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 196.00-digit and the GNFS difficulty is 125.96-digit. GNFS must be faster than SNFS. It will take about 4 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of GNFS

1. Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 10009_196.
2. Put the following polynomial file 10009_196.poly in there too.
3. And then, run "perl factMsieve.pl 10009_196".

# Murphy_E = 1.351230e-10, selected by Jeff Gilchrist
n: 914485651586525533357484598772878668557145673386605657821723195587345693907083602731033750236232276619318600012074196323998309
Y0: -2144555406043205821893227
Y1: 61024673734267
c0: -818182740052913052462095914974900
c1: 1380025804792599906456170268
c2: 3878402356972635969483
c3: -12185887410032392
c4: 21368068
c5: 20160
skew: 646983.34
type: gnfs
# selected mechanically
rlim: 7600000
alim: 7600000
lpbr: 27
lpba: 27
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

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 126-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)