Contribution and Reservation

(29·10²⁰²+43)/9 =: 3(2)₂₀₁7_<203>; = 13 · 37 · 67 · 281 · [3558191267332394437084509852343283054495674668830243271205718754451956767779787910451319385297183140705741226270253730815689704519576511927922136664899717961809638656719976101715093588466935256121_<196>] SUBMIT/RESERVE

Status

Expression:	(29·10²⁰²+43)/9
Composite Factor:	355819126733239443708450985234328305449567466883024327120571 875445195676777978791045131938529718314070574122627025373081 568970451957651192792213666489971796180963865671997610171509 3588466935256121 (196-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 204.37-digit and the GNFS difficulty is 195.55-digit. SNFS must be faster than GNFS. It will take about 27 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 32227_202.
Put the following polynomial file 32227_202.poly in there too.
And then, run "perl factMsieve.pl 32227_202".

32227_202.poly ^*1

n: 3558191267332394437084509852343283054495674668830243271205718754451956767779787910451319385297183140705741226270253730815689704519576511927922136664899717961809638656719976101715093588466935256121
m: 20000000000000000000000000000000000000000
deg: 5
c5: 725
c0: 344
skew: 0.86
type: snfs
lss: 1
rlim: 17800000
alim: 17800000
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 196-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 13, 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 3558191267332394437084509852343283054495674668830243271205718754451956767779787910451319385297183140705741226270253730815689704519576511927922136664899717961809638656719976101715093588466935256121 | ecm -n -c 825 1e6

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

echo 3558191267332394437084509852343283054495674668830243271205718754451956767779787910451319385297183140705741226270253730815689704519576511927922136664899717961809638656719976101715093588466935256121 | ecm -n -c 2336 3e6

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

echo 3558191267332394437084509852343283054495674668830243271205718754451956767779787910451319385297183140705741226270253730815689704519576511927922136664899717961809638656719976101715093588466935256121 | ecm -n -c 4479 11e6

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

echo 3558191267332394437084509852343283054495674668830243271205718754451956767779787910451319385297183140705741226270253730815689704519576511927922136664899717961809638656719976101715093588466935256121 | ecm -n -c 7553 43e6

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