Contribution and Reservation

(5·10¹⁹⁰-41)/9 =: (5)₁₈₉1_<190>; = 7 · 13 · 328671589 · 3040823366329553218801_<22> · 2640788558786029100848669_<25> · [23131250645136039124173437398550316889871557127081915222698595006677255786998338589830559546149712341137606558001486495150836722621421_<134>] SUBMIT/RESERVE

Status

Expression:	(5·10¹⁹⁰-41)/9
Composite Factor:	231312506451360391241734373985503168898715571270819152226985 950066772557869983385898305595461497123411376065580014864951 50836722621421 (134-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 190.70-digit and the GNFS difficulty is 133.36-digit. GNFS may be faster than SNFS. It will take about 9 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 55551_190.
Put the following polynomial file 55551_190.poly in there too.
And then, run "perl factMsieve.pl 55551_190".

55551_190.poly ^*1

# Murphy_E = 4.638935e-11, selected by Jeff Gilchrist
n: 23131250645136039124173437398550316889871557127081915222698595006677255786998338589830559546149712341137606558001486495150836722621421
Y0: -53470942235238467857570124
Y1: 649173555851929
c0: 9686870205118442292954702138454905
c1: 177634003343719421607244589417
c2: 197141587712728352622173
c3: -167968379679017545
c4: -99423583086
c5: 52920
skew: 1277096.76
type: gnfs
# selected mechanically
rlim: 12100000
alim: 12100000
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 134-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	118	Makoto Kamada	Apr 21, 2009
35	1e6	118 / 0
40	3e6	500	Erik Branger	May 11, 2009
		500 / 2318
		/ 1818
45	11e6	0 / 4365 (527)
45	11e6	/ 4365 (527)
50	43e6	0 / 7534 (1244)
50	43e6	/ 7534 (1244)
55	11e7	0 / 17765 (3125)
55	11e7	/ 17765 (3125)

Command line to find prime factors up to about 40-digit

echo 23131250645136039124173437398550316889871557127081915222698595006677255786998338589830559546149712341137606558001486495150836722621421 | ecm -n -c 1818 3e6

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

echo 23131250645136039124173437398550316889871557127081915222698595006677255786998338589830559546149712341137606558001486495150836722621421 | ecm -n -c 4365 11e6

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

echo 23131250645136039124173437398550316889871557127081915222698595006677255786998338589830559546149712341137606558001486495150836722621421 | ecm -n -c 7534 43e6

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

echo 23131250645136039124173437398550316889871557127081915222698595006677255786998338589830559546149712341137606558001486495150836722621421 | ecm -n -c 17765 11e7

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