Contribution and Reservation

(73·10²¹¹-1)/9 =: 8(1)₂₁₁_<212>; = 3 · 1239443 · 12124327781269997_<17> · [1799181048690032123073780432942837977523728759368683736311918117349597462503012648051967382121615634299199626745747712361576389588921600902359775051144873821818029952496987549022533082683547_<190>] SUBMIT/RESERVE

Status

Expression:	(73·10²¹¹-1)/9
Composite Factor:	179918104869003212307378043294283797752372875936868373631191 811734959746250301264805196738212161563429919962674574771236 157638958892160090235977505114487382181802995249698754902253 3082683547 (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 214.37-digit and the GNFS difficulty is 189.26-digit. SNFS must be faster than GNFS. It will take about 58 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 81111_211.
Put the following polynomial file 81111_211.poly in there too.
And then, run "perl factMsieve.pl 81111_211".

81111_211.poly ^*1

n: 1799181048690032123073780432942837977523728759368683736311918117349597462503012648051967382121615634299199626745747712361576389588921600902359775051144873821818029952496987549022533082683547
m: 200000000000000000000000000000000000
deg: 6
c6: 365
c0: -32
skew: 0.67
type: snfs
lss: 1
rlim: 26000000
alim: 26000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
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 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	118	Makoto Kamada	May 26, 2009
		409	Dmitry Domanov	Jun 2, 2009
		527 / 0
40	3e6	358	Dmitry Domanov	Jun 2, 2009
		358 / 1413
		/ 1055
45	11e6	230	Dmitry Domanov	Jun 2, 2009
		230 / 4377 (536)
		/ 4147 (306)
50	43e6	0 / 7485 (1182)
50	43e6	/ 7485 (1182)
55	11e7	0 / 17752 (3105)
55	11e7	/ 17752 (3105)

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

echo 1799181048690032123073780432942837977523728759368683736311918117349597462503012648051967382121615634299199626745747712361576389588921600902359775051144873821818029952496987549022533082683547 | ecm -n -c 1055 3e6

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

echo 1799181048690032123073780432942837977523728759368683736311918117349597462503012648051967382121615634299199626745747712361576389588921600902359775051144873821818029952496987549022533082683547 | ecm -n -c 4147 11e6

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

echo 1799181048690032123073780432942837977523728759368683736311918117349597462503012648051967382121615634299199626745747712361576389588921600902359775051144873821818029952496987549022533082683547 | ecm -n -c 7485 43e6

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

echo 1799181048690032123073780432942837977523728759368683736311918117349597462503012648051967382121615634299199626745747712361576389588921600902359775051144873821818029952496987549022533082683547 | ecm -n -c 17752 11e7

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