Contribution and Reservation

(64·10²⁷⁵-1)/9 =: 7(1)₂₇₅_<276>; = 3 · 79 · 1790856938042115890369_<22> · [1675437473265701383050110532511405313148703289895375624598592248584739907418598558720608617896580220416471752481115955646027622516248483437161444339644340430635957466539772897596760817048587862724446879436042817480333607110541706424452039114722880545987_<253>] SUBMIT/RESERVE

Status

Expression:	(64·10²⁷⁵-1)/9
Composite Factor:	167543747326570138305011053251140531314870328989537562459859 224858473990741859855872060861789658022041647175248111595564 602762251624848343716144433964434043063595746653977289759676 081704858786272444687943604281748033360711054170642445203911 4722880545987 (253-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 277.81-digit and the GNFS difficulty is 252.22-digit. SNFS must be faster than GNFS. It will take about 7586 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_275.
Put the following polynomial file 71111_275.poly in there too.
And then, run "perl factMsieve.pl 71111_275".

71111_275.poly ^*1

n: 1675437473265701383050110532511405313148703289895375624598592248584739907418598558720608617896580220416471752481115955646027622516248483437161444339644340430635957466539772897596760817048587862724446879436042817480333607110541706424452039114722880545987
m: 20000000000000000000000000000000000000000000000
deg: 6
c6: 1
c0: -10
skew: 1.47
type: snfs
lss: 1
rlim: 300000000
alim: 300000000
lpbr: 32
lpba: 32
mfbr: 65
mfba: 65
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 253-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 27, 2009
40	3e6	450 / 438
45	11e6	550	Serge Batalov	Jan 27, 2009
		550 / 4379
		/ 3829
50	43e6	0 / 7413 (1092)
50	43e6	/ 7413 (1092)
55	11e7	0 / 17732 (3075)
55	11e7	/ 17732 (3075)
60	26e7	0 / 42008 (7627)
60	26e7	/ 42008 (7627)

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

echo 1675437473265701383050110532511405313148703289895375624598592248584739907418598558720608617896580220416471752481115955646027622516248483437161444339644340430635957466539772897596760817048587862724446879436042817480333607110541706424452039114722880545987 | ecm -n -c 3829 11e6

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

echo 1675437473265701383050110532511405313148703289895375624598592248584739907418598558720608617896580220416471752481115955646027622516248483437161444339644340430635957466539772897596760817048587862724446879436042817480333607110541706424452039114722880545987 | ecm -n -c 7413 43e6

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

echo 1675437473265701383050110532511405313148703289895375624598592248584739907418598558720608617896580220416471752481115955646027622516248483437161444339644340430635957466539772897596760817048587862724446879436042817480333607110541706424452039114722880545987 | ecm -n -c 17732 11e7

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

echo 1675437473265701383050110532511405313148703289895375624598592248584739907418598558720608617896580220416471752481115955646027622516248483437161444339644340430635957466539772897596760817048587862724446879436042817480333607110541706424452039114722880545987 | ecm -n -c 42008 26e7

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