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 173.34-digit and the GNFS difficulty is 130.72-digit. SNFS must be faster than GNFS. It will take about 2 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 73333_172.
2. Put the following polynomial file 73333_172.poly in there too.
3. And then, run "perl factMsieve.pl 73333_172".

n: 52664802777632128483139943807112499915228136328357345310586727772346381267412255744083863646372276716206868216067462224684412144253
m: 10000000000000000000000000000000000
deg: 5
c5: 2200
c0: -1
skew: 0.21
type: snfs
lss: 1
rlim: 5400000
alim: 5400000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.4
alambda: 2.4

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 131-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-digit or more. Please report your efforts by ECM. (Anonymous reports are not acceptable)