Contribution and Reservation

(10²⁰⁷-7)/3 =: (3)₂₀₆1_<207>; = 42491 · [7844798506350364390890619974425956869297812085696578883371380606089132600629152840209299224149427721948961740917684529272865626446384724608348434570458057784785797776784103300306731621598299247683823241_<202>] RESERVED

Status

Expression:	(10²⁰⁷-7)/3
Composite Factor:	784479850635036439089061997442595686929781208569657888337138 060608913260062915284020929922414942772194896174091768452927 286562644638472460834843457045805778478579777678410330030673 1621598299247683823241 (202-digit)
Status:	Not factored. Reserved by Sinkiti Sibata 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 207.90-digit and the GNFS difficulty is 201.89-digit. SNFS must be faster than GNFS. It will take about 35 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 33331_207.
Put the following polynomial file 33331_207.poly in there too.
And then, run "perl factMsieve.pl 33331_207".

33331_207.poly ^*1

n: 7844798506350364390890619974425956869297812085696578883371380606089132600629152840209299224149427721948961740917684529272865626446384724608348434570458057784785797776784103300306731621598299247683823241
m: 200000000000000000000000000000000000000000
deg: 5
c5: 25
c0: -56
skew: 1.18
type: snfs
lss: 1
rlim: 20000000
alim: 20000000
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 202-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	0 / 0
40	3e6	300	Serge Batalov	Feb 17, 2009
		300 / 2336
		/ 2036
45	11e6	0 / 4413 (590)
45	11e6	/ 4413 (590)
50	43e6	0 / 7542 (1258)
50	43e6	/ 7542 (1258)
55	11e7	0 / 17767 (3129)
55	11e7	/ 17767 (3129)

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

echo 7844798506350364390890619974425956869297812085696578883371380606089132600629152840209299224149427721948961740917684529272865626446384724608348434570458057784785797776784103300306731621598299247683823241 | ecm -n -c 2036 3e6

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

echo 7844798506350364390890619974425956869297812085696578883371380606089132600629152840209299224149427721948961740917684529272865626446384724608348434570458057784785797776784103300306731621598299247683823241 | ecm -n -c 4413 11e6

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

echo 7844798506350364390890619974425956869297812085696578883371380606089132600629152840209299224149427721948961740917684529272865626446384724608348434570458057784785797776784103300306731621598299247683823241 | ecm -n -c 7542 43e6

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

echo 7844798506350364390890619974425956869297812085696578883371380606089132600629152840209299224149427721948961740917684529272865626446384724608348434570458057784785797776784103300306731621598299247683823241 | ecm -n -c 17767 11e7

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