2^212+1 = 6582018229284824168619876730229402019930943462534319453394436097
--------------------------------
bash-2.05$ ecm 100000000 <x64
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 6582018229284824168619876730229402019930943462534319453394436097 (64 digits)
Using B1=100000000, B2=135793107450, polynomial x^1, sigma=401102593
Step 1 took 4154162ms for 1311593670 muls, 3 gcdexts
********** Factor found in step 1: 28774970321
Found COMPOSITE factor of 11 digits: 28774970321
Composite cofactor 228741095328993655528152185934252940490841504438551857 has 54 digits
-----------------------------------
bash-2.05$ ./ecm 2000 <xxx6
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 28774970321 (11 digits)
Using B1=2000, B2=203742, polynomial x^1, sigma=131125570
Step 1 took 152ms for 25270 muls, 3 gcdexts
********** Factor found in step 1: 17
Found probable prime factor of 2 digits: 17
Probable prime cofactor 1692645313 has 10 digits
-----------------------------------
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 228741095328993655528152185934252940490841504438551857 (54 digits
)
recognized factor of 2^212+1, using special base-2 division
Using B1=220000000, B2=316850584050, polynomial x^1, sigma=1893326032
Step 1 took 11550532ms for -1405868853 muls, 3 gcdexts
Step 2 took 3892421ms for 1290896037 muls, 574203 gcdexts
********** Factor found in step 2: 10920513604018498900801
Found probable prime factor of 23 digits: 10920513604018498900801
Probable prime cofactor 20946001591429012199281424246257 has 32 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 1692645313
% Performing a quick compositeness test
% This number might be prime
% Entering ECPP
% Starting phase 1: building the sequence of primes
% Pmax=5000
% N_0=1692645313
% next D is 0
% Factorization completed using sieve only
% D[[0]]=-1
% Factor= 4057^1
% Factor= 53^1
% Factor= 41^1
% Factor= 3^1
% Factor= 2^6
% Cofactor is 1
% End of depth 0 at 0.096389 s

% Pmax=5000
% N_1=4057
% next D is 0
% Factorization completed using sieve only
% D[[1]]=-1
% Factor= 13^2
% Factor= 3^1
% Factor= 2^3
% Cofactor is 1

% Time for building is 0.037453 s

% Starting phase 2: proving
% Starting proving job for step 0
% Using complete factorization theorem
% b=1
% Nonresidue is 10
% b=1
% Nonresidue is 11
% N_0 is prime
% Time for proof[0] is 0.003585 s

% Starting proving job for step 1
% Using complete factorization theorem
% N_1 is prime
% Time for proof[1] is 0.000672 s
% Time for building is 0.037453 s
% Time for proving  is 0.005163 s
% Total time is        0.042712 s
This number is prime
% Time for this number is 0.101226s

Working on 10920513604018498900801
% Performing a quick compositeness test
% This number might be prime
% Entering ECPP
% Starting phase 1: building the sequence of primes
% Pmax=5000
% N_0=10920513604018498900801
% next D is 0
% Cofactor after sieve is a probable prime
% D[[0]]=-1
% Factor= 53^1
% Factor= 5^2
% Factor= 3^1
% Factor= 2^6
% End of depth 0 at 0.170095 s

% Pmax=5000
% N_1=42926547185607307
% next D is 0
% Cofactor after sieve is a probable prime
% D[[1]]=-1
% Factor= 13^1
% Factor= 3^1
% Factor= 2^1
% End of depth 1 at 0.196218 s

% Pmax=5000
% N_2=550340348533427
% next D is 0
% Cofactor after sieve is a probable prime
% D[[2]]=-1
% Factor= 757^1
% Factor= 11^1
% Factor= 2^1
% End of depth 2 at 0.219432 s

% Pmax=5000
% N_3=33045535519
% next D is 0
% Cofactor after sieve is a probable prime
% D[[3]]=-1
% Factor= 43^1
% Factor= 3^1
% Factor= 2^1
% End of depth 3 at 0.244015 s

% Pmax=5000
% N_4=128083471
% next D is 0
% Cofactor after sieve is a probable prime
% D[[4]]=-1
% Factor= 307^1
% Factor= 5^1
% Factor= 3^1
% Factor= 2^1
% End of depth 4 at 0.265440 s

% Pmax=5000
% N_5=13907
% next D is 0
% Factorization completed using sieve only
% D[[5]]=-1
% Factor= 409^1
% Factor= 17^1
% Factor= 2^1
% Cofactor is 1
% End of depth 5 at 0.286459 s

% Pmax=5000
% N_6=409
% next D is 0
% Factorization completed using sieve only
% D[[6]]=-1
% Factor= 17^1
% Factor= 3^1
% Factor= 2^3
% Cofactor is 1

% Time for building is 0.164796 s

% Starting phase 2: proving
% Starting proving job for step 0
% N_0 is prime
% Time for proof[0] is 0.004609 s

