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 190.70-digit and the GNFS difficulty is 133.36-digit. SNFS may be faster than GNFS. It will take about 9 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 55551_190.
2. Put the following polynomial file 55551_190.poly in there too.
3. And then, run "perl factMsieve.pl 55551_190".

n: 23131250645136039124173437398550316889871557127081915222698595006677255786998338589830559546149712341137606558001486495150836722621421
m: 100000000000000000000000000000000000000
deg: 5
c5: 5
c0: -41
skew: 1.52
type: snfs
lss: 1
rlim: 10600000
alim: 10600000
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;

Steps of GNFS

1. Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 55551_190.
2. Put the following polynomial file 55551_190.poly in there too.
3. And then, run "perl factMsieve.pl 55551_190".

# Murphy_E = 4.638935e-11, selected by Jeff Gilchrist
n: 23131250645136039124173437398550316889871557127081915222698595006677255786998338589830559546149712341137606558001486495150836722621421
Y0: -53470942235238467857570124
Y1: 649173555851929
c0: 9686870205118442292954702138454905
c1: 177634003343719421607244589417
c2: 197141587712728352622173
c3: -167968379679017545
c4: -99423583086
c5: 52920
skew: 1277096.76
type: gnfs
# selected mechanically
rlim: 12100000
alim: 12100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6

These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=5*10^(d/20-5)[hours]; rlim=round(3*10^(d/37+3)); lpbr=floor(d/18+21); mfbr=floor(d/5+28); rlambda=floor(d/26+21)/10;

See also

• How to contribute your factors

The efforts by ECM to find small factors of this 134-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)