Contribution and Reservation

(53·10²⁰³-71)/9 =: 5(8)₂₀₂1_<204>; = 97 · 378031809054421_<15> · [16059546651026268964409668584363046059215680836044311617331816381178824260303526325882771570296720082072128691536388982341201675338378757626417872870862967434248703998682944274217935072013_<188>] SUBMIT/RESERVE

Status

Expression:	(53·10²⁰³-71)/9
Composite Factor:	160595466510262689644096685843630460592156808360443116173318 163811788242603035263258827715702967200820721286915363889823 412016753383787576264178728708629674342487039986829442742179 35072013 (188-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 206.12-digit and the GNFS difficulty is 187.21-digit. SNFS must be faster than GNFS. It will take about 31 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 58881_203.
Put the following polynomial file 58881_203.poly in there too.
And then, run "perl factMsieve.pl 58881_203".

58881_203.poly ^*1

n: 16059546651026268964409668584363046059215680836044311617331816381178824260303526325882771570296720082072128691536388982341201675338378757626417872870862967434248703998682944274217935072013
m: 50000000000000000000000000000000000000000
deg: 5
c5: 424
c0: -1775
skew: 1.33
type: snfs
lss: 1
rlim: 19100000
alim: 19100000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
rlambda: 2.6
alambda: 2.6

*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 188-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	730	Dmitry Domanov	Aug 20, 2009
		730 / 4475
		/ 3745
50	43e6	0 / 7389 (1068)
50	43e6	/ 7389 (1068)
55	11e7	0 / 17724 (3065)
55	11e7	/ 17724 (3065)
60	26e7	0 / 42006 (7624)
60	26e7	/ 42006 (7624)

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

echo 16059546651026268964409668584363046059215680836044311617331816381178824260303526325882771570296720082072128691536388982341201675338378757626417872870862967434248703998682944274217935072013 | ecm -n -c 3745 11e6

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

echo 16059546651026268964409668584363046059215680836044311617331816381178824260303526325882771570296720082072128691536388982341201675338378757626417872870862967434248703998682944274217935072013 | ecm -n -c 7389 43e6

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

echo 16059546651026268964409668584363046059215680836044311617331816381178824260303526325882771570296720082072128691536388982341201675338378757626417872870862967434248703998682944274217935072013 | ecm -n -c 17724 11e7

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

echo 16059546651026268964409668584363046059215680836044311617331816381178824260303526325882771570296720082072128691536388982341201675338378757626417872870862967434248703998682944274217935072013 | ecm -n -c 42006 26e7

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