Contribution and Reservation

(79·10¹⁹⁴-7)/9 =: 8(7)₁₉₄_<195>; = 41887 · [20955852120652655424780427764647212208508075960984978102460853672446768156654278840159901109599106591013387871601637209104919850497237275951435475870264706896597459301878334036282803203327471_<191>] SUBMIT/RESERVE

Status

Expression:	(79·10¹⁹⁴-7)/9
Composite Factor:	209558521206526554247804277646472122085080759609849781024608 536724467681566542788401599011095991065910133878716016372091 049198504972372759514354758702647068965974593018783340362828 03203327471 (191-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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 195.90-digit and the GNFS difficulty is 190.32-digit. SNFS must be faster than GNFS. It will take about 14 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of SNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 87777_194.
Put the following polynomial file 87777_194.poly in there too.
And then, run "perl factMsieve.pl 87777_194".

87777_194.poly

n: 20955852120652655424780427764647212208508075960984978102460853672446768156654278840159901109599106591013387871601637209104919850497237275951435475870264706896597459301878334036282803203327471
m: 100000000000000000000000000000000000000
deg: 5
c5: 790000
c0: -7
skew: 0.10
type: snfs
lss: 1
rlim: 12900000
alim: 12900000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

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 191-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	400	Dmitry Domanov	May 10, 2009
		200	Dmitry Domanov	May 10, 2009
		736	Dmitry Domanov	Jan 11, 2010
		1336 / 4479
		/ 3143
50	43e6	0 / 7254 (896)
50	43e6	/ 7254 (896)
55	11e7	0 / 17686 (3009)
55	11e7	/ 17686 (3009)
60	26e7	0 / 41996 (7608)
60	26e7	/ 41996 (7608)

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

echo 20955852120652655424780427764647212208508075960984978102460853672446768156654278840159901109599106591013387871601637209104919850497237275951435475870264706896597459301878334036282803203327471 | ecm -n -c 3143 11e6

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

echo 20955852120652655424780427764647212208508075960984978102460853672446768156654278840159901109599106591013387871601637209104919850497237275951435475870264706896597459301878334036282803203327471 | ecm -n -c 7254 43e6

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

echo 20955852120652655424780427764647212208508075960984978102460853672446768156654278840159901109599106591013387871601637209104919850497237275951435475870264706896597459301878334036282803203327471 | ecm -n -c 17686 11e7

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

echo 20955852120652655424780427764647212208508075960984978102460853672446768156654278840159901109599106591013387871601637209104919850497237275951435475870264706896597459301878334036282803203327471 | ecm -n -c 41996 26e7

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