c76=2^251-1
------------------------------------
bash-2.05$ ecm 10000000 <c76
GMP-ECM 4c, by P. Zimmermann (Inria), 16 Dec 1999, with contributions from
T. Granlund, P. Leyland, C. Curry, A. Stuebinger, G. Woltman, JC. Meyrignac,
A. Yamasaki, and the invaluable help from P.L. Montgomery.
Input number is 3618502788666131106986593281521497120414687020801267626233049500247285301247 (76 digits)
recognized factor of 2^251-1, using special base-2 division
Using B1=10000000, B2=3890888820, polynomial x^60, sigma=347436000
Step 1 took 427189ms for 130559473 muls, 3 gcdexts
********** Factor found in step 1: 27271151
Found COMPOSITE factor of 8 digits: 27271151
Composite cofactor 132686104398972053177608575506090561429353935989033525802891469459697 has 69 digits
--------------------------------------------------
bash-2.05$ echo 27271151 | ./ecm 200
GMP-ECM 4c, by P. Zimmermann (Inria), 16 Dec 1999, with contributions from
T. Granlund, P. Leyland, C. Curry, A. Stuebinger, G. Woltman, JC. Meyrignac,
A. Yamasaki, and the invaluable help from P.L. Montgomery.
Input number is 27271151 (8 digits)
Using B1=200, B2=26040, polynomial x^1, sigma=7154688
Step 1 took 12ms for 2521 muls, 3 gcdexts
********** Factor found in step 1: 503
Found probable prime factor of 3 digits: 503
Probable prime cofactor 54217 has 5 digits
--------------------------------------------------
bash-2.05$ ecm 200000000 <c69
GMP-ECM 4c, by P. Zimmermann (Inria), 16 Dec 1999, with contributions from
T. Granlund, P. Leyland, C. Curry, A. Stuebinger, G. Woltman, JC. Meyrignac,
A. Yamasaki, and the invaluable help from P.L. Montgomery.
Input number is 132686104398972053177608575506090561429353935989033525802891469459697 (69 digits)
recognized factor of 2^251-1, using special base-2 division
Using B1=200000000, B2=316850584050, polynomial x^1, sigma=1053522506
Step 1 took 10441596ms for -1668973187 muls, 3 gcdexts
********** Factor found in step 1: 12070396178249893039969681
Found probable prime factor of 26 digits: 12070396178249893039969681
Composite cofactor 10992688428741403060242688435306818599261537 has 44 digits
----------------------------------------------------------
bash-2.05$ ecm 225000000 <c44
GMP-ECM 4c, by P. Zimmermann (Inria), 16 Dec 1999, with contributions from
T. Granlund, P. Leyland, C. Curry, A. Stuebinger, G. Woltman, JC. Meyrignac,
A. Yamasaki, and the invaluable help from P.L. Montgomery.
Input number is 10992688428741403060242688435306818599261537 (44 digits)
Using B1=225000000, B2=316850584050, polynomial x^1, sigma=1162883034
Step 1 took 6596516ms for -1340035794 muls, 3 gcdexts
Step 2 took 3550798ms for 1290896058 muls, 574210 gcdexts
********** Factor found in step 2: 61676882198695257501367
Found probable prime factor of 23 digits: 61676882198695257501367
Probable prime cofactor 178230287214063289511 has 21 digits
----------------------------------------------------
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                          %
%                           ECPP                           %
%                                                          %
%                  by Fran\c{c}ois MORAIN                  %
%                  morain@inria.inria.fr                   %
%                      Version V3.4.1                      %
%                                                          %
%           "3 is prime, 5 is prime, 7 is prime            %
%              so every odd number is prime"               %
%                                                          %
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
Working on 54217
% Performing a quick compositeness test
% This number might be prime
% Entering ECPP
% Starting phase 1: building the sequence of primes
% Pmax=5000
% N_0=54217
% next D is 0
% Factorization completed using sieve only
% D[[0]]=-1
% Factor= 251^1
% Factor= 3^3
% Factor= 2^3
% Cofactor is 1
% End of depth 0 at 0.032419 s

