Contribution and Reservation

(64·10²⁸⁹-1)/9 =: 7(1)₂₈₉_<290>; = 359 · 120940373 · [1637840900705606001031113543670906100243725583545177339417117486448075343621807280890304244724141228794397160491897525156681435426442206948875065655561020195598263443657186793243989588248536821690880326725681333161839301716308051771080634404145243762162840736689723056124559903773_<280>] SUBMIT/RESERVE

Status

Expression:	(64·10²⁸⁹-1)/9
Composite Factor:	163784090070560600103111354367090610024372558354517733941711 748644807534362180728089030424472414122879439716049189752515 668143542644220694887506565556102019559826344365718679324398 958824853682169088032672568133316183930171630805177108063440 4145243762162840736689723056124559903773 (280-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 290.81-digit and the GNFS difficulty is 279.21-digit. SNFS must be faster than GNFS. It will take about 20574 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 71111_289.
Put the following polynomial file 71111_289.poly in there too.
And then, run "perl factMsieve.pl 71111_289".

71111_289.poly ^*1

n: 1637840900705606001031113543670906100243725583545177339417117486448075343621807280890304244724141228794397160491897525156681435426442206948875065655561020195598263443657186793243989588248536821690880326725681333161839301716308051771080634404145243762162840736689723056124559903773
m: 2000000000000000000000000000000000000000000000000
deg: 6
c6: 10
c0: -1
skew: 0.68
type: snfs
lss: 1
rlim: 490000000
alim: 490000000
lpbr: 32
lpba: 32
mfbr: 67
mfba: 67
rlambda: 2.9
alambda: 2.9

*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 280-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 40-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
40	3e6	450	Serge Batalov	Jan 25, 2009
40	3e6	450 / 0
45	11e6	550	Serge Batalov	Jan 27, 2009
		500	Serge Batalov	Aug 20, 2009
		1050 / 4379
		/ 3329
50	43e6	0 / 7301 (949)
50	43e6	/ 7301 (949)
55	11e7	0 / 17700 (3029)
55	11e7	/ 17700 (3029)
60	26e7	0 / 42000 (7614)
60	26e7	/ 42000 (7614)

Command line to find prime factors up to about 45-digit

echo 1637840900705606001031113543670906100243725583545177339417117486448075343621807280890304244724141228794397160491897525156681435426442206948875065655561020195598263443657186793243989588248536821690880326725681333161839301716308051771080634404145243762162840736689723056124559903773 | ecm -n -c 3329 11e6

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

echo 1637840900705606001031113543670906100243725583545177339417117486448075343621807280890304244724141228794397160491897525156681435426442206948875065655561020195598263443657186793243989588248536821690880326725681333161839301716308051771080634404145243762162840736689723056124559903773 | ecm -n -c 7301 43e6

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

echo 1637840900705606001031113543670906100243725583545177339417117486448075343621807280890304244724141228794397160491897525156681435426442206948875065655561020195598263443657186793243989588248536821690880326725681333161839301716308051771080634404145243762162840736689723056124559903773 | ecm -n -c 17700 11e7

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

echo 1637840900705606001031113543670906100243725583545177339417117486448075343621807280890304244724141228794397160491897525156681435426442206948875065655561020195598263443657186793243989588248536821690880326725681333161839301716308051771080634404145243762162840736689723056124559903773 | ecm -n -c 42000 26e7

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