Contribution and Reservation

(86·10¹⁸⁵+31)/9 =: 9(5)₁₈₄9_<186>; = 11 · 79 · 109 · 89785291 · 1340814637898597_<16> · 106445252032344079296136072207_<30> · [787244138386490929876920510164611857119065256566549011183789719145870310160312863127858597915954078318413882086128479743889883711_<129>] (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=2257574016 for P30 / Feb 4, 2006) SUBMIT/RESERVE

Status

Expression:	(86·10¹⁸⁵+31)/9
Composite Factor:	787244138386490929876920510164611857119065256566549011183789 719145870310160312863127858597915954078318413882086128479743 889883711 (129-digit)
Status:	Not factored. Not reserved. You can submit its factors or reserve it for submitting in the future.

How to factor it

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 186.93-digit and the GNFS difficulty is 128.90-digit. GNFS must be faster than SNFS. It will take about 6 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of GNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 95559_185.
Put the following polynomial file 95559_185.poly in there too.
And then, run "perl factMsieve.pl 95559_185".

95559_185.poly

# Murphy_E = 8.923158e-11, selected by Jeff Gilchrist
n: 787244138386490929876920510164611857119065256566549011183789719145870310160312863127858597915954078318413882086128479743889883711
Y0: -7715118083049905073258985
Y1: 173676925309853
c0: -3944056329997987017880913756364288
c1: 17640317315402272449134041812
c2: 40732910165937384211472
c3: -70730198278169213
c4: 11962897560
c5: 28800
skew: 893901.51
type: gnfs
# selected mechanically
rlim: 9100000
alim: 9100000
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;

Efforts by ECM

The efforts by ECM to find small factors of this 129-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)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)	Name
40	3e6	2104	Wataru Sakai	Dec 6, 2009
40	3e6	2104 / 2104
45	11e6	0 / 3974
45	11e6	/ 3974
50	43e6	0 / 7469 (1133)
50	43e6	/ 7469 (1133)
55	11e7	0 / 17752 (3098)
55	11e7	/ 17752 (3098)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

Command line to find prime factors up to about 45-digit

echo 787244138386490929876920510164611857119065256566549011183789719145870310160312863127858597915954078318413882086128479743889883711 | ecm -n -c 3974 11e6

Command line to find prime factors up to about 50-digit

echo 787244138386490929876920510164611857119065256566549011183789719145870310160312863127858597915954078318413882086128479743889883711 | ecm -n -c 7469 43e6

Command line to find prime factors up to about 55-digit

echo 787244138386490929876920510164611857119065256566549011183789719145870310160312863127858597915954078318413882086128479743889883711 | ecm -n -c 17752 11e7

Command line to find prime factors up to about 60-digit

echo 787244138386490929876920510164611857119065256566549011183789719145870310160312863127858597915954078318413882086128479743889883711 | ecm -n -c 42014 26e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

NFS

Steps of GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation