Contribution and Reservation

4·10²²⁷+1 =: 4(0)₂₂₆1_<228>; = 7³ · 19 · [61377934632499616387908546877397575571582016265152677612398342795764922510357526469234310265459567285560840877704465244744514347092220346785330673622832591683289857296301979438391898112628510050636796071812183520024551173853_<224>] SUBMIT/RESERVE

Status

Expression:	4·10²²⁷+1
Composite Factor:	613779346324996163879085468773975755715820162651526776123983 427957649225103575264692343102654595672855608408777044652447 445143470922203467853306736228325916832898572963019794383918 98112628510050636796071812183520024551173853 (224-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 228.30-digit and the GNFS difficulty is 223.79-digit. SNFS must be faster than GNFS. It will take about 170 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 40001_227.
Put the following polynomial file 40001_227.poly in there too.
And then, run "perl factMsieve.pl 40001_227".

40001_227.poly ^*1

n: 61377934632499616387908546877397575571582016265152677612398342795764922510357526469234310265459567285560840877704465244744514347092220346785330673622832591683289857296301979438391898112628510050636796071812183520024551173853
m: 100000000000000000000000000000000000000
deg: 6
c6: 2
c0: 5
skew: 1.16
type: snfs
lss: 1
rlim: 45000000
alim: 45000000
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 224-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	324	Serge Batalov	Nov 4, 2008
		860	Serge Batalov	Dec 2, 2008
		1184 / 956
45	11e6	200	Serge Batalov	Nov 7, 2008
		150	Serge Batalov	Dec 2, 2008
		50	Serge Batalov	Dec 3, 2008
		400 / 4217
		/ 3817
50	43e6	0 / 7419 (1088)
50	43e6	/ 7419 (1088)
55	11e7	0 / 17735 (3078)
55	11e7	/ 17735 (3078)
60	26e7	0 / 42009 (7629)
60	26e7	/ 42009 (7629)

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

echo 61377934632499616387908546877397575571582016265152677612398342795764922510357526469234310265459567285560840877704465244744514347092220346785330673622832591683289857296301979438391898112628510050636796071812183520024551173853 | ecm -n -c 3817 11e6

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

echo 61377934632499616387908546877397575571582016265152677612398342795764922510357526469234310265459567285560840877704465244744514347092220346785330673622832591683289857296301979438391898112628510050636796071812183520024551173853 | ecm -n -c 7419 43e6

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

echo 61377934632499616387908546877397575571582016265152677612398342795764922510357526469234310265459567285560840877704465244744514347092220346785330673622832591683289857296301979438391898112628510050636796071812183520024551173853 | ecm -n -c 17735 11e7

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

echo 61377934632499616387908546877397575571582016265152677612398342795764922510357526469234310265459567285560840877704465244744514347092220346785330673622832591683289857296301979438391898112628510050636796071812183520024551173853 | ecm -n -c 42009 26e7

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