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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 189.00-digit and the GNFS difficulty is 178.34-digit. SNFS must be faster than GNFS. It will take about 8 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of SNFS

1. Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 11113_189.
2. Put the following polynomial file 11113_189.poly in there too.
3. And then, run "perl factMsieve.pl 11113_189".

n: 21958906088608981321695433530728218215090199741813458065495722066366833100600692351735304214843570352216418621025344044037211006170418991813902091046013306425893773538258824353777
m: 10000000000000000000000000000000000000
deg: 5
c5: 10000
c0: 17
skew: 0.28
type: snfs
lss: 1
rlim: 9900000
alim: 9900000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.5
alambda: 2.5

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 179-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 45-digit or more. Please report your efforts by ECM. (Anonymous reports are not acceptable)