Contribution and Reservation

(14·10¹⁹⁵-41)/9 =: 1(5)₁₉₄1_<196>; = 3⁴ · 11 · 23 · 733 · [103556177573133018405682967747850116427840601982119975586483199737357863691089377776123837684538310426669869807176400203973123591834775881982231816258262183397236001296257055901865905534679_<189>] SUBMIT/RESERVE

Status

Expression:	(14·10¹⁹⁵-41)/9
Composite Factor:	103556177573133018405682967747850116427840601982119975586483 199737357863691089377776123837684538310426669869807176400203 973123591834775881982231816258262183397236001296257055901865 905534679 (189-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 196.15-digit and the GNFS difficulty is 188.02-digit. SNFS must be faster than GNFS. 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 15551_195.
Put the following polynomial file 15551_195.poly in there too.
And then, run "perl factMsieve.pl 15551_195".

15551_195.poly ^*1

n: 103556177573133018405682967747850116427840601982119975586483199737357863691089377776123837684538310426669869807176400203973123591834775881982231816258262183397236001296257055901865905534679
m: 1000000000000000000000000000000000000000
deg: 5
c5: 14
c0: -41
skew: 1.24
type: snfs
lss: 1
rlim: 13000000
alim: 13000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

*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 189-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 20-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
20	11e3	74	Max Dettweiler	Mar 7, 2009
20	11e3	74 / 74
25	5e4	0 / 204
25	5e4	/ 204
30	25e4	0 / 430 (48)
30	25e4	/ 430 (48)
35	1e6	0 / 904 (118)
35	1e6	/ 904 (118)
40	3e6	0 / 2350 (322)
40	3e6	/ 2350 (322)

Command line to find prime factors up to about 25-digit

echo 103556177573133018405682967747850116427840601982119975586483199737357863691089377776123837684538310426669869807176400203973123591834775881982231816258262183397236001296257055901865905534679 | ecm -n -c 204 5e4

Command line to find prime factors up to about 30-digit

echo 103556177573133018405682967747850116427840601982119975586483199737357863691089377776123837684538310426669869807176400203973123591834775881982231816258262183397236001296257055901865905534679 | ecm -n -c 430 25e4

Command line to find prime factors up to about 35-digit

echo 103556177573133018405682967747850116427840601982119975586483199737357863691089377776123837684538310426669869807176400203973123591834775881982231816258262183397236001296257055901865905534679 | ecm -n -c 904 1e6

Command line to find prime factors up to about 40-digit

echo 103556177573133018405682967747850116427840601982119975586483199737357863691089377776123837684538310426669869807176400203973123591834775881982231816258262183397236001296257055901865905534679 | ecm -n -c 2350 3e6

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