Contribution and Reservation

(7·10²⁰⁶-43)/9 =: (7)₂₀₅3_<206>; = 19 · 53 · 117517 · [657242083716508989079792269550722296797134168378366823859537504322857231590189400371297272621587346649964943505334234494854827762947063212851629831407330944489332670386388330165046228328466882910767_<198>] SUBMIT/RESERVE

Status

Expression:	(7·10²⁰⁶-43)/9
Composite Factor:	657242083716508989079792269550722296797134168378366823859537 504322857231590189400371297272621587346649964943505334234494 854827762947063212851629831407330944489332670386388330165046 228328466882910767 (198-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 206.85-digit and the GNFS difficulty is 197.82-digit. SNFS must be faster than GNFS. It will take about 33 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 77773_206.
Put the following polynomial file 77773_206.poly in there too.
And then, run "perl factMsieve.pl 77773_206".

77773_206.poly ^*1

n: 657242083716508989079792269550722296797134168378366823859537504322857231590189400371297272621587346649964943505334234494854827762947063212851629831407330944489332670386388330165046228328466882910767
m: 100000000000000000000000000000000000000000
deg: 5
c5: 70
c0: -43
skew: 0.91
type: snfs
lss: 1
rlim: 19600000
alim: 19600000
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 198-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	118	Makoto Kamada	May 31, 2009
		400	Serge Batalov	Jun 4, 2009
		518 / 343
40	3e6	200	Serge Batalov	Jun 4, 2009
		200 / 2209
		/ 2009
45	11e6	0 / 4412 (583)
45	11e6	/ 4412 (583)
50	43e6	0 / 7543 (1258)
50	43e6	/ 7543 (1258)
55	11e7	0 / 17767 (3129)
55	11e7	/ 17767 (3129)

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

echo 657242083716508989079792269550722296797134168378366823859537504322857231590189400371297272621587346649964943505334234494854827762947063212851629831407330944489332670386388330165046228328466882910767 | ecm -n -c 2009 3e6

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

echo 657242083716508989079792269550722296797134168378366823859537504322857231590189400371297272621587346649964943505334234494854827762947063212851629831407330944489332670386388330165046228328466882910767 | ecm -n -c 4412 11e6

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

echo 657242083716508989079792269550722296797134168378366823859537504322857231590189400371297272621587346649964943505334234494854827762947063212851629831407330944489332670386388330165046228328466882910767 | ecm -n -c 7543 43e6

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

echo 657242083716508989079792269550722296797134168378366823859537504322857231590189400371297272621587346649964943505334234494854827762947063212851629831407330944489332670386388330165046228328466882910767 | ecm -n -c 17767 11e7

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