% Pmax=5000
% N_1=251
% next D is 0
% Factorization completed using sieve only
% D[[1]]=-1
% Factor= 5^3
% Factor= 2^1
% Cofactor is 1

% Time for building is 0.038313 s

% Starting phase 2: proving
% Starting proving job for step 0
% N_0 is prime
% Time for proof[0] is 0.000515 s

% Starting proving job for step 1
% Using complete factorization theorem
% b=1
% Nonresidue is 6
% N_1 is prime
% Time for proof[1] is 0.000789 s
% Time for building is 0.038313 s
% Time for proving  is 0.001865 s
% Total time is        0.040278 s
This number is prime
% Time for this number is 0.042547s

Working on 178230287214063289511
% Performing a quick compositeness test
% This number might be prime
% Entering ECPP
% Starting phase 1: building the sequence of primes
% Pmax=5000
% N_0=178230287214063289511
% next D is 0
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% next D is 11
% Cofactor after sieve is a probable prime
% D[[0]]=11
% A[[0]]=25233508515
% B[[0]]=2631819227
% m[[0]]=178230287188829780997
% Factor= 23^1
% Factor= 3^1
% End of depth 0 at 0.139295 s

% Pmax=5000
% N_1=2583047640417822913
% next D is 0
% Cofactor after sieve is a probable prime
% D[[1]]=-1
% Factor= 73^1
% Factor= 3^1
% Factor= 2^6
% End of depth 1 at 0.165643 s

% Pmax=5000
% N_2=184292782564057
% next D is 0
% Cofactor after sieve is a probable prime
% D[[2]]=-1
% Factor= 1061^1
% Factor= 199^1
% Factor= 3^1
% Factor= 2^3
% End of depth 2 at 0.189178 s

% Pmax=5000
% N_3=36368771
% next D is 0
% Cofactor after sieve is a probable prime
% D[[3]]=-1
% Factor= 5^1
% Factor= 2^1
% End of depth 3 at 0.200810 s

% Pmax=5000
% N_4=3636877
% next D is 0
% Cofactor after sieve is a probable prime
% D[[4]]=-1
% Factor= 3^1
% Factor= 2^2
% End of depth 4 at 0.224134 s

% Pmax=5000
% N_5=303073
% next D is 0
% Factorization completed using sieve only
% D[[5]]=-1
% Factor= 41^1
% Factor= 11^1
% Factor= 7^1
% Factor= 3^1
% Factor= 2^5
% Cofactor is 1

% Time for building is 0.158606 s

% Starting phase 2: proving
% Starting proving job for step 0
% File /home/his/ECPP/Ecpp/Data/Weber/h1g1.cwdx does not exist
% tpber=0.000126s
% j has been computed
% E found
% Suggested twist(11)=1
% N_0 is prime
% Time for proof[0] is 0.052115 s

% Starting proving job for step 1
% N_1 is prime
% Time for proof[1] is 0.002033 s

% Starting proving job for step 2
% N_2 is prime
% Time for proof[2] is 0.002370 s

% Starting proving job for step 3
% N_3 is prime
% Time for proof[3] is 0.000612 s

% Starting proving job for step 4
% N_4 is prime
% Time for proof[4] is 0.000564 s

% Starting proving job for step 5
% Using complete factorization theorem
% N_5 is prime
% Time for proof[5] is 0.001466 s
% Time for building is 0.158606 s
% Time for proving  is 0.060815 s
% Total time is        0.219545 s
This number is prime
% Time for this number is 0.250651s

Working on 61676882198695257501367
% Performing a quick compositeness test
% This number might be prime
% Entering ECPP
% Starting phase 1: building the sequence of primes
% Pmax=5000
% N_0=61676882198695257501367
% next D is 0
% Cofactor after sieve is a probable prime
% D[[0]]=-1
% Factor= 1901^1
% Factor= 251^1
% Factor= 3^2
% Factor= 2^1
% End of depth 0 at 0.355420 s

% Pmax=5000
% N_1=7181151156516637
% next D is 0
% Cofactor after sieve is a probable prime
% D[[1]]=-1
% Factor= 401^1
% Factor= 199^1
% Factor= 13^1
% Factor= 3^3
% Factor= 2^2
% End of depth 1 at 0.379300 s

