   n=264577: 531137092421756453;                                     gr-mfaktc 
   Sep 30, 2021   n=264601: 133028950330443877;                                     gr-mfaktc 
   Sep 30, 2021   n=264601: 6789270060317116627;                                    gr-mfaktc 	


-  Found by Kurt Beschorner      
   Sep 25, 2021   n=260467: 14669305149661043053;                                   gr-mfaktc
   Sep 25, 2021   n=260549: 90716828518731049;                                      gr-mfaktc
   Sep 25, 2021   n=260573: 579018005163918889;                                     gr-mfaktc
   Sep 25, 2021   n=260647: 653185308062163133;                                     gr-mfaktc
   Sep 25, 2021   n=260717: 308461534091793157;                                     gr-mfaktc
   Sep 25, 2021   n=260791: 85117970029703357;                                      gr-mfaktc
   Sep 25, 2021   n=260807: 4734748105716354631;                                    gr-mfaktc
   Sep 25, 2021   n=261059: 2059606927777270609;                                    gr-mfaktc
   Sep 25, 2021   n=261061: 286142140993767601;                                     gr-mfaktc
   Sep 25, 2021   n=261223: 183081674446280747;                                     gr-mfaktc
   Sep 25, 2021   n=261271: 8992682341945904999;                                    gr-mfaktc
   Sep 25, 2021   n=261301: 111093120622404413;                                     gr-mfaktc
   Sep 25, 2021   n=261427: 193770947831013649;                                     gr-mfaktc
   Sep 25, 2021   n=261881: 12275154902743119707;                                   gr-mfaktc
   Sep 25, 2021   n=261973: 758819301768866027;                                     gr-mfaktc
   Sep 25, 2021   n=262103: 440003148415726067;                                     gr-mfaktc
   Sep 25, 2021   n=262153: 3122762036115442477;                                    gr-mfaktc
   Sep 25, 2021   n=262231: 413584068560324813;                                     gr-mfaktc
   Sep 25, 2021   n=262271: 687397699819906879;                                     gr-mfaktc
   Sep 25, 2021   n=262313: 1144671893153998529;                                    gr-mfaktc
   Sep 25, 2021   n=262519: 153650199563912477;                                     gr-mfaktc
   Sep 25, 2021   n=262543: 2442294214225695083;                                    gr-mfaktc
   Sep 25, 2021   n=262597: 103337180753265203;                                     gr-mfaktc
   Sep 25, 2021   n=262697: 291885846247882961;                                     gr-mfaktc
   Sep 25, 2021   n=262739: 5027886529861221083;                                    gr-mfaktc


-  Found by Kurt Beschorner      
   Sep 17, 2021   n=259381: 494024863675173253;                                     gr-mfaktc
   Sep 17, 2021   n=259723: 3272885495691024637;                                    gr-mfaktc
   Sep 17, 2021   n=259771: 89352416850784249;                                      gr-mfaktc
   Sep 17, 2021   n=259771: 839529925709815799;                                     gr-mfaktc
   Sep 17, 2021   n=259993: 131620477273397773;                                     gr-mfaktc
   Sep 17, 2021   n=260009: 1146329613983650963;                                    gr-mfaktc
   Sep 17, 2021   n=260089: 122592744113216159;                                     gr-mfaktc
   Sep 17, 2021   n=260089: 1574156194848974479;                                    gr-mfaktc
   Sep 17, 2021   n=260171: 143069085845338889;                                     gr-mfaktc
   Sep 17, 2021   n=260191: 72953020984139519;                                      gr-mfaktc
   Sep 17, 2021   n=260207: 820437793632238907;                                     gr-mfaktc
   Sep 17, 2021   n=260231: 5562622050583748197;                                    gr-mfaktc
   Sep 17, 2021   n=260339: 1810171592554714199;                                    gr-mfaktc
   Sep 17, 2021   n=260339: 5928441234117631561;                                    gr-mfaktc
           
