Contribution and Reservation

(16·10²³¹-1)/3 =: 5(3)₂₃₁_<232>; = 31 · 277 · 7710733 · 4280023159_<10> · 998148406067_<12> · [18854731986613325965774130431915756435920897280369930080313080486123312847334040260710073874364087875322530539548956267699728925232946911944258007027196992960307185603033870902249922450177353428022991_<200>] SUBMIT/RESERVE

Status

Expression:	(16·10²³¹-1)/3
Composite Factor:	188547319866133259657741304319157564359208972803699300803130 804861233128473340402607100738743640878753225305395489562676 997289252329469119442580070271969929603071856030338709022499 22450177353428022991 (200-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.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 234.30-digit and the GNFS difficulty is 199.28-digit. SNFS must be faster than GNFS. It will take about 269 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 53333_231.
Put the following polynomial file 53333_231.poly in there too.
And then, run "perl factMsieve.pl 53333_231".

53333_231.poly ^*1

n: 18854731986613325965774130431915756435920897280369930080313080486123312847334040260710073874364087875322530539548956267699728925232946911944258007027196992960307185603033870902249922450177353428022991
m: 1000000000000000000000000000000000000000
deg: 6
c6: 2
c0: -125
skew: 1.99
type: snfs
lss: 1
rlim: 56000000
alim: 56000000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.7
alambda: 2.7

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: deg=expt<=105?4:expt<=210?5:6 or expt<=144?4:6; d=log10(c[deg])+deg*log10(m)[digits]; time=10^(d/30-4)[hours]; skew=|c0/c[deg]|^(1/deg); rlim=round(7*10^(d/60+3)); lpbr=floor(d/25+21); mfbr=floor(d/8+31); rlambda=floor(d/25+18)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 200-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 30-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
30	25e4	430	Makoto Kamada	Oct 31, 2008
30	25e4	430 / 430
35	1e6	0 / 825
35	1e6	/ 825
40	3e6	0 / 2336 (294)
40	3e6	/ 2336 (294)
45	11e6	0 / 4479 (677)
45	11e6	/ 4479 (677)
50	43e6	0 / 7553 (1277)
50	43e6	/ 7553 (1277)

Command line to find prime factors up to about 35-digit

echo 18854731986613325965774130431915756435920897280369930080313080486123312847334040260710073874364087875322530539548956267699728925232946911944258007027196992960307185603033870902249922450177353428022991 | ecm -n -c 825 1e6

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

echo 18854731986613325965774130431915756435920897280369930080313080486123312847334040260710073874364087875322530539548956267699728925232946911944258007027196992960307185603033870902249922450177353428022991 | ecm -n -c 2336 3e6

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

echo 18854731986613325965774130431915756435920897280369930080313080486123312847334040260710073874364087875322530539548956267699728925232946911944258007027196992960307185603033870902249922450177353428022991 | ecm -n -c 4479 11e6

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

echo 18854731986613325965774130431915756435920897280369930080313080486123312847334040260710073874364087875322530539548956267699728925232946911944258007027196992960307185603033870902249922450177353428022991 | ecm -n -c 7553 43e6

Submit factors

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