Contribution and Reservation

(10²¹⁰+17)/9 =: (1)₂₀₉3_<210>; = 991 · 17033 · [6582527613851446978131730819618752244107085954717989475947006360900491620682609825013574653008474800244477708589488281346603735332968305847034815192608016332462195046388618988800401944934168042595957471_<202>] SUBMIT/RESERVE

Status

Expression:	(10²¹⁰+17)/9
Composite Factor:	658252761385144697813173081961875224410708595471798947594700 636090049162068260982501357465300847480024447770858948828134 660373533296830584703481519260801633246219504638861898880040 1944934168042595957471 (202-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 210.00-digit and the GNFS difficulty is 201.82-digit. SNFS must be faster than GNFS. It will take about 42 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 11113_210.
Put the following polynomial file 11113_210.poly in there too.
And then, run "perl factMsieve.pl 11113_210".

11113_210.poly ^*1

n: 6582527613851446978131730819618752244107085954717989475947006360900491620682609825013574653008474800244477708589488281346603735332968305847034815192608016332462195046388618988800401944934168042595957471
m: 1000000000000000000000000000000000000000000
deg: 5
c5: 1
c0: 17
skew: 1.76
type: snfs
lss: 1
rlim: 22000000
alim: 22000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
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 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	2500	Dmitry Domanov	Jun 30, 2009
40	3e6	2500 / 1991
45	11e6	0 / 3867
45	11e6	/ 3867
50	43e6	0 / 7451 (1103)
50	43e6	/ 7451 (1103)
55	11e7	0 / 17748 (3091)
55	11e7	/ 17748 (3091)
60	26e7	0 / 42014 (7634)
60	26e7	/ 42014 (7634)

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

echo 6582527613851446978131730819618752244107085954717989475947006360900491620682609825013574653008474800244477708589488281346603735332968305847034815192608016332462195046388618988800401944934168042595957471 | ecm -n -c 3867 11e6

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

echo 6582527613851446978131730819618752244107085954717989475947006360900491620682609825013574653008474800244477708589488281346603735332968305847034815192608016332462195046388618988800401944934168042595957471 | ecm -n -c 7451 43e6

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

echo 6582527613851446978131730819618752244107085954717989475947006360900491620682609825013574653008474800244477708589488281346603735332968305847034815192608016332462195046388618988800401944934168042595957471 | ecm -n -c 17748 11e7

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

echo 6582527613851446978131730819618752244107085954717989475947006360900491620682609825013574653008474800244477708589488281346603735332968305847034815192608016332462195046388618988800401944934168042595957471 | ecm -n -c 42014 26e7

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