Contribution and Reservation

(4·10²⁴⁹-1)/3 =: 1(3)₂₄₉_<250>; = 6053 · 93479 · 194559763 · 5742410231_<10> · [2109146572492664200833189888679432741141410698175846645555481358572215317086928676198576012243208092477835642711625515904058473068213645330965596764323782869122075528121860707850933347072239125936470876584497400850618846603_<223>] SUBMIT/RESERVE

Status

Expression:	(4·10²⁴⁹-1)/3
Composite Factor:	210914657249266420083318988867943274114141069817584664555548 135857221531708692867619857601224320809247783564271162551590 405847306821364533096559676432378286912207552812186070785093 3347072239125936470876584497400850618846603 (223-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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 249.60-digit and the GNFS difficulty is 222.32-digit. SNFS must be faster than GNFS. It will take about 871 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of SNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 13333_249.
Put the following polynomial file 13333_249.poly in there too.
And then, run "perl factMsieve.pl 13333_249".

13333_249.poly

n: 2109146572492664200833189888679432741141410698175846645555481358572215317086928676198576012243208092477835642711625515904058473068213645330965596764323782869122075528121860707850933347072239125936470876584497400850618846603
m: 100000000000000000000000000000000000000000
deg: 6
c6: 4000
c0: -1
skew: 0.25
type: snfs
lss: 1
rlim: 101000000
alim: 101000000
lpbr: 30
lpba: 30
mfbr: 62
mfba: 62
rlambda: 2.7
alambda: 2.7

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 223-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 45-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
45	11e6	700	Dmitry Domanov	Jul 11, 2009
45	11e6	700 / 697
50	43e6	1078	yoyo@home	Jan 15, 2010
		1078 / 7396
		/ 6318
55	11e7	0 / 17341 (2621)
55	11e7	/ 17341 (2621)
60	26e7	0 / 41880 (7459)
60	26e7	/ 41880 (7459)
65	85e7	0 / 69380 (13567)
65	85e7	/ 69380 (13567)

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

echo 2109146572492664200833189888679432741141410698175846645555481358572215317086928676198576012243208092477835642711625515904058473068213645330965596764323782869122075528121860707850933347072239125936470876584497400850618846603 | ecm -n -c 6318 43e6

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

echo 2109146572492664200833189888679432741141410698175846645555481358572215317086928676198576012243208092477835642711625515904058473068213645330965596764323782869122075528121860707850933347072239125936470876584497400850618846603 | ecm -n -c 17341 11e7

Command line to find prime factors up to about 60-digit

echo 2109146572492664200833189888679432741141410698175846645555481358572215317086928676198576012243208092477835642711625515904058473068213645330965596764323782869122075528121860707850933347072239125936470876584497400850618846603 | ecm -n -c 41880 26e7

Command line to find prime factors up to about 65-digit

echo 2109146572492664200833189888679432741141410698175846645555481358572215317086928676198576012243208092477835642711625515904058473068213645330965596764323782869122075528121860707850933347072239125936470876584497400850618846603 | ecm -n -c 69380 85e7

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