Contribution and Reservation

10²⁴⁷-9 =: (9)₂₄₆1_<247>; = 44451761 · 1374902019013_<13> · 19945229229203232397679_<23> · [8203520121102992924527655815864204700509131223975388014600092794790532104667823841760331340262472670579150360549037086554402448433462480941173142178521283053388972682872569934752050230712834059531200108853_<205>] SUBMIT/RESERVE

Status

Expression:	10²⁴⁷-9
Composite Factor:	820352012110299292452765581586420470050913122397538801460009 279479053210466782384176033134026247267057915036054903708655 440244843346248094117314217852128305338897268287256993475205 0230712834059531200108853 (205-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 247.00-digit and the GNFS difficulty is 204.91-digit. SNFS must be faster than GNFS. It will take about 713 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 99991_247.
Put the following polynomial file 99991_247.poly in there too.
And then, run "perl factMsieve.pl 99991_247".

99991_247.poly ^*1

n: 8203520121102992924527655815864204700509131223975388014600092794790532104667823841760331340262472670579150360549037086554402448433462480941173142178521283053388972682872569934752050230712834059531200108853
m: 100000000000000000000000000000000000000000
deg: 6
c6: 10
c0: -9
skew: 0.98
type: snfs
lss: 1
rlim: 92000000
alim: 92000000
lpbr: 30
lpba: 30
mfbr: 61
mfba: 61
rlambda: 2.7
alambda: 2.7

*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 205-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	0 / 0
45	11e6	714	Dmitry Domanov	Jun 30, 2009
		714 / 4479
		/ 3765
50	43e6	0 / 7393 (1074)
50	43e6	/ 7393 (1074)
55	11e7	0 / 17725 (3067)
55	11e7	/ 17725 (3067)
60	26e7	0 / 42006 (7624)
60	26e7	/ 42006 (7624)

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

echo 8203520121102992924527655815864204700509131223975388014600092794790532104667823841760331340262472670579150360549037086554402448433462480941173142178521283053388972682872569934752050230712834059531200108853 | ecm -n -c 3765 11e6

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

echo 8203520121102992924527655815864204700509131223975388014600092794790532104667823841760331340262472670579150360549037086554402448433462480941173142178521283053388972682872569934752050230712834059531200108853 | ecm -n -c 7393 43e6

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

echo 8203520121102992924527655815864204700509131223975388014600092794790532104667823841760331340262472670579150360549037086554402448433462480941173142178521283053388972682872569934752050230712834059531200108853 | ecm -n -c 17725 11e7

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

echo 8203520121102992924527655815864204700509131223975388014600092794790532104667823841760331340262472670579150360549037086554402448433462480941173142178521283053388972682872569934752050230712834059531200108853 | ecm -n -c 42006 26e7

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