Contribution and Reservation

2·10¹⁸⁸-9 =: 1(9)₁₈₇1_<189>; = 17 · 156083835959_<12> · 116098705756986833_<18> · 1528557664610115047105616481_<28> · [424730979321609056444211982014719865751281575611959204819716385342249694232869193979489060533511688985047286901474261914078857029889_<132>] (Makoto Kamada / GMP-ECM 5.0.3 B1=4000000, sigma=1508648790 for P28) SUBMIT/RESERVE

Status

Expression:	2·10¹⁸⁸-9
Composite Factor:	424730979321609056444211982014719865751281575611959204819716 385342249694232869193979489060533511688985047286901474261914 078857029889 (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 188.60-digit and the GNFS difficulty is 131.63-digit. GNFS may 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 19991_188.
Put the following polynomial file 19991_188.poly in there too.
And then, run "perl factMsieve.pl 19991_188".

19991_188.poly ^*1

# Murphy_E = 6.27231e-11, selected by Jeff Gilchrist
n: 424730979321609056444211982014719865751281575611959204819716385342249694232869193979489060533511688985047286901474261914078857029889
Y0: -24115140840764330089204633
Y1: 415589386019699
c0: 533918440835784793304957895536160
c1: 866439391895401154778358452
c2: -9811553603072832927099
c3: -26377614099474532
c4: -42097964546
c5: 52080
skew: 492929.07
type: gnfs
# selected mechanically
rlim: 10800000
alim: 10800000
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 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	0 / 0
40	3e6	500	Erik Branger	Feb 3, 2009
		500 / 2350
		/ 1850
45	11e6	0 / 4370 (537)
45	11e6	/ 4370 (537)
50	43e6	0 / 7535 (1246)
50	43e6	/ 7535 (1246)
55	11e7	0 / 17766 (3126)
55	11e7	/ 17766 (3126)

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

echo 424730979321609056444211982014719865751281575611959204819716385342249694232869193979489060533511688985047286901474261914078857029889 | ecm -n -c 1850 3e6

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

echo 424730979321609056444211982014719865751281575611959204819716385342249694232869193979489060533511688985047286901474261914078857029889 | ecm -n -c 4370 11e6

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

echo 424730979321609056444211982014719865751281575611959204819716385342249694232869193979489060533511688985047286901474261914078857029889 | ecm -n -c 7535 43e6

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

echo 424730979321609056444211982014719865751281575611959204819716385342249694232869193979489060533511688985047286901474261914078857029889 | ecm -n -c 17766 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