Contribution and Reservation

(4·10²¹⁹-1)/3 =: 1(3)₂₁₉_<220>; = 641 · 1175849 · 870258161 · [2032736325950703580408682453333508994397754376887421232148671569874797892481678869944181360466239109880959712357775338854527948567395587732589778378820364726730047145134571445196091989925453649857570717_<202>] SUBMIT/RESERVE

Status

Expression:	(4·10²¹⁹-1)/3
Composite Factor:	203273632595070358040868245333350899439775437688742123214867 156987479789248167886994418136046623910988095971235777533885 452794856739558773258977837882036472673004714513457144519609 1989925453649857570717 (202-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 219.60-digit and the GNFS difficulty is 201.31-digit. SNFS must be faster than GNFS. It will take about 87 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_219.
Put the following polynomial file 13333_219.poly in there too.
And then, run "perl factMsieve.pl 13333_219".

13333_219.poly

n: 2032736325950703580408682453333508994397754376887421232148671569874797892481678869944181360466239109880959712357775338854527948567395587732589778378820364726730047145134571445196091989925453649857570717
m: 1000000000000000000000000000000000000
deg: 6
c6: 4000
c0: -1
skew: 0.25
type: snfs
lss: 1
rlim: 32000000
alim: 32000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6

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 202-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 / 699
50	43e6	1046	yoyo@home	Jan 15, 2010
		1046 / 7377
		/ 6331
55	11e7	0 / 17348 (2627)
55	11e7	/ 17348 (2627)
60	26e7	0 / 41883 (7462)
60	26e7	/ 41883 (7462)
65	85e7	0 / 69381 (13568)
65	85e7	/ 69381 (13568)

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

echo 2032736325950703580408682453333508994397754376887421232148671569874797892481678869944181360466239109880959712357775338854527948567395587732589778378820364726730047145134571445196091989925453649857570717 | ecm -n -c 6331 43e6

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

echo 2032736325950703580408682453333508994397754376887421232148671569874797892481678869944181360466239109880959712357775338854527948567395587732589778378820364726730047145134571445196091989925453649857570717 | ecm -n -c 17348 11e7

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

echo 2032736325950703580408682453333508994397754376887421232148671569874797892481678869944181360466239109880959712357775338854527948567395587732589778378820364726730047145134571445196091989925453649857570717 | ecm -n -c 41883 26e7

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

echo 2032736325950703580408682453333508994397754376887421232148671569874797892481678869944181360466239109880959712357775338854527948567395587732589778378820364726730047145134571445196091989925453649857570717 | ecm -n -c 69381 85e7

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