Contribution and Reservation

(73·10²⁰⁷-1)/9 =: 8(1)₂₀₇_<208>; = 29 · 16763589357458729_<17> · [16684582318618568175763483274357657706494546975413720403823679413383446702865955736660836679397750375535686929121718834964058280706153725071991677439498299978645727002723043246421244307314171_<191>] SUBMIT/RESERVE

Status

Expression:	(73·10²⁰⁷-1)/9
Composite Factor:	166845823186185681757634832743576577064945469754137204038236 794133834467028659557366608366793977503755356869291217188349 640582807061537250719916774394982999786457270027230432464212 44307314171 (191-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 210.96-digit and the GNFS difficulty is 190.22-digit. SNFS must be faster than GNFS. It will take about 45 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 81111_207.
Put the following polynomial file 81111_207.poly in there too.
And then, run "perl factMsieve.pl 81111_207".

81111_207.poly ^*1

n: 16684582318618568175763483274357657706494546975413720403823679413383446702865955736660836679397750375535686929121718834964058280706153725071991677439498299978645727002723043246421244307314171
m: 500000000000000000000000000000000000000000
deg: 5
c5: 292
c0: -125
skew: 0.84
type: snfs
lss: 1
rlim: 23000000
alim: 23000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
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 191-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	118	Makoto Kamada	May 26, 2009
		239	Dmitry Domanov	Jun 2, 2009
		357 / 0
40	3e6	290	Dmitry Domanov	Jun 2, 2009
		290 / 1270
		/ 980
45	11e6	285	Dmitry Domanov	Jun 2, 2009
		285 / 4400 (569)
		/ 4115 (284)
50	43e6	0 / 7476 (1173)
50	43e6	/ 7476 (1173)
55	11e7	0 / 17749 (3102)
55	11e7	/ 17749 (3102)

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

echo 16684582318618568175763483274357657706494546975413720403823679413383446702865955736660836679397750375535686929121718834964058280706153725071991677439498299978645727002723043246421244307314171 | ecm -n -c 980 3e6

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

echo 16684582318618568175763483274357657706494546975413720403823679413383446702865955736660836679397750375535686929121718834964058280706153725071991677439498299978645727002723043246421244307314171 | ecm -n -c 4115 11e6

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

echo 16684582318618568175763483274357657706494546975413720403823679413383446702865955736660836679397750375535686929121718834964058280706153725071991677439498299978645727002723043246421244307314171 | ecm -n -c 7476 43e6

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

echo 16684582318618568175763483274357657706494546975413720403823679413383446702865955736660836679397750375535686929121718834964058280706153725071991677439498299978645727002723043246421244307314171 | ecm -n -c 17749 11e7

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