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 188.30-digit and the GNFS difficulty is 131.63-digit. SNFS may 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 19991_188.
2. Put the following polynomial file 19991_188.poly in there too.
3. And then, run "perl factMsieve.pl 19991_188".

n: 424730979321609056444211982014719865751281575611959204819716385342249694232869193979489060533511688985047286901474261914078857029889
m: 10000000000000000000000000000000000000
deg: 5
c5: 2000
c0: -9
skew: 0.34
type: snfs
lss: 1
rlim: 9600000
alim: 9600000
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 19991_188.
2. Put the following polynomial file 19991_188.poly in there too.
3. And then, run "perl factMsieve.pl 19991_188".

# Murphy_E = 6.27231e-11, selected by Jeff Gilchrist
n: 424730979321609056444211982014719865751281575611959204819716385342249694232869193979489060533511688985047286901474261914078857029889
Y0: -24115140840764330089204633
Y1: 415589386019699
c0: 533918440835784793304957895536160
c1: 866439391895401154778358452
c2: -9811553603072832927099
c3: -26377614099474532
c4: -42097964546
c5: 52080
skew: 492929.07
type: gnfs
# selected mechanically
rlim: 10800000
alim: 10800000
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 132-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)