Contribution and Reservation

2·10¹⁹²+3 =: 2(0)₁₉₁3_<193>; = 79 · 173 · 276519843869_<12> · 35108586452041_<14> · 10356144553255211560838847446569517_<35> · [1455522925575811754655315825187997365065439919940867408609722558444730235468189624497400802537194515833119641347147862725255416513_<130>] (suberi / GMP-ECM 6.2.1 B1=3000000, sigma=1047461786 for P35 / Jun 26, 2008) SUBMIT/RESERVE

Status

Expression:	2·10¹⁹²+3
Composite Factor:	145552292557581175465531582518799736506543991994086740860972 255844473023546818962449740080253719451583311964134714786272 5255416513 (130-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 192.90-digit and the GNFS difficulty is 129.16-digit. GNFS must be faster than SNFS. It will take about 6 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 20003_192.
Put the following polynomial file 20003_192.poly in there too.
And then, run "perl factMsieve.pl 20003_192".

20003_192.poly ^*1

# Murphy_E = 9.051537e-11, selected by Jeff Gilchrist
n: 1455522925575811754655315825187997365065439919940867408609722558444730235468189624497400802537194515833119641347147862725255416513
Y0: -8049125284187443327156184
Y1: 193931526309517
c0: -278666818250518373561764913433555
c1: 3912957804861604662604954431
c2: -5599279232453505529919
c3: -56252619107943095
c4: -329669342
c5: 43080
skew: 484355.12
type: gnfs
# selected mechanically
rlim: 9300000
alim: 9300000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
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 130-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	Mar 17, 2009
		500 / 2336
		/ 1836
45	11e6	0 / 4368 (532)
45	11e6	/ 4368 (532)
50	43e6	0 / 7534 (1246)
50	43e6	/ 7534 (1246)
55	11e7	0 / 17766 (3126)
55	11e7	/ 17766 (3126)

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

echo 1455522925575811754655315825187997365065439919940867408609722558444730235468189624497400802537194515833119641347147862725255416513 | ecm -n -c 1836 3e6

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

echo 1455522925575811754655315825187997365065439919940867408609722558444730235468189624497400802537194515833119641347147862725255416513 | ecm -n -c 4368 11e6

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

echo 1455522925575811754655315825187997365065439919940867408609722558444730235468189624497400802537194515833119641347147862725255416513 | ecm -n -c 7534 43e6

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

echo 1455522925575811754655315825187997365065439919940867408609722558444730235468189624497400802537194515833119641347147862725255416513 | 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