digits factor from B1/B2 sigma date who
179230287218850527957657353501592644191394504497548357952951751379589766421112779711^306+1800e636481100212012-Aug-12S. Wagstaff
27718974159366624817405627752670504479132613571595050983959444958694223874973021N_1881e93663293892013-Jun-15S. Wagstaff
37533684202681448681641371253266567152551848723846153394578693778504847467532911^304+11e938855930152012-Aug-02S. Wagstaff
475227432689108589532754984915075774848386671439568260420754414940780761245893EM47850e622246483662012-Sep-11R. Propper
57318084223531773495645465120355125300012794812598542488604543489894510268872^1181-13e940000277792010-Mar-06J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery
67310428160429418457500429522066800897944150146683298503930319104835264564872^1163-13e930000851582010-Apr-18J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery
7722018991705156933308755627143166143636102292888469923265123047051651611833^713-16e816310368902012-Jan-01S. Wagstaff
8721566673573891590777656203412521732183501114352998589185992910774970255293^560-229e826778238952013-Jan-02R. Propper
9721054117896546655189879958827705741132992511483567301726119450853736814973^554-2260e69711774322013-Jan-02R. Propper
107123831310369329940284424897622931177276129265258901041211081029394362653134^134+135^1352.9e921988990522013-Feb-18R. Propper
11705289087042676468861217290554991265187804183644859386048140442629053859141^141+142^1427.6e912093559742013-Apr-30R. Propper
12702633079918766750130582962701074725510503525177187274307427718640470081144^144+145^145260e623511837302013-Apr-23R. Propper
137025382071298406877993352032594928704761862488966164013465000273117959832^1237-13e930000867872010-Oct-30J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery
147013797984257321030503952973261636181086560886279954467996235313469732893^607+1400e628263472882012-Jun-09B. Dodson
1569778690790153396854590214216181777523646970439474630791573244864151943149^149+150^1502.9e927096097962013-Feb-15R. Propper
16694749423393769674758719603217626142542908102430388804189710613422565292^1822+1400e616484708722011-Feb-20B. Dodson
17693624662300887872452037251506956081964465074167635004715575534886729733^1443+16e815740534842010-Nov-24S. Wagstaff
1869109733959547779654926866874550711330198507136524383634700803540817357F(1527)11e718365179462012-Mar-20B. Kelly
19684259378334615022318697944343788216432489200846285048000813413087360364*10^341-111e719989585862009-Dec-28yoyo@home/M. Thompson
2068129475608018812752124869004761220976883739752627847096567680323878332^1139-13e930000438372010-Sep-05J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery
2168117705885530736592421024548248586229721633871553332979778040669443317^763+19e842516892542011-Jun-12B. Dodson
2267444434979215670990789575255179863190894618060876873794628023807888110^381+1260e68344124112006-Aug-24B. Dodson
236733336054564524023812285094740439504209376377924059938955977537304216^415-1260e62:14997568892012-Mar-25C. Bouvier
246730433922592068709674825000822339863904242789573222588015845143343072^1151+11e910000215512011-May-06J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery
2567297050274636574987681892380898971302231984893104795658785668237445710^236+9^23611e713238779382013-May-03K. Schoenberger
26671476089794776829083186088935097008657059172428532830012025534581117Euler(130)1.1e940414279632013-Apr-09S. Wagstaff
2767116901951492961275863837267794391066135654620656366634031976107700112^350+1800e615974677522012-Nov-07S. Wagstaff
28667096016350822673209664240849557767897708647256439968854156766822973^466+111e718753778242005-Apr-06B. Dodson
29666942175353998476780484151131865777585076358222528038084736746800172^1073-13e930000006232010-May-31J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery
30662962694395357472529438944680703639380944872790430192699066352716515^725-143e636657671792008-Feb-02P. Zimmermann
31661462956874728820401487697317253666601470381451767583367407563407693^792+1900e622276821662012-Feb-07B. Dodson
32661009401163421619061324327172674066689373014504982739891292137842795^463-1900e635060870222011-Oct-13B. Dodson
33657187393919567533196954543536541942109485960792211129378072527385793^128+1300e611807662008-Oct-15A. Bhargava/S. Pelissier
34656525752677264494876479921288770257339188771523598153034370350673178^129-1300e64897312592007-May-03A. Bhargava/S. Pelissier
3565576701131418082522403523111427809684922231185206228971755210347576^822+1600e62159119182011-Dec-19S. Wagstaff
