Contribution and Reservation

(82·10¹⁹⁸+71)/9 =: 9(1)₁₉₇9_<199>; = 1075435001_<10> · [8472023974149146286815999873813955503863232652134139635567906452312975362340016596792083681783675842173106946433772533604856246547913044082811203864761614831532818142963817402397442624346119_<190>] SUBMIT/RESERVE

Status

Expression:	(82·10¹⁹⁸+71)/9
Composite Factor:	847202397414914628681599987381395550386323265213413963556790 645231297536234001659679208368178367584217310694643377253360 485624654791304408281120386476161483153281814296381740239744 2624346119 (190-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 201.31-digit and the GNFS difficulty is 189.93-digit. SNFS must be faster than GNFS. It will take about 21 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 91119_198.
Put the following polynomial file 91119_198.poly in there too.
And then, run "perl factMsieve.pl 91119_198".

91119_198.poly ^*1

n: 8472023974149146286815999873813955503863232652134139635567906452312975362340016596792083681783675842173106946433772533604856246547913044082811203864761614831532818142963817402397442624346119
m: 5000000000000000000000000000000000000000
deg: 5
c5: 656
c0: 1775
skew: 1.22
type: snfs
lss: 1
rlim: 15900000
alim: 15900000
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 190-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 8472023974149146286815999873813955503863232652134139635567906452312975362340016596792083681783675842173106946433772533604856246547913044082811203864761614831532818142963817402397442624346119 | ecm -n -c 204 5e4

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

echo 8472023974149146286815999873813955503863232652134139635567906452312975362340016596792083681783675842173106946433772533604856246547913044082811203864761614831532818142963817402397442624346119 | ecm -n -c 430 25e4

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

echo 8472023974149146286815999873813955503863232652134139635567906452312975362340016596792083681783675842173106946433772533604856246547913044082811203864761614831532818142963817402397442624346119 | ecm -n -c 904 1e6

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

echo 8472023974149146286815999873813955503863232652134139635567906452312975362340016596792083681783675842173106946433772533604856246547913044082811203864761614831532818142963817402397442624346119 | ecm -n -c 2350 3e6

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