% Pmax=5000
% N_2=64095791
% next D is 0
% Cofactor after sieve is a probable prime
% D[[2]]=-1
% Factor= 11^1
% Factor= 5^1
% Factor= 2^1
% End of depth 2 at 0.392545 s

% Pmax=5000
% N_3=582689
% next D is 0
% Factorization completed using sieve only
% D[[3]]=-1
% Factor= 139^1
% Factor= 131^1
% Factor= 2^5
% Cofactor is 1
% End of depth 3 at 0.414118 s

% Pmax=5000
% N_4=139
% next D is 0
% Factorization completed using sieve only
% D[[4]]=-1
% Factor= 23^1
% Factor= 3^1
% Factor= 2^1
% Cofactor is 1

% Time for building is 0.097607 s

% Starting phase 2: proving
% Starting proving job for step 0
% N_0 is prime
% Time for proof[0] is 0.003099 s

% Starting proving job for step 1
% N_1 is prime
% Time for proof[1] is 0.002673 s

% Starting proving job for step 2
% N_2 is prime
% Time for proof[2] is 0.000636 s

% Starting proving job for step 3
% Using complete factorization theorem
% N_3 is prime
% Time for proof[3] is 0.001201 s

% Starting proving job for step 4
% Using complete factorization theorem
% N_4 is prime
% Time for proof[4] is 0.000706 s
% Time for building is 0.097607 s
% Time for proving  is 0.009696 s
% Total time is        0.107427 s
This number is prime
% Time for this number is 0.138168s

Working on 12070396178249893039969681
% Performing a quick compositeness test
% This number might be prime
% Entering ECPP
% Starting phase 1: building the sequence of primes
% Pmax=5000
% N_0=12070396178249893039969681
% next D is 0
% Cofactor after sieve is a probable prime
% D[[0]]=-1
% Factor= 251^1
% Factor= 5^1
% Factor= 3^1
% Factor= 2^4
% End of depth 0 at 0.506411 s

% Pmax=5000
% N_1=200371782507468343957
% next D is 0
% itmax=0 ngcd=0 b1=0 b2=0
% Cofactor after sieve is a probable prime
% D[[1]]=1
% Factor= 971^1
% Factor= 2^1
% End of depth 1 at 0.526628 s

% Pmax=5000
% N_2=103178054844216449
% next D is 0
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% next D is 4
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% Cofactor after sieve is a probable prime
% D[[2]]=4
% A[[2]]=-595257410
% B[[2]]=-120810632
% m[[2]]=103178055439473860
% Factor= 937^1
% Factor= 233^1
% Factor= 73^1
% Factor= 17^1
% Factor= 5^1
% Factor= 2^2
% End of depth 2 at 0.577866 s

% Pmax=5000
% N_3=19041013
% next D is 0
% Factorization completed using sieve only
% D[[3]]=-1
% Factor= 883^1
% Factor= 599^1
% Factor= 3^2
% Factor= 2^2
% Cofactor is 1
% End of depth 3 at 0.601076 s

% Pmax=5000
% N_4=883
% next D is 0
% Factorization completed using sieve only
% D[[4]]=-1
% Factor= 7^2
% Factor= 3^2
% Factor= 2^1
% Cofactor is 1

% Time for building is 0.145341 s

% Starting phase 2: proving
% Starting proving job for step 0
% N_0 is prime
% Time for proof[0] is 0.004922 s

% Starting proving job for step 1
% N_1 is prime
% Time for proof[1] is 0.033649 s

% Starting proving job for step 2
% Entering the D=4 business
% E found
% Suggested twist(4)=1
% N_2 is prime
% Time for proof[2] is 0.279796 s

% Starting proving job for step 3
% Using complete factorization theorem
% b=1
% Nonresidue is 5
% N_3 is prime
% Time for proof[3] is 0.002196 s

% Starting proving job for step 4
% Using complete factorization theorem
% N_4 is prime
% Time for proof[4] is 0.001569 s
% Time for building is 0.145341 s
% Time for proving  is 0.323814 s
% Total time is        0.469288 s
This number is prime
% Time for this number is 0.500837s

% ==> Total time for the computations is 0.933894s