Contribution and Reservation

(8·10²⁰³+1)/9 =: (8)₂₀₂9_<203>; = 633488379927287_<15> · [140316526246450999561897379112199552920409139912543618683818119969691244922669376162749737000402297064074231504149955338170756330831670651911013990503337171204873631018628731944769752327247_<189>] SUBMIT/RESERVE

Status

Expression:	(8·10²⁰³+1)/9
Composite Factor:	140316526246450999561897379112199552920409139912543618683818 119969691244922669376162749737000402297064074231504149955338 170756330831670651911013990503337171204873631018628731944769 752327247 (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.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 205.30-digit and the GNFS difficulty is 188.15-digit. SNFS must be faster than GNFS. It will take about 29 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 88889_203.
Put the following polynomial file 88889_203.poly in there too.
And then, run "perl factMsieve.pl 88889_203".

88889_203.poly ^*1

n: 140316526246450999561897379112199552920409139912543618683818119969691244922669376162749737000402297064074231504149955338170756330831670651911013990503337171204873631018628731944769752327247
m: 100000000000000000000000000000000000000000
deg: 5
c5: 2
c0: 25
skew: 1.66
type: snfs
lss: 1
rlim: 18500000
alim: 18500000
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 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	0 / 0
40	3e6	0 / 266
40	3e6	/ 266
45	11e6	600	Dmitry Domanov	May 11, 2009
		600 / 4479 (677)
		/ 3879 (77)
50	43e6	0 / 7419 (1106)
50	43e6	/ 7419 (1106)
55	11e7	0 / 17732 (3078)
55	11e7	/ 17732 (3078)

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

echo 140316526246450999561897379112199552920409139912543618683818119969691244922669376162749737000402297064074231504149955338170756330831670651911013990503337171204873631018628731944769752327247 | ecm -n -c 266 3e6

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

echo 140316526246450999561897379112199552920409139912543618683818119969691244922669376162749737000402297064074231504149955338170756330831670651911013990503337171204873631018628731944769752327247 | ecm -n -c 3879 11e6

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

echo 140316526246450999561897379112199552920409139912543618683818119969691244922669376162749737000402297064074231504149955338170756330831670651911013990503337171204873631018628731944769752327247 | ecm -n -c 7419 43e6

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

echo 140316526246450999561897379112199552920409139912543618683818119969691244922669376162749737000402297064074231504149955338170756330831670651911013990503337171204873631018628731944769752327247 | ecm -n -c 17732 11e7

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