	 
-  Found by Kurt Beschorner      
   Sep 13, 2021   n =12827: 3420651094647875222135349699809 * 3418627192......c12565; ecm: B1 =25e4; sigma = 5949084999255270  
   Sep 13, 2021   n=257093: 11973496655447136289;                                   gr-mfaktc
   Sep 13, 2021   n=257123: 14059056411438657439;                                   gr-mfaktc
   Sep 13, 2021   n=257287: 748742445842445653;                                     gr-mfaktc
   Sep 13, 2021   n=257443: 9003159472438875517;                                    gr-mfaktc
   Sep 13, 2021   n=257539: 1840003021485910121;                                    gr-mfaktc
   Sep 13, 2021   n=257947: 424084740267833641;                                     gr-mfaktc
   Sep 13, 2021   n=257987: 350259166300276921;                                     gr-mfaktc
   Sep 13, 2021   n=257989: 334059181561951117;                                     gr-mfaktc
   Sep 13, 2021   n=258101: 6954651446027779453;                                    gr-mfaktc
   Sep 13, 2021   n=258233: 177060872911324951;                                     gr-mfaktc
   Sep 13, 2021   n=258389: 11225260356704408437;                                   gr-mfaktc
   Sep 13, 2021   n=258443: 126702734955020467;                                     gr-mfaktc 
   Sep 13, 2021   n=258527: 455311860875765969;                                     gr-mfaktc 
   Sep 13, 2021   n=258613: 241247720440584373;                                     gr-mfaktc 
   Sep 13, 2021   n=258631: 455218532296841917;                                     gr-mfaktc 
   Sep 13, 2021   n=258637: 1098464318277175711;                                    gr-mfaktc 
   Sep 13, 2021   n=258659: 6521376996805713569;                                    gr-mfaktc 
   Sep 13, 2021   n=258673: 3588404696309874929;                                    gr-mfaktc 
   Sep 13, 2021   n=258707: 79516796516923049;                                      gr-mfaktc 
   Sep 13, 2021   n=258743: 13908197957590415357;                                   gr-mfaktc 
   Sep 13, 2021   n=258967: 318740834096327959;                                     gr-mfaktc 
 

-  Found by Kurt Beschorner      
   Sep 07, 2021   n =15003: 294138061502033730180620742121;                         ecm: B1 = 1e6; sigma = 0:4611263169165355  
   Sep 07, 2021   n =15003: 49962356033970990727412679251053 * 2102951523......c9915; ecm: B1 = 1e6; sigma = 0:1140076183079191  
   Sep 07, 2021   n=254003: 4777919549849014271;                                    gr-mfaktc
   Sep 07, 2021   n=254213: 12765653634137948723;                                   gr-mfaktc
   Sep 07, 2021   n=254281: 7032550483060196201;                                    gr-mfaktc
   Sep 07, 2021   n=254299: 944782408445112271;                                     gr-mfaktc
   Sep 07, 2021   n=254729: 1004585176794113129;                                    gr-mfaktc
   Sep 07, 2021   n=254731: 14113142319537487679;                                   gr-mfaktc
   Sep 07, 2021   n=254929: 4397847576766510963;                                    gr-mfaktc
   Sep 07, 2021   n=254959: 879685502983347707;                                     gr-mfaktc
   Sep 07, 2021   n=255023: 14478789253991221813;                                   gr-mfaktc
   Sep 07, 2021   n=255121: 77009483786854601;                                      gr-mfaktc
   Sep 07, 2021   n=255137: 1031224378159265999;                                    gr-mfaktc
   Sep 07, 2021   n=255361: 1046626335364903009;                                    gr-mfaktc
   Sep 07, 2021   n=255457: 867765208348748561;                                     gr-mfaktc
   Sep 07, 2021   n=255571: 2512074677974695077;                                    gr-mfaktc 
   Sep 07, 2021   n=255653: 1066058928743713403;                                    gr-mfaktc 
   Sep 07, 2021   n=255679: 3671780424863095973;                                    gr-mfaktc 
   Sep 07, 2021   n=255961: 464829679233471997;                                     gr-mfaktc 
   Sep 07, 2021   n=255961: 977011258024640147;                                     gr-mfaktc 
   Sep 07, 2021   n=255989: 189063032938510799;                                     gr-mfaktc 
   Sep 07, 2021   n=256211: 825424188373735001;                                     gr-mfaktc 
   Sep 07, 2021   n=256279: 748075210390519751;                                     gr-mfaktc 
   Sep 07, 2021   n=256349: 153204910458341957;                                     gr-mfaktc 
   Sep 07, 2021   n=256369: 12459921043862680627;                                   gr-mfaktc 
   Sep 07, 2021   n=256391: 80355055110328991;                                      gr-mfaktc 
   Sep 07, 2021   n=256493: 1217866743965514427;                                    gr-mfaktc 
   Sep 07, 2021   n=256567: 258626770727066267;                                     gr-mfaktc 
   Sep 07, 2021   n=256589: 212949088688771893;                                     gr-mfaktc 
   Sep 07, 2021   n=256589: 9204677904045811951;                                    gr-mfaktc 
   Sep 07, 2021   n=256643: 16828307097845004677;                                   gr-mfaktc 
   Sep 07, 2021   n=256771: 367164345302148637;                                     gr-mfaktc 
   Sep 07, 2021   n=256877: 7753969678914857999;                                    gr-mfaktc 
   Sep 07, 2021   n=256967: 3200250217795107787;                                    gr-mfaktc 


