Contribution and Reservation

(65·10¹⁹⁷+43)/9 =: 7(2)₁₉₆7_<198>; = 11 · 337 · 5881 · [33128142207473777176945404153982601803048577023208399107348447299009815628994123133828678566876364239193891794405342788533236876415154600146050256727047700544305060079593266736695481983456081_<191>] SUBMIT/RESERVE

Status

Expression:	(65·10¹⁹⁷+43)/9
Composite Factor:	331281422074737771769454041539826018030485770232083991073484 472990098156289941231338286785668763642391938917944053427885 332368764151546001460502567270477005443050600795932667366954 81983456081 (191-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 200.21-digit and the GNFS difficulty is 190.52-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 72227_197.
Put the following polynomial file 72227_197.poly in there too.
And then, run "perl factMsieve.pl 72227_197".

72227_197.poly ^*1

n: 33128142207473777176945404153982601803048577023208399107348447299009815628994123133828678566876364239193891794405342788533236876415154600146050256727047700544305060079593266736695481983456081
m: 5000000000000000000000000000000000000000
deg: 5
c5: 52
c0: 1075
skew: 1.83
type: snfs
lss: 1
rlim: 15200000
alim: 15200000
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 191-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 20-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
20	11e3	74	Max Dettweiler	Mar 6, 2009
20	11e3	74 / 74
25	5e4	0 / 204
25	5e4	/ 204
30	25e4	0 / 430 (48)
30	25e4	/ 430 (48)
35	1e6	0 / 904 (118)
35	1e6	/ 904 (118)
40	3e6	0 / 2350 (322)
40	3e6	/ 2350 (322)

Command line to find prime factors up to about 25-digit

echo 33128142207473777176945404153982601803048577023208399107348447299009815628994123133828678566876364239193891794405342788533236876415154600146050256727047700544305060079593266736695481983456081 | ecm -n -c 204 5e4

Command line to find prime factors up to about 30-digit

echo 33128142207473777176945404153982601803048577023208399107348447299009815628994123133828678566876364239193891794405342788533236876415154600146050256727047700544305060079593266736695481983456081 | ecm -n -c 430 25e4

Command line to find prime factors up to about 35-digit

echo 33128142207473777176945404153982601803048577023208399107348447299009815628994123133828678566876364239193891794405342788533236876415154600146050256727047700544305060079593266736695481983456081 | ecm -n -c 904 1e6

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

echo 33128142207473777176945404153982601803048577023208399107348447299009815628994123133828678566876364239193891794405342788533236876415154600146050256727047700544305060079593266736695481983456081 | ecm -n -c 2350 3e6

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