Contribution and Reservation

(4·10²⁰⁹-1)/3 =: 1(3)₂₀₉_<210>; = 19231 · 216757 · [31986280186253368300341401699224642836459471684812419043939327668546639413565886858196416578773986305300121325136242255870774479974191671516784315015986077922290061734617089222384653857399481046801599_<200>] SUBMIT/RESERVE

Status

Expression:	(4·10²⁰⁹-1)/3
Composite Factor:	319862801862533683003414016992246428364594716848124190439393 276685466394135658868581964165787739863053001213251362422558 707744799741916715167843150159860779222900617346170892223846 53857399481046801599 (200-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 209.60-digit and the GNFS difficulty is 199.50-digit. SNFS must be faster than GNFS. It will take about 40 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_209.
Put the following polynomial file 13333_209.poly in there too.
And then, run "perl factMsieve.pl 13333_209".

13333_209.poly

n: 31986280186253368300341401699224642836459471684812419043939327668546639413565886858196416578773986305300121325136242255870774479974191671516784315015986077922290061734617089222384653857399481046801599
m: 200000000000000000000000000000000000000000
deg: 5
c5: 1250
c0: -1
skew: 0.24
type: snfs
lss: 1
rlim: 22000000
alim: 22000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
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 200-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	1034	yoyo@home	Jan 15, 2010
		1034 / 7372
		/ 6338
55	11e7	0 / 17352 (2629)
55	11e7	/ 17352 (2629)
60	26e7	0 / 41885 (7464)
60	26e7	/ 41885 (7464)
65	85e7	0 / 69381 (13568)
65	85e7	/ 69381 (13568)

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

echo 31986280186253368300341401699224642836459471684812419043939327668546639413565886858196416578773986305300121325136242255870774479974191671516784315015986077922290061734617089222384653857399481046801599 | ecm -n -c 6338 43e6

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

echo 31986280186253368300341401699224642836459471684812419043939327668546639413565886858196416578773986305300121325136242255870774479974191671516784315015986077922290061734617089222384653857399481046801599 | ecm -n -c 17352 11e7

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

echo 31986280186253368300341401699224642836459471684812419043939327668546639413565886858196416578773986305300121325136242255870774479974191671516784315015986077922290061734617089222384653857399481046801599 | ecm -n -c 41885 26e7

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

echo 31986280186253368300341401699224642836459471684812419043939327668546639413565886858196416578773986305300121325136242255870774479974191671516784315015986077922290061734617089222384653857399481046801599 | ecm -n -c 69381 85e7

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