Contribution and Reservation

(25·10²⁴⁹-1)/3 =: 8(3)₂₄₉_<250>; = 13 · 1627 · 33618632921338726333955479_<26> · [11719465355665184171058659060083251480068313727140504033923459478703367671508136055261114612417451605238345171349634229009514607183573381521120988029233255738012401567806726494056287627592353414999217031763959320714284077_<221>] SUBMIT/RESERVE

Status

Expression:	(25·10²⁴⁹-1)/3
Composite Factor:	117194653556651841710586590600832514800683137271405040339234 594787033676715081360552611146124174516052383451713496342290 095146071835733815211209880292332557380124015678067264940562 87627592353414999217031763959320714284077 (221-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 251.10-digit and the GNFS difficulty is 220.07-digit. SNFS must be faster than GNFS. It will take about 977 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 83333_249.
Put the following polynomial file 83333_249.poly in there too.
And then, run "perl factMsieve.pl 83333_249".

83333_249.poly ^*1

n: 11719465355665184171058659060083251480068313727140504033923459478703367671508136055261114612417451605238345171349634229009514607183573381521120988029233255738012401567806726494056287627592353414999217031763959320714284077
m: 500000000000000000000000000000000000000000
deg: 6
c6: 8
c0: -5
skew: 0.92
type: snfs
lss: 1
rlim: 107000000
alim: 107000000
lpbr: 31
lpba: 31
mfbr: 62
mfba: 62
rlambda: 2.8
alambda: 2.8

*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 221-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 30-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
30	25e4	430	Makoto Kamada	Oct 22, 2008
30	25e4	430 / 430
35	1e6	0 / 825
35	1e6	/ 825
40	3e6	0 / 2336 (294)
40	3e6	/ 2336 (294)
45	11e6	0 / 4479 (677)
45	11e6	/ 4479 (677)
50	43e6	0 / 7553 (1277)
50	43e6	/ 7553 (1277)

Command line to find prime factors up to about 35-digit

echo 11719465355665184171058659060083251480068313727140504033923459478703367671508136055261114612417451605238345171349634229009514607183573381521120988029233255738012401567806726494056287627592353414999217031763959320714284077 | ecm -n -c 825 1e6

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

echo 11719465355665184171058659060083251480068313727140504033923459478703367671508136055261114612417451605238345171349634229009514607183573381521120988029233255738012401567806726494056287627592353414999217031763959320714284077 | ecm -n -c 2336 3e6

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

echo 11719465355665184171058659060083251480068313727140504033923459478703367671508136055261114612417451605238345171349634229009514607183573381521120988029233255738012401567806726494056287627592353414999217031763959320714284077 | ecm -n -c 4479 11e6

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

echo 11719465355665184171058659060083251480068313727140504033923459478703367671508136055261114612417451605238345171349634229009514607183573381521120988029233255738012401567806726494056287627592353414999217031763959320714284077 | ecm -n -c 7553 43e6

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