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 222.60-digit and the GNFS difficulty is 176.82-digit. SNFS must be faster than GNFS. It will take about 110 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 40001_222.
2. Put the following polynomial file 40001_222.poly in there too.
3. And then, run "perl factMsieve.pl 40001_222".

n: 656058638890223304734304814532016364046521353594428916682596906758480771159191063541717990626390717402033424938857168466764328812593445093132882486910603381621639064614968488293
m: 10000000000000000000000000000000000000
deg: 6
c6: 4
c0: 1
skew: 0.79
type: snfs
lss: 1
rlim: 36000000
alim: 36000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6

*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 177-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 40-digit or more. Please report your efforts by ECM. (Anonymous reports are not acceptable)