Contribution and Reservation

(85·10¹⁹⁸+41)/9 =: 9(4)₁₉₇9_<199>; = 7 · 43 · 1307 · [24006803245606825614298790932658657432237973509481133900628215675990626614280997654958972373253257935025163366296086354448305303272296742163826379409732019116193775007675116214110182189041995807_<194>] SUBMIT/RESERVE

Status

Expression:	(85·10¹⁹⁸+41)/9
Composite Factor:	240068032456068256142987909326586574322379735094811339006282 156759906266142809976549589723732532579350251633662960863544 483053032722967421638263794097320191161937750076751162141101 82189041995807 (194-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 200.63-digit and the GNFS difficulty is 193.38-digit. SNFS must be faster than GNFS. It will take about 20 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 94449_198.
Put the following polynomial file 94449_198.poly in there too.
And then, run "perl factMsieve.pl 94449_198".

94449_198.poly ^*1

n: 24006803245606825614298790932658657432237973509481133900628215675990626614280997654958972373253257935025163366296086354448305303272296742163826379409732019116193775007675116214110182189041995807
m: 5000000000000000000000000000000000000000
deg: 5
c5: 136
c0: 205
skew: 1.09
type: snfs
lss: 1
rlim: 15400000
alim: 15400000
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 194-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	2500	Dmitry Domanov	Jul 11, 2009
40	3e6	2500 / 2009
45	11e6	0 / 3871
45	11e6	/ 3871
50	43e6	0 / 7452 (1104)
50	43e6	/ 7452 (1104)
55	11e7	0 / 17749 (3091)
55	11e7	/ 17749 (3091)
60	26e7	0 / 42014 (7635)
60	26e7	/ 42014 (7635)

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

echo 24006803245606825614298790932658657432237973509481133900628215675990626614280997654958972373253257935025163366296086354448305303272296742163826379409732019116193775007675116214110182189041995807 | ecm -n -c 3871 11e6

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

echo 24006803245606825614298790932658657432237973509481133900628215675990626614280997654958972373253257935025163366296086354448305303272296742163826379409732019116193775007675116214110182189041995807 | ecm -n -c 7452 43e6

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

echo 24006803245606825614298790932658657432237973509481133900628215675990626614280997654958972373253257935025163366296086354448305303272296742163826379409732019116193775007675116214110182189041995807 | ecm -n -c 17749 11e7

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

echo 24006803245606825614298790932658657432237973509481133900628215675990626614280997654958972373253257935025163366296086354448305303272296742163826379409732019116193775007675116214110182189041995807 | ecm -n -c 42014 26e7

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