Contribution and Reservation

(64·10²²²+53)/9 =: 7(1)₂₂₁7_<223>; = 13² · 246803 · 4770541 · 13798085473433_<14> · 133768138077661809781256269946047_<33> · [19362488808251570928408592638883352854542686275616458245323596532144869362459816277922928623970254458332657237249177487701925662754754556973546573906513628028715141_<164>] (Wataru Sakai / GMP-ECM 6.0.1 / B1=11000000, sigma=4134011925 for P33 / Jun 7, 2005) SUBMIT/RESERVE

Status

Expression:	(64·10²²²+53)/9
Composite Factor:	193624888082515709284085926388833528545426862756164582453235 965321448693624598162779229286239702544583326572372491774877 01925662754754556973546573906513628028715141 (164-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 223.81-digit and the GNFS difficulty is 163.29-digit. SNFS must be faster than GNFS. It will take about 120 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 71117_222.
Put the following polynomial file 71117_222.poly in there too.
And then, run "perl factMsieve.pl 71117_222".

71117_222.poly ^*1

n: 19362488808251570928408592638883352854542686275616458245323596532144869362459816277922928623970254458332657237249177487701925662754754556973546573906513628028715141
m: 20000000000000000000000000000000000000
deg: 6
c6: 1
c0: 53
skew: 1.94
type: snfs
lss: 1
rlim: 38000000
alim: 38000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
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 164-digit composite number are not reported yet. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)
20	11e3	0 / 74
20	11e3	/ 74
25	5e4	0 / 214 (21)
25	5e4	/ 214 (21)
30	25e4	0 / 430 (50)
30	25e4	/ 430 (50)
35	1e6	0 / 904 (118)
35	1e6	/ 904 (118)
40	3e6	0 / 2350 (322)
40	3e6	/ 2350 (322)

Command line to find prime factors up to about 20-digit

echo 19362488808251570928408592638883352854542686275616458245323596532144869362459816277922928623970254458332657237249177487701925662754754556973546573906513628028715141 | ecm -n -c 74 11e3

Command line to find prime factors up to about 25-digit

echo 19362488808251570928408592638883352854542686275616458245323596532144869362459816277922928623970254458332657237249177487701925662754754556973546573906513628028715141 | ecm -n -c 214 5e4

Command line to find prime factors up to about 30-digit

echo 19362488808251570928408592638883352854542686275616458245323596532144869362459816277922928623970254458332657237249177487701925662754754556973546573906513628028715141 | ecm -n -c 430 25e4

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

echo 19362488808251570928408592638883352854542686275616458245323596532144869362459816277922928623970254458332657237249177487701925662754754556973546573906513628028715141 | ecm -n -c 904 1e6

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

echo 19362488808251570928408592638883352854542686275616458245323596532144869362459816277922928623970254458332657237249177487701925662754754556973546573906513628028715141 | ecm -n -c 2350 3e6

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