bash-2.05$ ./ecm -k 10 100000 217 <xx
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 2228957842262951197934756066684920769745080717495763357756967413121 (67 digits)
Using B1=100000, B2=14164920, polynomial x^3, sigma=217
Step 1 took 25355ms for 1290471 muls, 3 gcdexts
Step 2 took 14583ms for 557160 muls, 3958 gcdexts
********** Factor found in step 2: 316955440822738177
Found probable prime factor of 18 digits: 316955440822738177
Probable prime cofactor 7032401262704707649518767703756385761576062060673 has 49 digits
---------------------------------------------------------------
c1 = (11**64+1)/2
print("c1=",c1,"\n")

t1=Time::new
k=1.lcm_to(35000)
t2=Time::new
print("k=lcm{1,..,35000}=",k,"\n")
print("time=",(t2-t1),"[s]\n")

FiniteField.setorder(c1)
p31.pp(k,0,100000)
-------------------------------------------------------------
k(3 1)=(936187782979879600049270272014561445110067157267257974949978172172 1535310199409217855625269619412289538258935107272556224658944331395)
time=496.320809[s]
y^2=x^3+55x+(-191)
k(3 1)=(2046727272924645423629264200586572714484137917145166578699464765392 2031068060471866059115510709995170483967196884618271445542699172391)
time=495.957106[s]
y^2=x^3+56x+(-194)
k(3 1)=(1663460500911700236760820184096934210318592635077207051732698918020 2046627737730596953066390591426045601424905378824623924647159462315)
time=496.452837[s]
y^2=x^3+57x+(-197)
k(3 1)=(1449558686102138719381604990230659996256068928584450540115613023286 280850308629848431556123695090067829504925158467072443801854528811)
time=496.028748[s]
y^2=x^3+58x+(-200)
k(3 1)=(316955440822738177 nil)
time=495.909986[s]
----------------------------------------------------------
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                          %
%                           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 316955440822738177
% Performing a quick compositeness test
% This number might be prime
% Entering ECPP
% Starting phase 1: building the sequence of primes
% Pmax=5000
% N_0=316955440822738177
% next D is 0
% itmax=0 ngcd=0 b1=0 b2=0
% Cofactor after sieve is a probable prime
% D[[0]]=1
% Factor= 251^1
% Factor= 2^1
% End of depth 0 at 0.056471 s

% Pmax=5000
% N_1=631385340284339
% next D is 0
% Cofactor after sieve is a probable prime
% D[[1]]=-1
% Factor= 2^1
% End of depth 1 at 0.080716 s

% Pmax=5000
% N_2=315692670142169
% next D is 0
% Cofactor after sieve is a probable prime
% D[[2]]=-1
% Factor= 827^1
% Factor= 149^1
% Factor= 113^1
% Factor= 11^1
% Factor= 2^3
% End of depth 2 at 0.096013 s

% Pmax=5000
% N_3=257639
% next D is 0
% Cofactor after sieve is a probable prime
% D[[3]]=-1
% Factor= 2^1
% End of depth 3 at 0.117412 s

% Pmax=5000
% N_4=128819
% next D is 0
% Factorization completed using sieve only
% D[[4]]=-1
% Factor= 2221^1
% Factor= 29^1
% Factor= 2^1
% Cofactor is 1
% End of depth 4 at 0.139006 s

% Pmax=5000
% N_5=2221
% next D is 0
% Factorization completed using sieve only
% D[[5]]=-1
% Factor= 37^1
% Factor= 5^1
% Factor= 3^1
% Factor= 2^2
% Cofactor is 1

% Time for building is 0.132266 s

% Starting phase 2: proving
% Starting proving job for step 0
% N_0 is prime
% Time for proof[0] is 0.047699 s

% Starting proving job for step 1
% N_1 is prime
% Time for proof[1] is 0.001432 s

