53625112691923843508117942311516428173021903300344567
The above 53-digit factor is the new record for the largest
factor found by ECM. It is a factor of the Mersenne number
M677. It was previously known
2^677 - 1 = 1943118631 *
531132717139346021081 *
978146583988637765536217 *
c150
The previous record was a 49 digit factor of 2^1071+1 found
by Paul Zimmermann on June 19, 1998. The new record was found
on September 14, 1998 after 7964 curves at B1=11e6 and B2=100*B1
using George Woltman's mprime program. The calculation was
performed using the idle CPU time of 16 dual-processor Pentiums
from the School of Mathematical Sciences at the University of
Southern Mississippi.
I was fortunate to have a very smooth group order. With
sigma = 8689346476060549 the group order is
2^4*3^9*3079*152077*172259*1067063*3682177*3815423*8867563*15880351
The cofactor is prime, which completes the factorization of M677.
ECM on M677: s = 8689346476060549, B1 = 11000000, B2 = 1100000000
Stage 1 complete. Time: 949.940 sec.
Stage 2 complete. Time: 530.390 sec.
ECM found a factor in stage #2
Sigma = 8689346476060549, B1 = 11000000, B2 = 1100000000.
M677 has a factor: 53625112691923843508117942311516428173021903300344567
Cofactor is a probable prime!