36653849768706134664981729511785296829962099521828674095247139447985710^328+1900e68871276832011-Oct-09B. Dodson
37653511471504296527410116962551605409853838129285504878533424501403723773^31-1850e63114689642013-Jan-27R. Propper
386521409755852155829640600817278566515575581623831146350895229829607739^83-111e712108199972012-Jan-02R. Hooft
39651773062209097153559783477252680994319827556170366141404951309667129^167-11e918183022011-Jun-22A. Bhargava/S. Pelissier
406516785703768734933461785568830025208537214399823278256352088003411A(3678,3033)1e728062721182010-Nov-10T. Womack
4164729199122792425867141672666230536139443602501438315428414697153311^278+1400e620109436512012-Dec-23B. Dodson
426472138209024349633641511865605591584209215863398450383284683056773^634+1400e618819412032011-Mar-27S. Wagstaff
4364598530857787612465027882535141710864838607399598786674191234190917^173-1300e614869152010-May-16A. Bhargava/S. Pelissier
446446503840557912877153186123140195337328717863408217842274320516012^1175+13e970030732012-Oct-28J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery
4564434467305871495447776131479343739290067288544536110390554895093310^311-185e719177328412005-Sep-05K. Aoki & T. Shimoyama
466430991179455811575174725608173535487742824502995399036887473666092^964+11e910000103592011-Apr-04J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery
476429857053402558779743844577552178758001520211821514688754861213472^1051+11e910000264752011-May-12J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery
4864121082572604117260820560686363850457878463087074156705615935085112^341-1800e626112312872012-Nov-04S. Wagstaff
49638444196124521985613107200800387993419728117183908113734158447773^723-1450e638963933492011-Apr-24S. Wagstaff
50637677495871880808912468227314966416444238486126959293711451772192^1049+11e910000064862011-Mar-10J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery
eFT means eCompute Factoring Team. The notation [x^e] after the first limit bound B1 means that this factor was used with Suyama's extension, implemented up from version 3 of GMP-ECM, and that the smallest polynomial which finds this factor is x^e. a(n,k) denotes the n-th term from the sequence defined by a(1,k)=1 and a(n,k)=(1+sum(a(i,k),i=1..n-1))/(n-1). a(n,2) is sequence M0728 from the Encyclopedia of Integer Sequences, a(n,3) is sequence M1551, and a(n,4) is sequence M1957; A(n,k) denotes the k-th term of the aliquot sequence starting from n, i.e. A(n,0)=n and A(n,k+1)=sigma(A(n,k))-A(n,k) where sigma(m) is the sum of the divisors of m; AF(n) denotes the n-th alternating factorial n!-(n-1)!+(n-2)!-...; B(n) denotes the n-th Bell number, which is the numerator of the coefficient of x^n in the series expansion of exp(exp(x)-1) at x=0; Bern(n) denotes the numerator of the n-th Bernoulli number; C(n) denotes the n-th Cullen number n*2^n+1; C(n,k) denotes the binomial coefficient binomial(n,k); cp(n,k) denotes the n-th term from the concatenated primefactors sequence starting from n; E(n) is the n-th Euler number, i.e. the numerator of the coefficient of x^n in the series expansion of sec(x)+tan(x); HPnn(k) is the k-th of the Home Prime Sequence of nn; j(n) is the n-th coefficient of the elliptic modular function j(tau), i.e. the coefficient of x^n in series(jell(x),x) in Pari; J(n) is the n-th Jones number, i.e. binomial(2n-1,n)-1; L(n) is the n-th Lucas number; Mxxxx(n) represents the n-th term from sequence Mxxxx in Sloane and Plouffe Encyclopedia of Integer Sequences; M(a,n) denotes (a^n-1)^n+a^n-1; p(n) denotes the n-th partition number; RSm(n) denotes the n-th reverse Smarandache number; SC(n) denotes a term from the sigma-chain of n; SymSm(n) denotes the n-th symmetric Smarandache number, i.e. the concatenation of Sm(n) and RSm(n); T(n) is the n-th tangent number, i.e. the numerator of the coefficient of x^n in the series expansion of tan(x); V(p,q,n) is a^n+b^n where (a,b) are roots of x^2-p*x+q [sum(k^n, k=RootOf(x^2-p*x+q)) in Maple-notation]; W(n) denotes the n-th Woodall number n*2^n-1; W1(n) is the numerator of the n-th Wolstenholme number 1+1/2+...+1/n.
[*] factor found in step 1;
[s/r] George Woltman's mprime program was used for step 1, and gmp-ecm for step 2, with the -resume option.
[c/s] factor found with the client/server setup
(1) K64=1!+2!+3!+...+64!;
(2) P1*P2*...*P66+P67 where Pn denotes the nth prime;
(3) special numbers: c93 is a divisor of p118-1, where p118 is a divisor of 10^211-1.
(4) these numbers had been independently factored by Samuel S. Wagstaff, Jr in 1995;