Contribution and Reservation

(31·10²⁰³+23)/9 =: 3(4)₂₀₂7_<204>; = 67 · 227 · 8741 · 72767 · 2591233 · 5846821 · 1059062499515903_<16> · 4586078381562718593317867_<25> · [483875470280837336255542149154427432353441547998373920017796951532203742209861594912364898662007571446937552737300384418769857421502561373_<138>] SUBMIT/RESERVE

Status

Expression:	(31·10²⁰³+23)/9
Composite Factor:	483875470280837336255542149154427432353441547998373920017796 951532203742209861594912364898662007571446937552737300384418 769857421502561373 (138-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.

GNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 205.89-digit and the GNFS difficulty is 137.68-digit. GNFS must be faster than SNFS. It will take about 15 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 34447_203.
Put the following polynomial file 34447_203.poly in there too.
And then, run "perl factMsieve.pl 34447_203".

34447_203.poly ^*1

# Murphy_E = 2.694393e-11, selected by Jeff Gilchrist
n: 483875470280837336255542149154427432353441547998373920017796951532203742209861594912364898662007571446937552737300384418769857421502561373
Y0: -364640102714123495544211069
Y1: 2105452856511889
c0: 12598143934036582270344891056646240
c1: 207034316160790590442850683932
c2: -138822338787456655980090
c3: -280596800640292696
c4: 86671117871
c5: 75060
skew: 1227653.56
type: gnfs
# selected mechanically
rlim: 15800000
alim: 15800000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=10^(d/21-4)[hours]; rlim=round(3*10^(d/37+3)); lpbr=floor(d/18+21); mfbr=floor(d/5+28); rlambda=floor(d/26+21)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 138-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	400	Serge Batalov	Nov 23, 2008
		290	Serge Batalov	Nov 23, 2008
		1646	Wataru Sakai	Nov 25, 2009
		2336 / 2336
45	11e6	0 / 3962
45	11e6	/ 3962
50	43e6	0 / 7465 (1130)
50	43e6	/ 7465 (1130)
55	11e7	0 / 17751 (3097)
55	11e7	/ 17751 (3097)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 483875470280837336255542149154427432353441547998373920017796951532203742209861594912364898662007571446937552737300384418769857421502561373 | ecm -n -c 3962 11e6

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

echo 483875470280837336255542149154427432353441547998373920017796951532203742209861594912364898662007571446937552737300384418769857421502561373 | ecm -n -c 7465 43e6

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

echo 483875470280837336255542149154427432353441547998373920017796951532203742209861594912364898662007571446937552737300384418769857421502561373 | ecm -n -c 17751 11e7

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

echo 483875470280837336255542149154427432353441547998373920017796951532203742209861594912364898662007571446937552737300384418769857421502561373 | ecm -n -c 42014 26e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation