Contribution and Reservation

(31·10¹⁹³+41)/9 =: 3(4)₁₉₂9_<194>; = 3 · 13 · 163 · 2116949 · 1376577774668539_<16> · 22323435390822061_<17> · 106959258746048575463_<21> · [778711179907145946703809146425264094365928916950301812360903975979379774142384741289352609527127356119460156803125537925466464018609_<132>] SUBMIT/RESERVE

Status

Expression:	(31·10¹⁹³+41)/9
Composite Factor:	778711179907145946703809146425264094365928916950301812360903 975979379774142384741289352609527127356119460156803125537925 466464018609 (132-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 195.89-digit and the GNFS difficulty is 131.89-digit. GNFS must be faster than SNFS. It will take about 8 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 34449_193.
Put the following polynomial file 34449_193.poly in there too.
And then, run "perl factMsieve.pl 34449_193".

34449_193.poly ^*1

# Murphy_E = 5.77117e-11, selected by Jeff Gilchrist
n: 778711179907145946703809146425264094365928916950301812360903975979379774142384741289352609527127356119460156803125537925466464018609
Y0: -28190218129938487726195799
Y1: 402613261432427
c0: -4090406779116688783403810000088000
c1: -61771776958174656222136490536
c2: 20533574232382503730382
c3: -55219507358287059
c4: 38429261928
c5: 43740
skew: 1103725.87
type: gnfs
# selected mechanically
rlim: 11000000
alim: 11000000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
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 132-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	300	Serge Batalov	Nov 23, 2008
		2036	Wataru Sakai	Nov 24, 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 778711179907145946703809146425264094365928916950301812360903975979379774142384741289352609527127356119460156803125537925466464018609 | ecm -n -c 3962 11e6

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

echo 778711179907145946703809146425264094365928916950301812360903975979379774142384741289352609527127356119460156803125537925466464018609 | ecm -n -c 7465 43e6

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

echo 778711179907145946703809146425264094365928916950301812360903975979379774142384741289352609527127356119460156803125537925466464018609 | ecm -n -c 17751 11e7

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

echo 778711179907145946703809146425264094365928916950301812360903975979379774142384741289352609527127356119460156803125537925466464018609 | 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