Contribution and Reservation

(14·10¹⁸⁹+31)/9 =: 1(5)₁₈₈9_<190>; = 269 · [5782734407269723254853366377529946303180503923998347790169351507641470466749277158199091284593143329202808756712102437009500206526228831061544816191656340355225113589425857083849648905411_<187>] SUBMIT/RESERVE

Status

Expression:	(14·10¹⁸⁹+31)/9
Composite Factor:	578273440726972325485336637752994630318050392399834779016935 150764147046674927715819909128459314332920280875671210243700 950020652622883106154481619165634035522511358942585708384964 8905411 (187-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 190.85-digit and the GNFS difficulty is 186.76-digit. SNFS must be faster than GNFS. It will take about 10 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 15559_189.
Put the following polynomial file 15559_189.poly in there too.
And then, run "perl factMsieve.pl 15559_189".

15559_189.poly ^*1

n: 5782734407269723254853366377529946303180503923998347790169351507641470466749277158199091284593143329202808756712102437009500206526228831061544816191656340355225113589425857083849648905411
m: 100000000000000000000000000000000000000
deg: 5
c5: 7
c0: 155
skew: 1.86
type: snfs
lss: 1
rlim: 10600000
alim: 10600000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
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 187-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	825	Wataru Sakai	Aug 1, 2009
35	1e6	825 / 0
40	3e6	1735	Wataru Sakai	Aug 3, 2009
		1735 / 2111
		/ 376
45	11e6	0 / 4057 (109)
45	11e6	/ 4057 (109)
50	43e6	0 / 7483 (1157)
50	43e6	/ 7483 (1157)
55	11e7	0 / 17755 (3104)
55	11e7	/ 17755 (3104)

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

echo 5782734407269723254853366377529946303180503923998347790169351507641470466749277158199091284593143329202808756712102437009500206526228831061544816191656340355225113589425857083849648905411 | ecm -n -c 376 3e6

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

echo 5782734407269723254853366377529946303180503923998347790169351507641470466749277158199091284593143329202808756712102437009500206526228831061544816191656340355225113589425857083849648905411 | ecm -n -c 4057 11e6

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

echo 5782734407269723254853366377529946303180503923998347790169351507641470466749277158199091284593143329202808756712102437009500206526228831061544816191656340355225113589425857083849648905411 | ecm -n -c 7483 43e6

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

echo 5782734407269723254853366377529946303180503923998347790169351507641470466749277158199091284593143329202808756712102437009500206526228831061544816191656340355225113589425857083849648905411 | ecm -n -c 17755 11e7

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