Contribution and Reservation

(16·10²²⁵-1)/3 =: 5(3)₂₂₅_<226>; = 792957982049_<12> · [6725871299702442038912364051878132799716624614477011125192204431582246581365269932860623006659087777499713764449939491088048973407041047524745544467727927675258163776508505224031424879907184683863717363808579686517_<214>] SUBMIT/RESERVE

Status

Expression:	(16·10²²⁵-1)/3
Composite Factor:	672587129970244203891236405187813279971662461447701112519220 443158224658136526993286062300665908777749971376444993949108 804897340704104752474554446772792767525816377650850522403142 4879907184683863717363808579686517 (214-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 228.30-digit and the GNFS difficulty is 213.83-digit. SNFS must be faster than GNFS. It will take about 170 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 53333_225.
Put the following polynomial file 53333_225.poly in there too.
And then, run "perl factMsieve.pl 53333_225".

53333_225.poly ^*1

n: 6725871299702442038912364051878132799716624614477011125192204431582246581365269932860623006659087777499713764449939491088048973407041047524745544467727927675258163776508505224031424879907184683863717363808579686517
m: 100000000000000000000000000000000000000
deg: 6
c6: 2
c0: -125
skew: 1.99
type: snfs
lss: 1
rlim: 45000000
alim: 45000000
lpbr: 30
lpba: 30
mfbr: 59
mfba: 59
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 214-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 31, 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 6725871299702442038912364051878132799716624614477011125192204431582246581365269932860623006659087777499713764449939491088048973407041047524745544467727927675258163776508505224031424879907184683863717363808579686517 | ecm -n -c 825 1e6

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

echo 6725871299702442038912364051878132799716624614477011125192204431582246581365269932860623006659087777499713764449939491088048973407041047524745544467727927675258163776508505224031424879907184683863717363808579686517 | ecm -n -c 2336 3e6

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

echo 6725871299702442038912364051878132799716624614477011125192204431582246581365269932860623006659087777499713764449939491088048973407041047524745544467727927675258163776508505224031424879907184683863717363808579686517 | ecm -n -c 4479 11e6

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

echo 6725871299702442038912364051878132799716624614477011125192204431582246581365269932860623006659087777499713764449939491088048973407041047524745544467727927675258163776508505224031424879907184683863717363808579686517 | ecm -n -c 7553 43e6

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