Contribution and Reservation

8·10²⁴⁸-1 =: 7(9)₂₄₈_<249>; = 79 · 33721 · 51199 · 90239890184072888912403022400057_<32> · [64998362226240895181515724899074333746449115099884028313907317961225310385451807687976589551503950863613688396430537361321212297582395707795762523271386416606017656678835739145316249302906092607291527484127_<206>] (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=3329867724 for P32 / Jul 24, 2008) SUBMIT/RESERVE

Status

Expression:	8·10²⁴⁸-1
Composite Factor:	649983622262408951815157248990743337464491150998840283139073 179612253103854518076879765895515039508636136883964305373613 212122975823957077957625232713864166060176566788357391453162 49302906092607291527484127 (206-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 249.20-digit and the GNFS difficulty is 205.81-digit. SNFS must be faster than GNFS. It will take about 844 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 79999_248.
Put the following polynomial file 79999_248.poly in there too.
And then, run "perl factMsieve.pl 79999_248".

79999_248.poly ^*1

n: 64998362226240895181515724899074333746449115099884028313907317961225310385451807687976589551503950863613688396430537361321212297582395707795762523271386416606017656678835739145316249302906092607291527484127
m: 200000000000000000000000000000000000000000
deg: 6
c6: 25
c0: -2
skew: 0.66
type: snfs
lss: 1
rlim: 100000000
alim: 100000000
lpbr: 30
lpba: 30
mfbr: 62
mfba: 62
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 206-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	Jul 24, 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 64998362226240895181515724899074333746449115099884028313907317961225310385451807687976589551503950863613688396430537361321212297582395707795762523271386416606017656678835739145316249302906092607291527484127 | ecm -n -c 825 1e6

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

echo 64998362226240895181515724899074333746449115099884028313907317961225310385451807687976589551503950863613688396430537361321212297582395707795762523271386416606017656678835739145316249302906092607291527484127 | ecm -n -c 2336 3e6

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

echo 64998362226240895181515724899074333746449115099884028313907317961225310385451807687976589551503950863613688396430537361321212297582395707795762523271386416606017656678835739145316249302906092607291527484127 | ecm -n -c 4479 11e6

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

echo 64998362226240895181515724899074333746449115099884028313907317961225310385451807687976589551503950863613688396430537361321212297582395707795762523271386416606017656678835739145316249302906092607291527484127 | ecm -n -c 7553 43e6

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