Contribution and Reservation

10²⁴¹-9 =: (9)₂₄₀1_<241>; = 283 · 9479 · 804191 · [4635449272261294629377779703213468681518891331407530241149702094172616188345007537004333603269446014961055482551795100190895076971961332333666078422686195261794517524762612532237148044926410799595122348018765894789486716644728093_<229>] SUBMIT/RESERVE

Status

Expression:	10²⁴¹-9
Composite Factor:	463544927226129462937777970321346868151889133140753024114970 209417261618834500753700433360326944601496105548255179510019 089507697196133233366607842268619526179451752476261253223714 8044926410799595122348018765894789486716644728093 (229-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 241.00-digit and the GNFS difficulty is 228.67-digit. SNFS must be faster than GNFS. It will take about 450 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_241.
Put the following polynomial file 99991_241.poly in there too.
And then, run "perl factMsieve.pl 99991_241".

99991_241.poly ^*1

n: 4635449272261294629377779703213468681518891331407530241149702094172616188345007537004333603269446014961055482551795100190895076971961332333666078422686195261794517524762612532237148044926410799595122348018765894789486716644728093
m: 10000000000000000000000000000000000000000
deg: 6
c6: 10
c0: -9
skew: 0.98
type: snfs
lss: 1
rlim: 73000000
alim: 73000000
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 229-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	700	Dmitry Domanov	Jun 30, 2009
		700 / 4479
		/ 3779
50	43e6	0 / 7396 (1078)
50	43e6	/ 7396 (1078)
55	11e7	0 / 17726 (3068)
55	11e7	/ 17726 (3068)
60	26e7	0 / 42006 (7625)
60	26e7	/ 42006 (7625)

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

echo 4635449272261294629377779703213468681518891331407530241149702094172616188345007537004333603269446014961055482551795100190895076971961332333666078422686195261794517524762612532237148044926410799595122348018765894789486716644728093 | ecm -n -c 3779 11e6

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

echo 4635449272261294629377779703213468681518891331407530241149702094172616188345007537004333603269446014961055482551795100190895076971961332333666078422686195261794517524762612532237148044926410799595122348018765894789486716644728093 | ecm -n -c 7396 43e6

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

echo 4635449272261294629377779703213468681518891331407530241149702094172616188345007537004333603269446014961055482551795100190895076971961332333666078422686195261794517524762612532237148044926410799595122348018765894789486716644728093 | ecm -n -c 17726 11e7

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

echo 4635449272261294629377779703213468681518891331407530241149702094172616188345007537004333603269446014961055482551795100190895076971961332333666078422686195261794517524762612532237148044926410799595122348018765894789486716644728093 | ecm -n -c 42006 26e7

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