Contribution and Reservation

(52·10²⁰⁴-43)/9 =: 5(7)₂₀₃3_<205>; = 47 · 2119643 · [57996295640529207319825342505014747292478906878324861407339738370613190450625740938227421674890212371047286031614835840107777460616112560522187671263688390257706863119571066446223193062366230637913_<197>] SUBMIT/RESERVE

Status

Expression:	(52·10²⁰⁴-43)/9
Composite Factor:	579962956405292073198253425050147472924789068783248614073397 383706131904506257409382274216748902123710472860316148358401 077774606161125605221876712636883902577068631195710664462231 93062366230637913 (197-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 206.41-digit and the GNFS difficulty is 196.76-digit. SNFS must be faster than GNFS. It will take about 32 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 57773_204.
Put the following polynomial file 57773_204.poly in there too.
And then, run "perl factMsieve.pl 57773_204".

57773_204.poly ^*1

n: 57996295640529207319825342505014747292478906878324861407339738370613190450625740938227421674890212371047286031614835840107777460616112560522187671263688390257706863119571066446223193062366230637913
m: 100000000000000000000000000000000000000000
deg: 5
c5: 26
c0: -215
skew: 1.53
type: snfs
lss: 1
rlim: 19300000
alim: 19300000
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 197-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	Apr 3, 2009
		100	Lionel Debroux	Oct 2, 2009
		200	Lionel Debroux	Oct 3, 2009
		100	Lionel Debroux	Oct 3, 2009
		600	Lionel Debroux	Oct 3, 2009
		1118 / 904
40	3e6	0 / 2045
40	3e6	/ 2045
45	11e6	0 / 4429 (593)
45	11e6	/ 4429 (593)
50	43e6	0 / 7547 (1263)
50	43e6	/ 7547 (1263)
55	11e7	0 / 17768 (3131)
55	11e7	/ 17768 (3131)

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

echo 57996295640529207319825342505014747292478906878324861407339738370613190450625740938227421674890212371047286031614835840107777460616112560522187671263688390257706863119571066446223193062366230637913 | ecm -n -c 2045 3e6

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

echo 57996295640529207319825342505014747292478906878324861407339738370613190450625740938227421674890212371047286031614835840107777460616112560522187671263688390257706863119571066446223193062366230637913 | ecm -n -c 4429 11e6

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

echo 57996295640529207319825342505014747292478906878324861407339738370613190450625740938227421674890212371047286031614835840107777460616112560522187671263688390257706863119571066446223193062366230637913 | ecm -n -c 7547 43e6

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

echo 57996295640529207319825342505014747292478906878324861407339738370613190450625740938227421674890212371047286031614835840107777460616112560522187671263688390257706863119571066446223193062366230637913 | ecm -n -c 17768 11e7

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