Contribution and Reservation

ECM, P-1, P+1

Look for prime factors by GMP-ECM first. Refer to the section "Efforts by ECM". Not only ECM but also P-1/P+1 may be helpful.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 191.58-digit and the GNFS difficulty is 139.06-digit. SNFS must be faster than GNFS. It will take about 10 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

1. Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 42221_190.
2. Put the following polynomial file 42221_190.poly in there too.
3. And then, run "perl factMsieve.pl 42221_190".

n: 11423221085120340579545361167269171223913106595103975549804255038207855774958663802606112931530323074845877567277804479976788835638913385519
m: 100000000000000000000000000000000000000
deg: 5
c5: 38
c0: -11
skew: 0.78
type: snfs
lss: 1
rlim: 10900000
alim: 10900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: deg=expt<=105?4:expt<=210?5:6 or expt<=144?4:6; d=log10(c[deg])+deg*log10(m)[digits]; time=10^(d/30-4)[hours]; skew=|c0/c[deg]|^(1/deg); rlim=round(7*10^(d/60+3)); lpbr=floor(d/25+21); mfbr=floor(d/8+31); rlambda=floor(d/25+18)/10;

See also

• How to contribute your factors

The efforts by ECM to find small factors of this 140-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 30-digit or more. Please report your efforts by ECM. (Anonymous reports are not acceptable)