% Starting proving job for step 2
% Using complete factorization theorem
% b=1
% Nonresidue is 6
% N_2 is prime
% Time for proof[2] is 0.008862 s

% Starting proving job for step 3
% N_3 is prime
% Time for proof[3] is 0.000553 s

% Starting proving job for step 4
% N_4 is prime
% Time for proof[4] is 0.000490 s

% Starting proving job for step 5
% Using complete factorization theorem
% N_5 is prime
% Time for proof[5] is 0.000921 s
% Time for building is 0.132266 s
% Time for proving  is 0.061523 s
% Total time is        0.193911 s
This number is prime
% Time for this number is 0.222589s

% ==> Total time for the computations is 0.222785s
------------------------------------------------------------
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%                                                          %
%                           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 7032401262704707649518767703756385761576062060673
% Performing a quick compositeness test
% This number might be prime
% Entering ECPP
% Starting phase 1: building the sequence of primes
% Pmax=9000
% N_0=7032401262704707649518767703756385761576062060673
% 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
% Cofactor after sieve is a probable prime
% D[[0]]=3
% A[[0]]=-2252004112966430725791170
% B[[0]]=2772368573741059543071792
% m[[0]]=7032401262704707649518769955760498728006787851844
% Factor= 13^2
% Factor= 7^1
% Factor= 2^2
% End of depth 0 at 0.234124 s

% Pmax=7000
% N_1=1486137206826861295333636930634086797972693967
% 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
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% next D is 19
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% next D is 67
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% next D is 24
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% next D is 123
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% next D is 267
% itmax=0 ngcd=0 b1=0 b2=0
% Cofactor after sieve is a probable prime
% D[[1]]=267
% A[[1]]=-10700707995248550454579
% B[[1]]=-4672833141889359610491
% m[[1]]=1486137206826861295333647631342082046523148547
% Factor= 1259^1
% Factor= 1097^1
% Factor= 29^1
% Factor= 3^2
% End of depth 1 at 0.685341 s

% Pmax=7000
% N_2=4122740904823795675356248788809305549
% 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]]=-3211819285031403340
% B[[2]]=-1242495523090078157
% m[[2]]=4122740904823795678568068073840708890
% Factor= 29^1
% Factor= 17^1
% Factor= 5^1
% Factor= 2^1
% End of depth 2 at 0.792591 s

% Pmax=7000
% N_3=836255761627544762387032063659373
% 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
% Cofactor after sieve is a probable prime
% D[[3]]=3
% A[[3]]=-4722234248400335
% B[[3]]=33280242137607783
% m[[3]]=836255761627544767109266312059709
% Factor= 4801^1
% Factor= 109^1
% End of depth 3 at 0.878209 s

% Pmax=5000
% N_4=1598015248404947683126539601
% next D is 0
% itmax=0 ngcd=0 b1=0 b2=0
% Cofactor after sieve is a probable prime
% D[[4]]=1
% Factor= 2^1
% End of depth 4 at 0.912909 s

% Pmax=5000
% N_5=799007624202473841563269801
% next D is 0
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% next D is 3
% Cofactor after sieve is a probable prime
% m is prime, we forget about it
% Cofactor after sieve is a probable prime
% D[[5]]=3
% A[[5]]=-10394885946001
% B[[5]]=32083104811201
% m[[5]]=799007624202484236449215803
% Factor= 31^1
% Factor= 7^1
% Factor= 3^1
% End of depth 5 at 0.979806 s

% Pmax=5000
% N_6=1227354261447748443086353
% next D is 0
% itmax=0 ngcd=0 b1=0 b2=0
% itmax=0 ngcd=0 b1=0 b2=0
% next D is 3
% Cofactor after sieve is a probable prime
% D[[6]]=3
% A[[6]]=1093192336670
% B[[6]]=-1112706544248
% m[[6]]=1227354261446655250749684
% Factor= 3^2
% Factor= 2^2
% End of depth 6 at 1.016891 s

