Contribution and Reservation

(22·10¹⁹⁴-1)/3 =: 7(3)₁₉₄_<195>; = 293 · 161053 · 664237943 · 13277658923_<11> · 261808352967983_<15> · 546971401602934643_<18> · [12304718427269283800902907487934827867943758170285765616212565770340367363761946855762373015366862036631276682662670554821256333345435997_<137>] SUBMIT/RESERVE

Status

Expression:	(22·10¹⁹⁴-1)/3
Composite Factor:	123047184272692838009029074879348278679437581702857656162125 657703403673637619468557623730153668620366312766826626705548 21256333345435997 (137-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 196.04-digit and the GNFS difficulty is 136.09-digit. GNFS may be faster than SNFS. It will take about 13 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 73333_194.
Put the following polynomial file 73333_194.poly in there too.
And then, run "perl factMsieve.pl 73333_194".

73333_194.poly ^*1

# Murphy_E = 3.306119e-11, selected by Jeff Gilchrist
n: 12304718427269283800902907487934827867943758170285765616212565770340367363761946855762373015366862036631276682662670554821256333345435997
Y0: -171063612339546388700661089
Y1: 1426111797788099
c0: 381358818013890308637082151278080
c1: 14698438336285870899649449696
c2: -40213231164874646972516
c3: -106549955009215427
c4: 97448428940
c5: 84000
skew: 609154.88
type: gnfs
# selected mechanically
rlim: 14300000
alim: 14300000
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 137-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	500	Erik Branger	Jan 30, 2009
		1850	Wataru Sakai	Aug 23, 2009
		2350 / 2350
45	11e6	0 / 3961
45	11e6	/ 3961
50	43e6	0 / 7465 (1129)
50	43e6	/ 7465 (1129)
55	11e7	0 / 17751 (3097)
55	11e7	/ 17751 (3097)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 12304718427269283800902907487934827867943758170285765616212565770340367363761946855762373015366862036631276682662670554821256333345435997 | ecm -n -c 3961 11e6

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

echo 12304718427269283800902907487934827867943758170285765616212565770340367363761946855762373015366862036631276682662670554821256333345435997 | ecm -n -c 7465 43e6

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

echo 12304718427269283800902907487934827867943758170285765616212565770340367363761946855762373015366862036631276682662670554821256333345435997 | ecm -n -c 17751 11e7

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

echo 12304718427269283800902907487934827867943758170285765616212565770340367363761946855762373015366862036631276682662670554821256333345435997 | 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