Contribution and Reservation

(25·10¹⁹⁶-43)/9 =: 2(7)₁₉₅3_<197>; = 19 · 110063 · [13283195116374869406267213360471432283891846525113500917310888346615731458001220247436170661003137331288146347655327440589183026648267847447073507554657824096810476381602392207801454276081009_<191>] SUBMIT/RESERVE

Status

Expression:	(25·10¹⁹⁶-43)/9
Composite Factor:	132831951163748694062672133604714322838918465251135009173108 883466157314580012202474361706610031373312881463476553274405 891830266482678474470735075546578240968104763816023922078014 54276081009 (191-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 197.40-digit and the GNFS difficulty is 190.12-digit. SNFS must be faster than GNFS. It will take about 16 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 27773_196.
Put the following polynomial file 27773_196.poly in there too.
And then, run "perl factMsieve.pl 27773_196".

27773_196.poly ^*1

n: 13283195116374869406267213360471432283891846525113500917310888346615731458001220247436170661003137331288146347655327440589183026648267847447073507554657824096810476381602392207801454276081009
m: 1000000000000000000000000000000000000000
deg: 5
c5: 250
c0: -43
skew: 0.70
type: snfs
lss: 1
rlim: 13600000
alim: 13600000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

*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 191-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 40-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
40	3e6	2111	Wataru Sakai	Sep 10, 2009
40	3e6	2111 / 2111
45	11e6	0 / 3974
45	11e6	/ 3974
50	43e6	0 / 7469 (1133)
50	43e6	/ 7469 (1133)
55	11e7	0 / 17752 (3098)
55	11e7	/ 17752 (3098)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 13283195116374869406267213360471432283891846525113500917310888346615731458001220247436170661003137331288146347655327440589183026648267847447073507554657824096810476381602392207801454276081009 | ecm -n -c 3974 11e6

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

echo 13283195116374869406267213360471432283891846525113500917310888346615731458001220247436170661003137331288146347655327440589183026648267847447073507554657824096810476381602392207801454276081009 | ecm -n -c 7469 43e6

Command line to find prime factors up to about 55-digit

echo 13283195116374869406267213360471432283891846525113500917310888346615731458001220247436170661003137331288146347655327440589183026648267847447073507554657824096810476381602392207801454276081009 | ecm -n -c 17752 11e7

Command line to find prime factors up to about 60-digit

echo 13283195116374869406267213360471432283891846525113500917310888346615731458001220247436170661003137331288146347655327440589183026648267847447073507554657824096810476381602392207801454276081009 | ecm -n -c 42014 26e7

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