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 187.74-digit and the GNFS difficulty is 130.48-digit. GNFS may be faster than SNFS. It will take about 7 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 61111_186.
2. Put the following polynomial file 61111_186.poly in there too.
3. And then, run "perl factMsieve.pl 61111_186".

# Murphy_E = 6.653532e-11, selected by Jeff Gilchrist
n: 30432007612762592127740722716171171102859925693933640724003695911511703991755647177815675322306750808454459955192348410131047397127
Y0: -15577273573146209665776506
Y1: 297692296275319
c0: -219739078460408925067011684484071
c1: -24260873678142118954039942
c2: 8341108626032587786947
c3: -7198912295874522
c4: -12048017912
c5: 33180
skew: 442353.27
type: gnfs
# selected mechanically
rlim: 10100000
alim: 10100000
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;

Steps of SNFS

1. Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 61111_186.
2. Put the following polynomial file 61111_186.poly in there too.
3. And then, run "perl factMsieve.pl 61111_186".

n: 30432007612762592127740722716171171102859925693933640724003695911511703991755647177815675322306750808454459955192348410131047397127
m: 10000000000000000000000000000000000000
deg: 5
c5: 550
c0: -1
skew: 0.28
type: snfs
lss: 1
rlim: 9400000
alim: 9400000
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;

See also

• How to contribute your factors

The efforts by ECM to find small factors of this 131-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)