Contribution and Reservation

(16·10²¹⁸-61)/9 =: 1(7)₂₁₇1_<219>; = 3² · 19 · 463 · 2237 · 3767 · [266464137760785282591389428891644459884472153606747186478922452063212446347576031678930570090419406648631483796157778775929598522271625056588463939454049429242617369186720009600208565899133698990025836436413_<207>] SUBMIT/RESERVE

Status

Expression:	(16·10²¹⁸-61)/9
Composite Factor:	266464137760785282591389428891644459884472153606747186478922 452063212446347576031678930570090419406648631483796157778775 929598522271625056588463939454049429242617369186720009600208 565899133698990025836436413 (207-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 219.20-digit and the GNFS difficulty is 206.43-digit. SNFS must be faster than GNFS. It will take about 84 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 17771_218.
Put the following polynomial file 17771_218.poly in there too.
And then, run "perl factMsieve.pl 17771_218".

17771_218.poly ^*1

n: 266464137760785282591389428891644459884472153606747186478922452063212446347576031678930570090419406648631483796157778775929598522271625056588463939454049429242617369186720009600208565899133698990025836436413
m: 2000000000000000000000000000000000000
deg: 6
c6: 25
c0: -61
skew: 1.16
type: snfs
lss: 1
rlim: 32000000
alim: 32000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
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 207-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	2350	Serge Batalov	Aug 2, 2008
40	3e6	2350 / 0
45	11e6	1343	Serge Batalov	Aug 2, 2008
		1343 / 3918
		/ 2575
50	43e6	0 / 7158 (734)
50	43e6	/ 7158 (734)
55	11e7	0 / 17666 (2969)
55	11e7	/ 17666 (2969)
60	26e7	0 / 41993 (7599)
60	26e7	/ 41993 (7599)

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

echo 266464137760785282591389428891644459884472153606747186478922452063212446347576031678930570090419406648631483796157778775929598522271625056588463939454049429242617369186720009600208565899133698990025836436413 | ecm -n -c 2575 11e6

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

echo 266464137760785282591389428891644459884472153606747186478922452063212446347576031678930570090419406648631483796157778775929598522271625056588463939454049429242617369186720009600208565899133698990025836436413 | ecm -n -c 7158 43e6

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

echo 266464137760785282591389428891644459884472153606747186478922452063212446347576031678930570090419406648631483796157778775929598522271625056588463939454049429242617369186720009600208565899133698990025836436413 | ecm -n -c 17666 11e7

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

echo 266464137760785282591389428891644459884472153606747186478922452063212446347576031678930570090419406648631483796157778775929598522271625056588463939454049429242617369186720009600208565899133698990025836436413 | ecm -n -c 41993 26e7

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