Contribution and Reservation

(25·10²¹³-1)/3 =: 8(3)₂₁₃_<214>; = 13 · 961547 · 39231453158165518643_<20> · [16993016904867797473243782110692885758656261026655530747493183438908488546972288819686384906350382774695186208518723731872352052180968541916306459299745326978232411432137555108638822030521_<188>] SUBMIT/RESERVE

Status

Expression:	(25·10²¹³-1)/3
Composite Factor:	169930169048677974732437821106928857586562610266555307474931 834389084885469722888196863849063503827746951862085187237318 723520521809685419163064592997453269782324114321375551086388 22030521 (188-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 215.10-digit and the GNFS difficulty is 187.23-digit. SNFS must be faster than GNFS. It will take about 62 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 83333_213.
Put the following polynomial file 83333_213.poly in there too.
And then, run "perl factMsieve.pl 83333_213".

83333_213.poly ^*1

n: 16993016904867797473243782110692885758656261026655530747493183438908488546972288819686384906350382774695186208518723731872352052180968541916306459299745326978232411432137555108638822030521
m: 500000000000000000000000000000000000
deg: 6
c6: 8
c0: -5
skew: 0.92
type: snfs
lss: 1
rlim: 27000000
alim: 27000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
rlambda: 2.6
alambda: 2.6

*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 188-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 22, 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 16993016904867797473243782110692885758656261026655530747493183438908488546972288819686384906350382774695186208518723731872352052180968541916306459299745326978232411432137555108638822030521 | ecm -n -c 825 1e6

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

echo 16993016904867797473243782110692885758656261026655530747493183438908488546972288819686384906350382774695186208518723731872352052180968541916306459299745326978232411432137555108638822030521 | ecm -n -c 2336 3e6

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

echo 16993016904867797473243782110692885758656261026655530747493183438908488546972288819686384906350382774695186208518723731872352052180968541916306459299745326978232411432137555108638822030521 | ecm -n -c 4479 11e6

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

echo 16993016904867797473243782110692885758656261026655530747493183438908488546972288819686384906350382774695186208518723731872352052180968541916306459299745326978232411432137555108638822030521 | ecm -n -c 7553 43e6

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