Contribution and Reservation

(16·10²²⁸-7)/9 =: 1(7)₂₂₈_<229>; = 29 · 12322061273_<11> · [4975034666209873565441882737027213303911130167863740458175940026420234767120978148057720884698958692213521332195548015775496113009394851549251261933724306651360828575881510525417782278930155897335159296460287429417581_<217>] SUBMIT/RESERVE

Status

Expression:	(16·10²²⁸-7)/9
Composite Factor:	497503466620987356544188273702721330391113016786374045817594 002642023476712097814805772088469895869221352133219554801577 549611300939485154925126193372430665136082857588151052541778 2278930155897335159296460287429417581 (217-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 229.20-digit and the GNFS difficulty is 216.70-digit. SNFS must be faster than GNFS. It will take about 182 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 17777_228.
Put the following polynomial file 17777_228.poly in there too.
And then, run "perl factMsieve.pl 17777_228".

17777_228.poly ^*1

n: 4975034666209873565441882737027213303911130167863740458175940026420234767120978148057720884698958692213521332195548015775496113009394851549251261933724306651360828575881510525417782278930155897335159296460287429417581
m: 100000000000000000000000000000000000000
deg: 6
c6: 16
c0: -7
skew: 0.87
type: snfs
lss: 1
rlim: 46000000
alim: 46000000
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 217-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	4500	Dmitry Domanov	Sep 2, 2009
45	11e6	4500 / 3859
50	43e6	0 / 6439
50	43e6	/ 6439
55	11e7	0 / 17466 (2671)
55	11e7	/ 17466 (2671)
60	26e7	0 / 41942 (7513)
60	26e7	/ 41942 (7513)
65	85e7	0 / 69396 (13587)
65	85e7	/ 69396 (13587)

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

echo 4975034666209873565441882737027213303911130167863740458175940026420234767120978148057720884698958692213521332195548015775496113009394851549251261933724306651360828575881510525417782278930155897335159296460287429417581 | ecm -n -c 6439 43e6

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

echo 4975034666209873565441882737027213303911130167863740458175940026420234767120978148057720884698958692213521332195548015775496113009394851549251261933724306651360828575881510525417782278930155897335159296460287429417581 | ecm -n -c 17466 11e7

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

echo 4975034666209873565441882737027213303911130167863740458175940026420234767120978148057720884698958692213521332195548015775496113009394851549251261933724306651360828575881510525417782278930155897335159296460287429417581 | ecm -n -c 41942 26e7

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

echo 4975034666209873565441882737027213303911130167863740458175940026420234767120978148057720884698958692213521332195548015775496113009394851549251261933724306651360828575881510525417782278930155897335159296460287429417581 | ecm -n -c 69396 85e7

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