Contribution and Reservation

(5·10¹⁸⁵-11)/3 =: 1(6)₁₈₄3_<186>; = 7² · 59 · 113 · 10613443 · 376249199 · 797447023 · 8135443271429033355255125923_<28> · [19692791211172800770661361543715530698386254859842480921441843066219836880760087738951228836681805302494516289712201674684984637_<128>] SUBMIT/RESERVE

Status

Expression:	(5·10¹⁸⁵-11)/3
Composite Factor:	196927912111728007706613615437155306983862548598424809214418 430662198368807600877389512288366818053024945162897122016746 84984637 (128-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 185.70-digit and the GNFS difficulty is 127.29-digit. GNFS must 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 16663_185.
Put the following polynomial file 16663_185.poly in there too.
And then, run "perl factMsieve.pl 16663_185".

16663_185.poly ^*1

# Murphy_E = 1.027464e-10, selected by Jeff Gilchrist
n: 19692791211172800770661361543715530698386254859842480921441843066219836880760087738951228836681805302494516289712201674684984637
Y0: -3912516862124374238665335
Y1: 100050211141963
c0: -6205241930850353191497698806336
c1: 596383772445320160036275336
c2: 2714425793852706710744
c3: -8009974377609284
c4: -15689406301
c5: 21480
skew: 385821.23
type: gnfs
# selected mechanically
rlim: 8300000
alim: 8300000
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 128-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 19692791211172800770661361543715530698386254859842480921441843066219836880760087738951228836681805302494516289712201674684984637 | ecm -n -c 1836 3e6

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

echo 19692791211172800770661361543715530698386254859842480921441843066219836880760087738951228836681805302494516289712201674684984637 | ecm -n -c 4368 11e6

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

echo 19692791211172800770661361543715530698386254859842480921441843066219836880760087738951228836681805302494516289712201674684984637 | ecm -n -c 7534 43e6

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

echo 19692791211172800770661361543715530698386254859842480921441843066219836880760087738951228836681805302494516289712201674684984637 | 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