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 179.91-digit and the GNFS difficulty is 126.39-digit. SNFS may be faster than GNFS. It will take about 4 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 91111_178.
2. Put the following polynomial file 91111_178.poly in there too.
3. And then, run "perl factMsieve.pl 91111_178".

n: 2447136927405070783899910400185679436463368048567186805831816231554248577600543284597724005877617171570089597948621925536285837
m: 100000000000000000000000000000000000
deg: 5
c5: 82000
c0: -1
skew: 0.10
type: snfs
lss: 1
rlim: 7000000
alim: 7000000
lpbr: 28
lpba: 28
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: 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 91111_178.
2. Put the following polynomial file 91111_178.poly in there too.
3. And then, run "perl factMsieve.pl 91111_178".

# Murphy_E = 1.232134e-10, selected by Jeff Gilchrist
n: 2447136927405070783899910400185679436463368048567186805831816231554248577600543284597724005877617171570089597948621925536285837
Y0: -2369529150349378980128455
Y1: 47862860182511
c0: 232678753995997350188832252107232
c1: 10325331511197178898573571616
c2: -8444053540704336255914
c3: -41048977619589689
c4: 15305847174
c5: 32760
skew: 709302.38
type: gnfs
# selected mechanically
rlim: 7800000
alim: 7800000
lpbr: 28
lpba: 28
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 127-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)