-  Found by Kurt Beschorner      
   Sep 01, 2021   n=253229: 110787135947992597;                                     gr-mfaktc
   Sep 01, 2021   n=253247: 1382964275588158369;                                    gr-mfaktc
   Sep 01, 2021   n=253367: 1130372410351006871;                                    gr-mfaktc
   Sep 01, 2021   n=253381: 1526355646880706533;                                    gr-mfaktc
   Sep 01, 2021   n=253447: 86383496659889311;                                      gr-mfaktc
   Sep 01, 2021   n=253607: 662552958646755881;                                     gr-mfaktc
   Sep 01, 2021   n=253637: 1470238546086099871;                                    gr-mfaktc
   Sep 01, 2021   n=253751: 332836669304084041;                                     gr-mfaktc
   Sep 01, 2021   n=253811: 233042119074213157;                                     gr-mfaktc
   Sep 01, 2021   n=253909: 988958808683274911;                                     gr-mfaktc
   Sep 01, 2021   n=253949: 498065550677811031;                                     gr-mfaktc


-  Found by Alfred Eichhorn 
   Aug 31, 2021   n =42349: 34068973227298816567389271 * 3261357786......c42323;    ecm: B1 = 5e4; sigma = 3894331124445607   


-  Found by Yousuke Koide 
   Aug 30, 2021   n =  890: 630859966703635424146382843107732835487998079409968772589281; ecm: B1 = 3e8; sigma = 2:7216577815049336811   


-  Found by Kurt Beschorner      
   Aug 27, 2021   n =60001: 5065105765505227441465483 * 8258196552......c57871;     ecm: B1 =25e4; sigma = 0:1208954549013749 
   Aug 27, 2021   n=252013: 18358839216615453533;                                   gr-mfaktc
   Aug 27, 2021   n=252079: 90712887425683031;                                      gr-mfaktc
   Aug 27, 2021   n=252181: 1392425437132051477;                                    gr-mfaktc
   Aug 27, 2021   n=252233: 1111886761656101329;                                    gr-mfaktc
   Aug 27, 2021   n=252313: 2817295116682243031;                                    gr-mfaktc
   Aug 27, 2021   n=252533: 120123691326229889;                                     gr-mfaktc
   Aug 27, 2021   n=252541: 85713936029669039;                                      gr-mfaktc
   Aug 27, 2021   n=252727: 262063627740335203;                                     gr-mfaktc
   Aug 27, 2021   n=252727: 1362909995272310893;                                    gr-mfaktc
   Aug 27, 2021   n=252767: 75928273063353239;                                      gr-mfaktc
   Aug 27, 2021   n=252887: 10892926902237539837;                                   gr-mfaktc
 

-  Found by Kurt Beschorner     
   Aug 25, 2021   n=249107: 87054406307185003;                                      gr-mfaktc   
   Aug 25, 2021   n=249133: 15055734325953684761;                                   gr-mfaktc   
   Aug 25, 2021   n=249233: 952183344616210477;                                     gr-mfaktc   
   Aug 25, 2021   n=249497: 136487899802507879;                                     gr-mfaktc   
   Aug 25, 2021   n=249533: 11147015626643624677;                                   gr-mfaktc   
   Aug 25, 2021   n=249583: 771905387595091523;                                     gr-mfaktc   
   Aug 25, 2021   n=249727: 4707843178118370067;                                    gr-mfaktc   
   Aug 25, 2021   n=249857: 381613159797916027;                                     gr-mfaktc   
   Aug 25, 2021   n=249989: 146041027730531987;                                     gr-mfaktc   
   Aug 25, 2021   n=250031: 1064302112414759123;                                    gr-mfaktc   
   Aug 25, 2021   n=250153: 202047029602899401;                                     gr-mfaktc   
   Aug 25, 2021   n=250199: 157290852985743403;                                     gr-mfaktc   
   Aug 25, 2021   n=250433: 988359342121314043;                                     gr-mfaktc   
   Aug 25, 2021   n=250501: 13780805198050651723;                                   gr-mfaktc   
   Aug 25, 2021   n=250619: 7485114914614458227;                                    gr-mfaktc   
   Aug 25, 2021   n=250693: 307519012975842893;                                     gr-mfaktc   
   Aug 25, 2021   n=250741: 121841019765478757;                                     gr-mfaktc   
   Aug 25, 2021   n=250871: 315008549200864039;                                     gr-mfaktc   
   Aug 25, 2021   n=250951: 103064735947687721;                                     gr-mfaktc   
   Aug 25, 2021   n=250993: 1920252971241238043;                                    gr-mfaktc   
   Aug 25, 2021   n=251443: 8592645122685955963;                                    gr-mfaktc   
   Aug 25, 2021   n=251539: 632711389633213361;                                     gr-mfaktc   
   Aug 25, 2021   n=251609: 87626335953845597;                                      gr-mfaktc   
   Aug 25, 2021   n=251809: 78692798083976191;                                      gr-mfaktc   
   Aug 25, 2021   n=251857: 1197240147374305747;                                    gr-mfaktc   
   Aug 25, 2021   n=251903: 2993653572847659037;                                    gr-mfaktc   
   
