Contribution and Reservation

(17·10¹⁹⁴+1)/9 =: 1(8)₁₉₃9_<195>; = 3 · 7 · 69997 · [128501349982270593153916724926911077746113533361558276911792062441375983384926625351214976484630898391488131048397916977998981513417846403545790662381373411846146391912639037515817949265097_<189>] SUBMIT/RESERVE

Status

Expression:	(17·10¹⁹⁴+1)/9
Composite Factor:	128501349982270593153916724926911077746113533361558276911792 062441375983384926625351214976484630898391488131048397916977 998981513417846403545790662381373411846146391912639037515817 949265097 (189-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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 195.23-digit and the GNFS difficulty is 188.11-digit. SNFS must be faster than GNFS. It will take about 13 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of SNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 18889_194.
Put the following polynomial file 18889_194.poly in there too.
And then, run "perl factMsieve.pl 18889_194".

18889_194.poly

n: 128501349982270593153916724926911077746113533361558276911792062441375983384926625351214976484630898391488131048397916977998981513417846403545790662381373411846146391912639037515817949265097
m: 100000000000000000000000000000000000000
deg: 5
c5: 170000
c0: 1
skew: 0.09
type: snfs
lss: 1
rlim: 12600000
alim: 12600000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

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 189-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	825	Wataru Sakai	Dec 10, 2009
35	1e6	825 / 825
40	3e6	0 / 2111
40	3e6	/ 2111
45	11e6	0 / 4441 (612)
45	11e6	/ 4441 (612)
50	43e6	0 / 7548 (1266)
50	43e6	/ 7548 (1266)
55	11e7	0 / 17769 (3131)
55	11e7	/ 17769 (3131)

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

echo 128501349982270593153916724926911077746113533361558276911792062441375983384926625351214976484630898391488131048397916977998981513417846403545790662381373411846146391912639037515817949265097 | ecm -n -c 2111 3e6

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

echo 128501349982270593153916724926911077746113533361558276911792062441375983384926625351214976484630898391488131048397916977998981513417846403545790662381373411846146391912639037515817949265097 | ecm -n -c 4441 11e6

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

echo 128501349982270593153916724926911077746113533361558276911792062441375983384926625351214976484630898391488131048397916977998981513417846403545790662381373411846146391912639037515817949265097 | ecm -n -c 7548 43e6

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

echo 128501349982270593153916724926911077746113533361558276911792062441375983384926625351214976484630898391488131048397916977998981513417846403545790662381373411846146391912639037515817949265097 | ecm -n -c 17769 11e7

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