Contribution and Reservation

(32·10¹⁹⁰+13)/9 =: 3(5)₁₈₉7_<191>; = 37 · 113 · 485964719904233782920111577_<27> · 699056118054564041970473612040807401_<36> · [25032862789153365018478740251724706852131249447149089422041868395151290097102441153373002551131680579832018686146524928049361_<125>] (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=4191816949 for P36 / Nov 25, 2008) SUBMIT/RESERVE

Status

Expression:	(32·10¹⁹⁰+13)/9
Composite Factor:	250328627891533650184787402517247068521312494471490894220418 683951512900971024411533730025511316805798320186861465249280 49361 (125-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 191.51-digit and the GNFS difficulty is 124.40-digit. GNFS must be faster than SNFS. It will take about 3 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 35557_190.
Put the following polynomial file 35557_190.poly in there too.
And then, run "perl factMsieve.pl 35557_190".

35557_190.poly ^*1

# Murphy_E = 1.604357e-10, selected by Jeff Gilchrist
n: 25032862789153365018478740251724706852131249447149089422041868395151290097102441153373002551131680579832018686146524928049361
Y0: -1083035137779722956252865
Y1: 37604900821339
c0: -16994854296384507659410836952896
c1: 335190533629780316787685986
c2: 1366293918137746938067
c3: -10057301805631826
c4: -12809279096
c5: 16800
skew: 346117.02
type: gnfs
# selected mechanically
rlim: 6900000
alim: 6900000
lpbr: 27
lpba: 27
mfbr: 52
mfba: 52
rlambda: 2.5
alambda: 2.5

*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 125-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	500	Erik Branger	Mar 5, 2009
		1836	Wataru Sakai	Aug 23, 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 25032862789153365018478740251724706852131249447149089422041868395151290097102441153373002551131680579832018686146524928049361 | ecm -n -c 3962 11e6

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

echo 25032862789153365018478740251724706852131249447149089422041868395151290097102441153373002551131680579832018686146524928049361 | ecm -n -c 7465 43e6

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

echo 25032862789153365018478740251724706852131249447149089422041868395151290097102441153373002551131680579832018686146524928049361 | ecm -n -c 17751 11e7

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

echo 25032862789153365018478740251724706852131249447149089422041868395151290097102441153373002551131680579832018686146524928049361 | 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