digits factor from B1/B2 sigma date who
17318084223531773495645465120355125300012794812598542488604543489894510268872^1181-13e940000277792010-Mar-06J. Bos/T. Kleinjung/A. Lenstra/P. Montgomery
2684259378334615022318697944343788216432489200846285048000813413087360364*10^341-111e719989585862009-Dec-28yoyo@home/M. Thompson
367444434979215670990789575255179863190894618060876873794628023807888110^381+1260e68344124112006-Aug-24B. Dodson
4667096016350822673209664240849557767897708647256439968854156766822973^466+111e718753778242005-Apr-06B. Dodson
5662962694395357472529438944680703639380944872790430192699066352716515^725-143e636657671792008-Feb-02P. Zimmermann
6657187393919567533196954543536541942109485960792211129378072527385793^128+1300e611807662008-Oct-15A. Bhargava/S. Pelissier
7656525752677264494876479921288770257339188771523598153034370350673178^129-1300e64897312592007-May-03A. Bhargava/S. Pelissier
864434467305871495447776131479343739290067288544536110390554895093310^311-185e719177328412005-Sep-05K. Aoki & T. Shimoyama
9635164699331306316872669671949821694146264036853603881462315812673^533+111e730011674172005-Nov-10A. Kruppa
10631533278332859984538742027679425703436499713936400682045716943692^1187-13e930000005882010-Jan-30J. Bos/T. Kleinjung
1162440980705463163360697328911242994791672535751313418972483724336^344+1260e636606903262010-Feb-10B. Dodson
1262310691503788737908952080468957713609494632935464121059514494292^2034+111e715074674572005-Apr-10B. Dodson
1362238304057506098873184202486358581654763680206073966336991419512^977-1110e614082127262007-Nov-12B. Dodson
146213055369049845151421562673963068310715129211918218895785368571HP49(100)260e617658170062010-Feb-08N. Daminelli
156210902279470188834915776493427283420460074278957518730285170913761^68+111e627073610242007-Oct-25R. Hooft
1661845244690710948240607535422620066647006561114102225534469755777^103-1260e612155283692007-Jan-19CWI
1761781919897344868678956873258393150732185255488033133848503606961^141+1300e623345995702007-Apr-14A. Bhargava/S. Pelissier
18614431999617245557152985439095075047794565394448680658709169377c23443e631089102592009-Oct-02T. Izu
196126647978140582122865605334549604467922100161808758092435998172^1087-126e72600058142010-Feb-20J. Bos/T. Kleinjung
206120488151802155134633883355760712141682290776778586418092310812^905+143e622516622242006-Sep-02B. Dodson
2161163589403051162227159600352579281064155093972727121081450315359^142+1300e611078262008-Apr-27A. Bhargava/S. Pelissier
226112919429437721065295000993251946628913374682274879837540438732^2018+143e620048168522007-Apr-04B. Dodson
236071039759092664914142122865674739196718154815932936540190912144^124+1300e611610682008-Sep-27A. Bhargava/S. Pelissier
24602548560045052385578347532596153558163380306948545004771321416^365+111e720501478332007-Feb-19B. Dodson
25602371927163673198085254196819954407189255682069873722715480972^2098+143e632334687692008-Jul-24K. Aoki
26601863479638752902446077850151151151861851514604981633423269932^1099+111e725041478972005-Oct-03B. Dodson
276016787445637575097611646923449857387033930797362147195377513744^133+1300e65401182008-Mar-12A. Bhargava/S. Pelissier
28601516342449174162060351011148649376472830164481791073896444736^292+1260e638370769182007-Oct-08B. Dodson
2960112653507736977123212855475998117625287101801671405101833429113!-1110e611699500162007-May-02S. Irvine
30597088203059559671138275684991577025859181687153688740555491130^155+1300e61000197872008-Feb-24A. Bhargava/S. Pelissier
3159593314649163093923096343308801397767678815983882380775542097^296+143e63733414502008-Dec-09K. Aoki
3259567955284704450614948092460763897262479288795947168673684411950691^29-143e639164352362009-Jul-12yoyo@home
33595444084377427190745830698015890510194248112556217179258454944^131+1300e611620992008-Sep-28A. Bhargava/S. Pelissier
345943976229065455869110045557754921993324851820720678681937281687^64+111e624081382912010-Jan-25T. Adachi
3559411209125668130186754723214356097283494734935822253446618732^1013-126e72634000102010-Mar-03J. Bos/T. Kleinjung
3659375973763237543573441974066649958340472497021459699704982936^334+1260e639024212542009-Oct-20B. Dodson
3759247026668419183640914822533935766195553006322862834236017132^932+143e633564205122007-Jun-07B. Dodson
385921206963047213924100449174648127600105136716298220374685897136^76+76^136300e620322256952009-Jun-07J. Gilchrist
39592013149212082891981448485729887467415529871114239776918134710^233-126e741146008192005-Feb-20B. Dodson
405914311578668849306832064176821408791945900114506618448115473prSm(73)43e624777052412005-Oct-05S. Chong
415859070905863132865363135605748276956944852181208651941677617^361+1260e614082930542007-Dec-26B. Dodson
425850078611297377498490139255118291976664051215455077991014412^1195+1300e630110082010-Feb-22A. Bhargava/S. Pelissier
435844248172865304828264204599924146315180160544307958224557013^538+1110e628490279072007-Jul-30B. Dodson
44583967882017033636507059526462153963313366766975977666433309889*2^889-111e642064739612009-May-14P. Leyland
45583933722077254573047641104432697964360070287393192927208173369*9^369+13e632021840982009-Sep-27P. Leyland
465832131622766403394135660479154180649695503836925499813337018*10^141-17389750027356753862003-Nov-01R. Backstrom
4758288334186496446413973708910363987740734714476964919582680195^127+1300e6200146392008-Sep-27A. Bhargava/S. Pelissier
4858284378954434221476566772314057476662720695108332976221079198^121-1300e670003082010-Jan-15A. Bhargava/S. Pelissier
4958281167914494190328615316253232633083205763608315921354711191^107+1300e610631222008-Jan-09A. Bhargava/S. Pelissier
505827400249266510431675753993368380258419800073596859472440697^277-5^27711e6806750652009-Dec-02J. Becker
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;