Contribution and Reservation

(68·10¹⁸⁹+13)/9 =: 7(5)₁₈₈7_<190>; = 3² · 11 · 933389 · 3475483210660030976531_<22> · 167456950534562681320501751047_<30> · [140491534853109484986754548242952399389515438770363777285457862248011616087412384135885187516878636187876872889038035235947402642391_<132>] (Kenichiro Yamaguchi / GMP-ECM 6.0.1 B1=3000000, sigma=1903957270 for P30 / Oct 25, 2005) SUBMIT/RESERVE

Status

Expression:	(68·10¹⁸⁹+13)/9
Composite Factor:	140491534853109484986754548242952399389515438770363777285457 862248011616087412384135885187516878636187876872889038035235 947402642391 (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 191.53-digit and the GNFS difficulty is 131.15-digit. GNFS must be faster than SNFS. It will take about 7 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 75557_189.
Put the following polynomial file 75557_189.poly in there too.
And then, run "perl factMsieve.pl 75557_189".

75557_189.poly ^*1

# Murphy_E = 6.908832e-11, selected by Jeff Gilchrist
n: 140491534853109484986754548242952399389515438770363777285457862248011616087412384135885187516878636187876872889038035235947402642391
Y0: -19828123453435259353602040
Y1: 286324364531239
c0: 40009859384266013014481207169
c1: 104466149555195946470101054
c2: 948509336049825522348
c3: -4553911342473909
c4: -18441570302
c5: 45840
skew: 206649.46
type: gnfs
# selected mechanically
rlim: 10500000
alim: 10500000
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	500	Erik Branger	Feb 2, 2009
		1850	Wataru Sakai	Jul 26, 2009
		2350 / 2350
45	11e6	0 / 3961
45	11e6	/ 3961
50	43e6	0 / 7465 (1129)
50	43e6	/ 7465 (1129)
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 140491534853109484986754548242952399389515438770363777285457862248011616087412384135885187516878636187876872889038035235947402642391 | ecm -n -c 3961 11e6

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

echo 140491534853109484986754548242952399389515438770363777285457862248011616087412384135885187516878636187876872889038035235947402642391 | ecm -n -c 7465 43e6

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

echo 140491534853109484986754548242952399389515438770363777285457862248011616087412384135885187516878636187876872889038035235947402642391 | ecm -n -c 17751 11e7

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

echo 140491534853109484986754548242952399389515438770363777285457862248011616087412384135885187516878636187876872889038035235947402642391 | 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