Contribution and Reservation

8·10¹⁸⁴+3 =: 8(0)₁₈₃3_<185>; = 7 · 11 · 2376827 · 2051700983727498703133_<22> · 1110318608754654894718951253_<28> · [191884548366709150431536014176499504017574488166176366425076129509061213590000797073040315891921077084427847623834050555538185693_<129>] SUBMIT/RESERVE

Status

Expression:	8·10¹⁸⁴+3
Composite Factor:	191884548366709150431536014176499504017574488166176366425076 129509061213590000797073040315891921077084427847623834050555 538185693 (129-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 185.60-digit and the GNFS difficulty is 128.28-digit. GNFS may be faster than SNFS. It will take about 5 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 80003_184.
Put the following polynomial file 80003_184.poly in there too.
And then, run "perl factMsieve.pl 80003_184".

80003_184.poly ^*1

# Murphy_E = 9.138569e-11, selected by Jeff Gilchrist
n: 191884548366709150431536014176499504017574488166176366425076129509061213590000797073040315891921077084427847623834050555538185693
Y0: -5255035719953050427007553
Y1: 162880655429063
c0: 35518694983023701538747700790760
c1: 706604018367058233074458736
c2: -1796133301785010656598
c3: -29883179064605314
c4: 26680209807
c5: 47880
skew: 314855.18
type: gnfs
# selected mechanically
rlim: 8800000
alim: 8800000
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 129-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 191884548366709150431536014176499504017574488166176366425076129509061213590000797073040315891921077084427847623834050555538185693 | ecm -n -c 1836 3e6

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

echo 191884548366709150431536014176499504017574488166176366425076129509061213590000797073040315891921077084427847623834050555538185693 | ecm -n -c 4368 11e6

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

echo 191884548366709150431536014176499504017574488166176366425076129509061213590000797073040315891921077084427847623834050555538185693 | ecm -n -c 7534 43e6

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

echo 191884548366709150431536014176499504017574488166176366425076129509061213590000797073040315891921077084427847623834050555538185693 | 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