Contribution and Reservation

(8·10¹⁹⁸-17)/9 =: (8)₁₉₇7_<198>; = 29 · 2551 · 26987713 · 24810652678294736989_<20> · 122763886401873301220354203087_<30> · [146171976769747747349388334776423064471607044898176691920488992333574187962280014690489994846698316344610133907207472343085837277045010167_<138>] (Serge Batalov / GMP-ECM 6.2.1 B1=1000000, sigma=2642279068 for P30 / Jul 12, 2008) SUBMIT/RESERVE

Status

Expression:	(8·10¹⁹⁸-17)/9
Composite Factor:	146171976769747747349388334776423064471607044898176691920488 992333574187962280014690489994846698316344610133907207472343 085837277045010167 (138-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.

GNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 198.90-digit and the GNFS difficulty is 137.16-digit. GNFS must be faster than SNFS. It will take about 14 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 88887_198.
Put the following polynomial file 88887_198.poly in there too.
And then, run "perl factMsieve.pl 88887_198".

88887_198.poly ^*1

# Murphy_E = 2.872651e-11, selected by Jeff Gilchrist
n: 146171976769747747349388334776423064471607044898176691920488992333574187962280014690489994846698316344610133907207472343085837277045010167
Y0: -280498990387771382082764511
Y1: 2231100036308239
c0: -35230007717335944522081291396290
c1: -397404970165680737245927553
c2: 6560922738801171369066
c3: 4012194026297967
c4: -32003471249
c5: 84180
skew: 266754.77
type: gnfs
# selected mechanically
rlim: 15300000
alim: 15300000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=10^(d/21-4)[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 138-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	Jul 26, 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 146171976769747747349388334776423064471607044898176691920488992333574187962280014690489994846698316344610133907207472343085837277045010167 | ecm -n -c 3974 11e6

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

echo 146171976769747747349388334776423064471607044898176691920488992333574187962280014690489994846698316344610133907207472343085837277045010167 | ecm -n -c 7469 43e6

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

echo 146171976769747747349388334776423064471607044898176691920488992333574187962280014690489994846698316344610133907207472343085837277045010167 | ecm -n -c 17752 11e7

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

echo 146171976769747747349388334776423064471607044898176691920488992333574187962280014690489994846698316344610133907207472343085837277045010167 | ecm -n -c 42014 26e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation