Contribution and Reservation

(16·10²²¹-7)/9 =: 1(7)₂₂₁_<222>; = 3² · 5101 · 28001 · 22725397492201404743_<20> · [6085476790705247003577571722046306629197440098706501318731712270192779067167796770813668386620188701406440511970060988837373832623176490005480333071884302565442911451338300035021455337942640971_<193>] SUBMIT/RESERVE

Status

Expression:	(16·10²²¹-7)/9
Composite Factor:	608547679070524700357757172204630662919744009870650131873171 227019277906716779677081366838662018870140644051197006098883 737383262317649000548033307188430256544291145133830003502145 5337942640971 (193-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 222.90-digit and the GNFS difficulty is 192.78-digit. SNFS must be faster than GNFS. It will take about 112 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_221.
Put the following polynomial file 17777_221.poly in there too.
And then, run "perl factMsieve.pl 17777_221".

17777_221.poly ^*1

n: 6085476790705247003577571722046306629197440098706501318731712270192779067167796770813668386620188701406440511970060988837373832623176490005480333071884302565442911451338300035021455337942640971
m: 10000000000000000000000000000000000000
deg: 6
c6: 8
c0: -35
skew: 1.28
type: snfs
lss: 1
rlim: 36000000
alim: 36000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6

*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 193-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 / 3830
50	43e6	0 / 6435
50	43e6	/ 6435
55	11e7	0 / 17466 (2670)
55	11e7	/ 17466 (2670)
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 6085476790705247003577571722046306629197440098706501318731712270192779067167796770813668386620188701406440511970060988837373832623176490005480333071884302565442911451338300035021455337942640971 | ecm -n -c 6435 43e6

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

echo 6085476790705247003577571722046306629197440098706501318731712270192779067167796770813668386620188701406440511970060988837373832623176490005480333071884302565442911451338300035021455337942640971 | ecm -n -c 17466 11e7

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

echo 6085476790705247003577571722046306629197440098706501318731712270192779067167796770813668386620188701406440511970060988837373832623176490005480333071884302565442911451338300035021455337942640971 | ecm -n -c 41942 26e7

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

echo 6085476790705247003577571722046306629197440098706501318731712270192779067167796770813668386620188701406440511970060988837373832623176490005480333071884302565442911451338300035021455337942640971 | ecm -n -c 69396 85e7

Submit factors

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