Contribution and Reservation

(73·10²¹⁵-1)/9 =: 8(1)₂₁₅_<216>; = 7 · 60703 · 46556683 · [41000591769915992650624685900215425173676179282747544366872394202746012313294795808275600671604961939655719121126219244892539983521958586571985291144644644511001816700675738379278427549751480290175791677_<203>] SUBMIT/RESERVE

Status

Expression:	(73·10²¹⁵-1)/9
Composite Factor:	410005917699159926506246859002154251736761792827475443668723 942027460123132947958082756006716049619396557191211262192448 925399835219585865719852911446446445110018167006757383792784 27549751480290175791677 (203-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 217.86-digit and the GNFS difficulty is 202.61-digit. SNFS must be faster than GNFS. It will take about 76 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_215.
Put the following polynomial file 81111_215.poly in there too.
And then, run "perl factMsieve.pl 81111_215".

81111_215.poly ^*1

n: 41000591769915992650624685900215425173676179282747544366872394202746012313294795808275600671604961939655719121126219244892539983521958586571985291144644644511001816700675738379278427549751480290175791677
m: 1000000000000000000000000000000000000
deg: 6
c6: 73
c0: -10
skew: 0.72
type: snfs
lss: 1
rlim: 30000000
alim: 30000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
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 203-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
		240	Dmitry Domanov	Jun 2, 2009
		358 / 0
40	3e6	643	Dmitry Domanov	Jun 2, 2009
		643 / 1601
		/ 958
45	11e6	189	Dmitry Domanov	Jun 2, 2009
		189 / 4322 (467)
		/ 4133 (278)
50	43e6	0 / 7485 (1178)
50	43e6	/ 7485 (1178)
55	11e7	0 / 17752 (3105)
55	11e7	/ 17752 (3105)

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

echo 41000591769915992650624685900215425173676179282747544366872394202746012313294795808275600671604961939655719121126219244892539983521958586571985291144644644511001816700675738379278427549751480290175791677 | ecm -n -c 958 3e6

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

echo 41000591769915992650624685900215425173676179282747544366872394202746012313294795808275600671604961939655719121126219244892539983521958586571985291144644644511001816700675738379278427549751480290175791677 | ecm -n -c 4133 11e6

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

echo 41000591769915992650624685900215425173676179282747544366872394202746012313294795808275600671604961939655719121126219244892539983521958586571985291144644644511001816700675738379278427549751480290175791677 | ecm -n -c 7485 43e6

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

echo 41000591769915992650624685900215425173676179282747544366872394202746012313294795808275600671604961939655719121126219244892539983521958586571985291144644644511001816700675738379278427549751480290175791677 | ecm -n -c 17752 11e7

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