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 198.30-digit and the GNFS difficulty is 146.65-digit. SNFS must be faster than GNFS. It will take about 17 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 19991_198.
2. Put the following polynomial file 19991_198.poly in there too.
3. And then, run "perl factMsieve.pl 19991_198".

n: 445227056823413204335080095187015621695823394884255936475263332923408208646560723205386467339105880811035168419307597227960941801394154491792686551
m: 1000000000000000000000000000000000000000
deg: 5
c5: 2000
c0: -9
skew: 0.34
type: snfs
lss: 1
rlim: 14100000
alim: 14100000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
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 147-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)