% Starting proving job for step 1
% N_1 is prime
% Time for proof[1] is 0.001565 s

% Starting proving job for step 2
% N_2 is prime
% Time for proof[2] is 0.001368 s

% Starting proving job for step 3
% N_3 is prime
% Time for proof[3] is 0.000995 s

% Starting proving job for step 4
% N_4 is prime
% Time for proof[4] is 0.000567 s

% Starting proving job for step 5
% N_5 is prime
% Time for proof[5] is 0.000405 s

% Starting proving job for step 6
% Using complete factorization theorem
% b=1
% Nonresidue is 11
% b=1
% Nonresidue is 13
% b=1
% Nonresidue is 14
% b=1
% Nonresidue is 19
% b=1
% Nonresidue is 21
% N_6 is prime
% Time for proof[6] is 0.003648 s
% Time for building is 0.164796 s
% Time for proving  is 0.014765 s
% Total time is        0.179673 s
This number is prime
% Time for this number is 0.200276s

Working on 20946001591429012199281424246257
% Performing a quick compositeness test
% This number might be prime
% Entering ECPP
% Starting phase 1: building the sequence of primes
% Pmax=7000
% N_0=20946001591429012199281424246257
% next D is 0
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% next D is 3
% itmax=0 ngcd=0 b1=0 b2=0
% 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[[0]]=3
% A[[0]]=8490208393339715
% B[[0]]=1974872806316051
% m[[0]]=20946001591429003709073030906543
% Factor= 3^1
% End of depth 0 at 0.479962 s

% Pmax=7000
% N_1=6982000530476334569691010302181
% next D is 0
% Cofactor after sieve is a probable prime
% D[[1]]=-1
% Factor= 5^1
% Factor= 3^1
% Factor= 2^2
% End of depth 1 at 0.520562 s

% Pmax=7000
% N_2=116366675507938909494850171703
% next D is 0
% Cofactor after sieve is a probable prime
% D[[2]]=-1
% Factor= 211^1
% Factor= 2^1
% End of depth 2 at 0.559969 s

% Pmax=5000
% N_3=275750415895589832926185241
% next D is 0
% Cofactor after sieve is a probable prime
% D[[3]]=-1
% Factor= 941^1
% Factor= 83^1
% Factor= 43^1
% Factor= 7^2
% Factor= 5^1
% Factor= 2^3
% End of depth 3 at 0.588493 s

% Pmax=5000
% N_4=41891309210893411
% next D is 0
% Cofactor after sieve is a probable prime
% D[[4]]=-1
% Factor= 107^1
% Factor= 31^1
% Factor= 5^1
% Factor= 3^5
% Factor= 2^1
% End of depth 4 at 0.612580 s

% Pmax=5000
% N_5=5197233011
% next D is 0
% Cofactor after sieve is a probable prime
% D[[5]]=-1
% Factor= 5^1
% Factor= 2^1
% End of depth 5 at 0.626094 s

% Pmax=5000
% N_6=519723301
% next D is 0
% Cofactor after sieve is a probable prime
% D[[6]]=-1
% Factor= 53^1
% Factor= 5^2
% Factor= 3^1
% Factor= 2^2
% End of depth 6 at 0.639921 s

% Pmax=5000
% N_7=32687
% next D is 0
% Factorization completed using sieve only
% D[[7]]=-1
% Factor= 277^1
% Factor= 59^1
% Factor= 2^1
% Cofactor is 1
% End of depth 7 at 0.661290 s

% Pmax=5000
% N_8=277
% next D is 0
% Factorization completed using sieve only
% D[[8]]=-1
% Factor= 23^1
% Factor= 3^1
% Factor= 2^2
% Cofactor is 1

% Time for building is 0.316743 s

% Starting phase 2: proving
% Starting proving job for step 0
% Entering the D=3 business
% E found
% Suggested twist(3)=1
% N_0 is prime
% Time for proof[0] is 0.165813 s

% Starting proving job for step 1
% N_1 is prime
% Time for proof[1] is 0.005978 s

% Starting proving job for step 2
% N_2 is prime
% Time for proof[2] is 0.004655 s

% Starting proving job for step 3
% N_3 is prime
% Time for proof[3] is 0.003684 s

% Starting proving job for step 4
% N_4 is prime
% Time for proof[4] is 0.001804 s

% Starting proving job for step 5
% N_5 is prime
% Time for proof[5] is 0.000865 s

% Starting proving job for step 6
% N_6 is prime
% Time for proof[6] is 0.000641 s

% Starting proving job for step 7
% N_7 is prime
% Time for proof[7] is 0.000484 s

% Starting proving job for step 8
% Using complete factorization theorem
% b=1
% Nonresidue is 5
% N_8 is prime
% Time for proof[8] is 0.001108 s
% Time for building is 0.316743 s
% Time for proving  is 0.180062 s
% Total time is        0.496928 s
This number is prime
% Time for this number is 0.534546s

% ==> Total time for the computations is 0.837867s