														   
-  Bo Chen, Wenjie Fang, Alfred Eichhorn, Danilo Nitsche, Kurt Beschorner 
   Aug 23, 2021   n = 1008: 11824792503914776383865492901019100670460517256833712771719617457; SNFS   
                  msieve-logfile abstract:
                  - SNFS-difficult = 288; setting target matrix density to 130 
                  - begin with 729425851 relations and 611973089 unique ideals
                  - found 31674616 cycles, need 31654077
                  - commencing linear algebra      
                  - matrix is 31654188 x 31654077 
                  - commencing square root phase
                  - read 15822694 cycles
                  - cycles contain 56703378 unique relations
                  - read 56703378 relations
                  - multiplying 56703378 relations
                  - multiply complete, coefficients have about 1565.85 million bits
                  - initial square root is modulo 10567147
                  - GCD is N, no factor found
                  - reading relations for dependency 2
                  - read 15828748 cycles
                  - cycles contain 56713100 unique relations
                  - read 56713100 relations
                  - multiplying 56713100 relations
                  - multiply complete, coefficients have about 1566.11 million bits
                  - initial square root is modulo 10596463
                  - p65 factor: 11824792503914776383865492901019100670460517256833712771719617457
                  - p185 factor: 75863646933147015591828268401923986261986397730196168081539267851470929961346053360645853358874777126920177958883875403750336775844271700524766982560221150310256906229475838502330430737

 
-  Found by Alfred Eichhorn 
   Aug 23, 2021   n =96953: 276214772174133244027973609 * 4022634641......c96926;   ecm: B1 = 5e4; sigma = 2473481238973593
ECM efforts
with Rn: 1 < n < 2000 (Nov 24, 2021)	with Rn: 1999 < n < 3000 (Oct 24, 2021)
with Rn: 2999 < n < 4000 (Nov 19, 2021)	with Rn: 3999 < n < 5000 (Jul 23, 2019)
with Rn: 4999 < n < 6000 (Nov 03, 2021)	with Rn: 5999 < n < 7000 (Dec 02, 2021)
with Rn: 6999 < n < 8000 (Aug 31, 2021)	with Rn: 7999 < n < 9000 (Nov 24, 2021)
with Rn: 8999 < n <10000 (Oct 10, 2021)	with Rn: 9999 < n <11000 (Nov 10, 2021)
with Rn: 10999 < n <12000 (Oct 06, 2021)	with Rn: 11999 < n <14980L/M (Nov 27, 2021)
currently ECM-efforts by yoyo@home: ecm-curves
B1 = 43e6/8600 curves/ numbers < 1001 digits	1255 working	1463 working	1475 working	7980L working	8460M working
B1 = 11e7/18400 curves/ numbers < 701 digits	611 working	617 working	619 working	625 working	641 working
B1 = 26e7/46000 curves/ numbers < 450 digits	469 working	475 working	521 working	1136 working	1160 working
B1 = 85e7/75000 curves/ numbers < 250 digits	609 working	735 working	1188 working	1200 working	1320 working
Factorizations
Repunits: R1 - R2500 (Nov 24, 2021)	Repunits: R2501 - R5000 (Nov 02, 2021)
Repunits: R5001 - R7500 (Nov 03, 2021)	Repunits: R7501 - R10000 (May 28, 2021)
Repunits: R10001 - R12500 (Nov 10, 2021)	Repunits: R12501 - R14980L/M (Sep 19, 2020)
Rprime project; base 10

last update: Aug 25, 2021

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 = PRP Harvey Dubner (Sep 1999)
- 10ˆ100000	R86453 = PRP Lew Baxter (Oct 2000)
- 10ˆ250000	R109297 = PRP Paul Bourdelais - Harvey Dubner (Apr 2007)
- 10ˆ500000	R270343 = PRP Maksym Voznyy - Anton Budnyy (Jul 2007)
- 10ˆ7500000	R5794777 = PRP S. Batalov - Ryan Propper (Apr 2021)
- 10ˆ10000000	R8177207 = PRP S. Batalov - Ryan Propper (May 2021)
Visitors since Oct 27, 2020: zur Webseite
Factorizations of repunit numbers of the form (10ⁿ-1)/9 (111111...)

related links news ecm efforts currently efforts by YOYO factor tables Rprime project

Related links:

News

Rprime project; base 10

last update: Aug 25, 2021

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

Overview

Top of page

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

related links news ecm efforts currently efforts by YOYO factor tables Rprime project

Related links:

News

Rprime project; base 10

last update: Aug 25, 2021

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

Overview

Top of page

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

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
