Contribution and Reservation

(68·10¹⁹⁹+13)/9 =: 7(5)₁₉₈7_<200>; = 7 · 11 · 151 · [6498284643980008218418814445304511529677092590999875768087688617489941993253251531397226761465172061198551264776430339344246629014840935370736695240006498284643980008218418814445304511529677092591_<196>] SUBMIT/RESERVE

Status

Expression:	(68·10¹⁹⁹+13)/9
Composite Factor:	649828464398000821841881444530451152967709259099987576808768 861748994199325325153139722676146517206119855126477643033934 424662901484093537073669524000649828464398000821841881444530 4511529677092591 (196-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 201.53-digit and the GNFS difficulty is 195.81-digit. SNFS must be faster than GNFS. It will take about 22 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 75557_199.
Put the following polynomial file 75557_199.poly in there too.
And then, run "perl factMsieve.pl 75557_199".

75557_199.poly ^*1

n: 6498284643980008218418814445304511529677092590999875768087688617489941993253251531397226761465172061198551264776430339344246629014840935370736695240006498284643980008218418814445304511529677092591
m: 10000000000000000000000000000000000000000
deg: 5
c5: 34
c0: 65
skew: 1.14
type: snfs
lss: 1
rlim: 16000000
alim: 16000000
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 196-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	470	Serge Batalov	Nov 25, 2008
		470 / 2350
		/ 1880
45	11e6	0 / 4377 (545)
45	11e6	/ 4377 (545)
50	43e6	0 / 7536 (1248)
50	43e6	/ 7536 (1248)
55	11e7	0 / 17766 (3126)
55	11e7	/ 17766 (3126)

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

echo 6498284643980008218418814445304511529677092590999875768087688617489941993253251531397226761465172061198551264776430339344246629014840935370736695240006498284643980008218418814445304511529677092591 | ecm -n -c 1880 3e6

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

echo 6498284643980008218418814445304511529677092590999875768087688617489941993253251531397226761465172061198551264776430339344246629014840935370736695240006498284643980008218418814445304511529677092591 | ecm -n -c 4377 11e6

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

echo 6498284643980008218418814445304511529677092590999875768087688617489941993253251531397226761465172061198551264776430339344246629014840935370736695240006498284643980008218418814445304511529677092591 | ecm -n -c 7536 43e6

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

echo 6498284643980008218418814445304511529677092590999875768087688617489941993253251531397226761465172061198551264776430339344246629014840935370736695240006498284643980008218418814445304511529677092591 | ecm -n -c 17766 11e7

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