Contribution and Reservation

(25·10²⁴³-1)/3 =: 8(3)₂₄₃_<244>; = 13 · 227 · 10519601 · 47491140997_<11> · 584997921511_<12> · [9662363014582797162068979012663340250660073310141396699778016308317504703735373281075177229808755471301761532856652489972339188944684912064506918976067716212569672101703299842473541285416386256331417056980994449_<211>] SUBMIT/RESERVE

Status

Expression:	(25·10²⁴³-1)/3
Composite Factor:	966236301458279716206897901266334025066007331014139669977801 630831750470373537328107517722980875547130176153285665248997 233918894468491206450691897606771621256967210170329984247354 1285416386256331417056980994449 (211-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 245.10-digit and the GNFS difficulty is 210.99-digit. SNFS must be faster than GNFS. It will take about 616 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_243.
Put the following polynomial file 83333_243.poly in there too.
And then, run "perl factMsieve.pl 83333_243".

83333_243.poly ^*1

n: 9662363014582797162068979012663340250660073310141396699778016308317504703735373281075177229808755471301761532856652489972339188944684912064506918976067716212569672101703299842473541285416386256331417056980994449
m: 50000000000000000000000000000000000000000
deg: 6
c6: 8
c0: -5
skew: 0.92
type: snfs
lss: 1
rlim: 85000000
alim: 85000000
lpbr: 30
lpba: 30
mfbr: 61
mfba: 61
rlambda: 2.7
alambda: 2.7

*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 211-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 9662363014582797162068979012663340250660073310141396699778016308317504703735373281075177229808755471301761532856652489972339188944684912064506918976067716212569672101703299842473541285416386256331417056980994449 | ecm -n -c 825 1e6

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

echo 9662363014582797162068979012663340250660073310141396699778016308317504703735373281075177229808755471301761532856652489972339188944684912064506918976067716212569672101703299842473541285416386256331417056980994449 | ecm -n -c 2336 3e6

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

echo 9662363014582797162068979012663340250660073310141396699778016308317504703735373281075177229808755471301761532856652489972339188944684912064506918976067716212569672101703299842473541285416386256331417056980994449 | ecm -n -c 4479 11e6

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

echo 9662363014582797162068979012663340250660073310141396699778016308317504703735373281075177229808755471301761532856652489972339188944684912064506918976067716212569672101703299842473541285416386256331417056980994449 | ecm -n -c 7553 43e6

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