Contribution and Reservation

(28·10¹⁹⁹+53)/9 =: 3(1)₁₉₈7_<200>; = 37 · 131 · [6418632372830846113288861380464433899548403365197258327029319395731609472067487334662907181991151456800311762143823212525502601838479701075120922449166723975884281227792678174357563670540769777411_<196>] SUBMIT/RESERVE

Status

Expression:	(28·10¹⁹⁹+53)/9
Composite Factor:	641863237283084611328886138046443389954840336519725832702931 939573160947206748733466290718199115145680031176214382321252 550260183847970107512092244916672397588428122779267817435756 3670540769777411 (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 201.15-digit and the GNFS difficulty is 195.81-digit. SNFS must be faster than GNFS. It will take about 21 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 31117_199.
Put the following polynomial file 31117_199.poly in there too.
And then, run "perl factMsieve.pl 31117_199".

31117_199.poly ^*1

n: 6418632372830846113288861380464433899548403365197258327029319395731609472067487334662907181991151456800311762143823212525502601838479701075120922449166723975884281227792678174357563670540769777411
m: 10000000000000000000000000000000000000000
deg: 5
c5: 14
c0: 265
skew: 1.80
type: snfs
lss: 1
rlim: 15800000
alim: 15800000
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 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 1, 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 6418632372830846113288861380464433899548403365197258327029319395731609472067487334662907181991151456800311762143823212525502601838479701075120922449166723975884281227792678174357563670540769777411 | ecm -n -c 3974 11e6

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

echo 6418632372830846113288861380464433899548403365197258327029319395731609472067487334662907181991151456800311762143823212525502601838479701075120922449166723975884281227792678174357563670540769777411 | ecm -n -c 7469 43e6

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

echo 6418632372830846113288861380464433899548403365197258327029319395731609472067487334662907181991151456800311762143823212525502601838479701075120922449166723975884281227792678174357563670540769777411 | ecm -n -c 17752 11e7

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

echo 6418632372830846113288861380464433899548403365197258327029319395731609472067487334662907181991151456800311762143823212525502601838479701075120922449166723975884281227792678174357563670540769777411 | ecm -n -c 42014 26e7

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