Contribution and Reservation

(46·10¹⁹¹+17)/9 =: 5(1)₁₉₀3_<192>; = 3³ · 2203 · [8592846641971572621696190566922397254772298904038451120712683228444563997093376222846137608834940756058423885124848457677428273080666281856577917504936216793784756663659170341976616249073_<187>] SUBMIT/RESERVE

Status

Expression:	(46·10¹⁹¹+17)/9
Composite Factor:	859284664197157262169619056692239725477229890403845112071268 322844456399709337622284613760883494075605842388512484845767 742827308066628185657791750493621679378475666365917034197661 6249073 (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 193.57-digit and the GNFS difficulty is 186.93-digit. SNFS must be faster than GNFS. It will take about 12 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 51113_191.
Put the following polynomial file 51113_191.poly in there too.
And then, run "perl factMsieve.pl 51113_191".

51113_191.poly ^*1

n: 8592846641971572621696190566922397254772298904038451120712683228444563997093376222846137608834940756058423885124848457677428273080666281856577917504936216793784756663659170341976616249073
m: 200000000000000000000000000000000000000
deg: 5
c5: 115
c0: 136
skew: 1.03
type: snfs
lss: 1
rlim: 11800000
alim: 11800000
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 187-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	2318	Wataru Sakai	Aug 17, 2009
40	3e6	2318 / 2318
45	11e6	0 / 3963
45	11e6	/ 3963
50	43e6	0 / 7465 (1130)
50	43e6	/ 7465 (1130)
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 8592846641971572621696190566922397254772298904038451120712683228444563997093376222846137608834940756058423885124848457677428273080666281856577917504936216793784756663659170341976616249073 | ecm -n -c 3963 11e6

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

echo 8592846641971572621696190566922397254772298904038451120712683228444563997093376222846137608834940756058423885124848457677428273080666281856577917504936216793784756663659170341976616249073 | ecm -n -c 7465 43e6

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

echo 8592846641971572621696190566922397254772298904038451120712683228444563997093376222846137608834940756058423885124848457677428273080666281856577917504936216793784756663659170341976616249073 | ecm -n -c 17751 11e7

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

echo 8592846641971572621696190566922397254772298904038451120712683228444563997093376222846137608834940756058423885124848457677428273080666281856577917504936216793784756663659170341976616249073 | ecm -n -c 42014 26e7

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