Contribution and Reservation

(25·10¹⁹³+11)/9 =: 2(7)₁₉₂9_<194>; = 487219 · [57012919811784388083752435306869760370136997485274132941814210401847583484588609593997314919528544202458807595306787661765608027966433529434972317946914586208209814842561102456549883682241_<188>] SUBMIT/RESERVE

Status

Expression:	(25·10¹⁹³+11)/9
Composite Factor:	570129198117843880837524353068697603701369974852741329418142 104018475834845886095939973149195285442024588075953067876617 656080279664335294349723179469145862082098148425611024565498 83682241 (188-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 194.40-digit and the GNFS difficulty is 187.76-digit. SNFS must be faster than GNFS. It will take about 13 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 27779_193.
Put the following polynomial file 27779_193.poly in there too.
And then, run "perl factMsieve.pl 27779_193".

27779_193.poly ^*1

n: 57012919811784388083752435306869760370136997485274132941814210401847583484588609593997314919528544202458807595306787661765608027966433529434972317946914586208209814842561102456549883682241
m: 500000000000000000000000000000000000000
deg: 5
c5: 8
c0: 11
skew: 1.07
type: snfs
lss: 1
rlim: 12200000
alim: 12200000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

*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 188-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	1733	Wataru Sakai	Aug 3, 2009
		1733 / 2336
		/ 603
45	11e6	0 / 4096 (175)
45	11e6	/ 4096 (175)
50	43e6	0 / 7488 (1168)
50	43e6	/ 7488 (1168)
55	11e7	0 / 17756 (3106)
55	11e7	/ 17756 (3106)

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

echo 57012919811784388083752435306869760370136997485274132941814210401847583484588609593997314919528544202458807595306787661765608027966433529434972317946914586208209814842561102456549883682241 | ecm -n -c 603 3e6

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

echo 57012919811784388083752435306869760370136997485274132941814210401847583484588609593997314919528544202458807595306787661765608027966433529434972317946914586208209814842561102456549883682241 | ecm -n -c 4096 11e6

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

echo 57012919811784388083752435306869760370136997485274132941814210401847583484588609593997314919528544202458807595306787661765608027966433529434972317946914586208209814842561102456549883682241 | ecm -n -c 7488 43e6

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

echo 57012919811784388083752435306869760370136997485274132941814210401847583484588609593997314919528544202458807595306787661765608027966433529434972317946914586208209814842561102456549883682241 | ecm -n -c 17756 11e7

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