Contribution and Reservation

(8·10²²⁴+7)/3 =: 2(6)₂₂₃9_<225>; = 3329 · 15401 · 3187375632545219403643_<22> · [1631821940572169617249126281167168031848116293033767557627692737351456411306170942645064118341084979142508845487091994715999497383361319399501338733458196406583174844614004633063576106064198544927_<196>] SUBMIT/RESERVE

Status

Expression:	(8·10²²⁴+7)/3
Composite Factor:	163182194057216961724912628116716803184811629303376755762769 273735145641130617094264506411834108497914250884548709199471 599949738336131939950133873345819640658317484461400463306357 6106064198544927 (196-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.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 225.20-digit and the GNFS difficulty is 195.21-digit. SNFS must be faster than GNFS. It will take about 134 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 26669_224.
Put the following polynomial file 26669_224.poly in there too.
And then, run "perl factMsieve.pl 26669_224".

26669_224.poly ^*1

n: 1631821940572169617249126281167168031848116293033767557627692737351456411306170942645064118341084979142508845487091994715999497383361319399501338733458196406583174844614004633063576106064198544927
m: 20000000000000000000000000000000000000
deg: 6
c6: 25
c0: 14
skew: 0.91
type: snfs
lss: 1
rlim: 40000000
alim: 40000000
lpbr: 30
lpba: 30
mfbr: 59
mfba: 59
rlambda: 2.7
alambda: 2.7

*1 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;

Efforts by ECM

The efforts by ECM to find small factors of this 196-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	0 / 0
45	11e6	0 / 1668
45	11e6	/ 1668
50	43e6	800	Dmitry Domanov	Oct 30, 2009
		800 / 7553 (1276)
		/ 6753 (476)
55	11e7	0 / 17484 (2801)
55	11e7	/ 17484 (2801)
60	26e7	0 / 41924 (7521)
60	26e7	/ 41924 (7521)

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

echo 1631821940572169617249126281167168031848116293033767557627692737351456411306170942645064118341084979142508845487091994715999497383361319399501338733458196406583174844614004633063576106064198544927 | ecm -n -c 1668 11e6

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

echo 1631821940572169617249126281167168031848116293033767557627692737351456411306170942645064118341084979142508845487091994715999497383361319399501338733458196406583174844614004633063576106064198544927 | ecm -n -c 6753 43e6

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

echo 1631821940572169617249126281167168031848116293033767557627692737351456411306170942645064118341084979142508845487091994715999497383361319399501338733458196406583174844614004633063576106064198544927 | ecm -n -c 17484 11e7

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

echo 1631821940572169617249126281167168031848116293033767557627692737351456411306170942645064118341084979142508845487091994715999497383361319399501338733458196406583174844614004633063576106064198544927 | ecm -n -c 41924 26e7

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