% Pmax=5000
% N_7=34093173929073756965269
% next D is 0
% itmax=0 ngcd=0 b1=0 b2=0
% Cofactor after sieve is a probable prime
% D[[7]]=1
% Factor= 439^1
% Factor= 37^1
% Factor= 19^1
% Factor= 11^1
% Factor= 5^1
% Factor= 2^1
% End of depth 7 at 1.047629 s

% Pmax=5000
% N_8=1004280207538021
% next D is 0
% Cofactor after sieve is a probable prime
% D[[8]]=-1
% Factor= 7^1
% Factor= 5^1
% Factor= 3^1
% Factor= 2^2
% End of depth 8 at 1.072626 s

% Pmax=5000
% N_9=2391143351281
% next D is 0
% Cofactor after sieve is a probable prime
% D[[9]]=-1
% Factor= 5^1
% Factor= 3^1
% Factor= 2^4
% End of depth 9 at 1.097905 s

% Pmax=5000
% N_10=9963097297
% next D is 0
% itmax=0 ngcd=0 b1=0 b2=0
% Cofactor after sieve is a probable prime
% D[[10]]=1
% Factor= 19^1
% Factor= 11^1
% Factor= 7^1
% Factor= 2^1
% End of depth 10 at 1.122671 s

% Pmax=5000
% N_11=3405023
% next D is 0
% Cofactor after sieve is a probable prime
% D[[11]]=-1
% Factor= 2^1
% End of depth 11 at 1.135576 s

% Pmax=5000
% N_12=1702511
% next D is 0
% Factorization completed using sieve only
% D[[12]]=-1
% Factor= 2791^1
% Factor= 61^1
% Factor= 5^1
% Factor= 2^1
% Cofactor is 1
% End of depth 12 at 1.157303 s

% Pmax=5000
% N_13=2791
% next D is 0
% Factorization completed using sieve only
% D[[13]]=-1
% Factor= 31^1
% Factor= 5^1
% Factor= 3^2
% Factor= 2^1
% Cofactor is 1

% Time for building is 1.099987 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 0.415547 s

% Starting proving job for step 1
% File /home/his/ECPP/Ecpp/Data/Weber/h2g2.cwdx does not exist
% tpber=0.000157s
% j has been computed
% E found
% N_1 is prime
% Time for proof[1] is 0.607146 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 0.186196 s

% Starting proving job for step 3
% Entering the D=3 business
% E found
% Suggested twist(3)=1
% N_3 is prime
% Time for proof[3] is 0.169183 s

% Starting proving job for step 4
% N_4 is prime
% Time for proof[4] is 0.089360 s

% Starting proving job for step 5
% Entering the D=3 business
% E found
% Suggested twist(3)=1
% N_5 is prime
% Time for proof[5] is 0.096088 s

% Starting proving job for step 6
% Entering the D=3 business
% E found
% Suggested twist(3)=1
% N_6 is prime
% Time for proof[6] is 0.075290 s

% Starting proving job for step 7
% N_7 is prime
% Time for proof[7] is 0.068849 s

% Starting proving job for step 8
% N_8 is prime
% Time for proof[8] is 0.001819 s

% Starting proving job for step 9
% N_9 is prime
% Time for proof[9] is 0.001484 s

% Starting proving job for step 10
% N_10 is prime
% Time for proof[10] is 0.025472 s

% Starting proving job for step 11
% N_11 is prime
% Time for proof[11] is 0.000684 s

% Starting proving job for step 12
% N_12 is prime
% Time for proof[12] is 0.000723 s

% Starting proving job for step 13
% Using complete factorization theorem
% b=1
% Nonresidue is 6
% N_13 is prime
% Time for proof[13] is 0.001464 s
% Time for building is 1.099987 s
% Time for proving  is 1.744028 s
% Total time is        2.844170 s
This number is prime
% Time for this number is 2.903704s

% ==> Total time for the computations is 2.905273s