Contribution and Reservation

4·10²⁰⁵-9 =: 3(9)₂₀₄1_<206>; = 71 · 64845766618293547_<17> · [8688004029721909942175244154709669118988350636890249453474633452691937733425391096642439015015723799168359501222655677453767063989307255031591129889665034649016117880912025795132376173043_<187>] SUBMIT/RESERVE

Status

Expression:	4·10²⁰⁵-9
Composite Factor:	868800402972190994217524415470966911898835063689024945347463 345269193773342539109664243901501572379916835950122265567745 376706398930725503159112988966503464901611788091202579513237 6173043 (187-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 205.60-digit and the GNFS difficulty is 186.94-digit. SNFS must be faster than GNFS. It will take about 30 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 39991_205.
Put the following polynomial file 39991_205.poly in there too.
And then, run "perl factMsieve.pl 39991_205".

39991_205.poly ^*1

n: 8688004029721909942175244154709669118988350636890249453474633452691937733425391096642439015015723799168359501222655677453767063989307255031591129889665034649016117880912025795132376173043
m: 100000000000000000000000000000000000000000
deg: 5
c5: 4
c0: -9
skew: 1.18
type: snfs
lss: 1
rlim: 18700000
alim: 18700000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
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 187-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	Nov 3, 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 8688004029721909942175244154709669118988350636890249453474633452691937733425391096642439015015723799168359501222655677453767063989307255031591129889665034649016117880912025795132376173043 | ecm -n -c 825 1e6

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

echo 8688004029721909942175244154709669118988350636890249453474633452691937733425391096642439015015723799168359501222655677453767063989307255031591129889665034649016117880912025795132376173043 | ecm -n -c 2336 3e6

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

echo 8688004029721909942175244154709669118988350636890249453474633452691937733425391096642439015015723799168359501222655677453767063989307255031591129889665034649016117880912025795132376173043 | ecm -n -c 4479 11e6

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

echo 8688004029721909942175244154709669118988350636890249453474633452691937733425391096642439015015723799168359501222655677453767063989307255031591129889665034649016117880912025795132376173043 | ecm -n -c 7553 43e6

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