Contribution and Reservation

(22·10¹⁹⁰-1)/3 =: 7(3)₁₉₀_<191>; = 13 · 29² · [6707521570779596938931064971493033324186713009542973871154608372206469709442361047592914418122503734869965547730113722979359126802646422147016677337723711088752705875179121314674227872801_<187>] SUBMIT/RESERVE

Status

Expression:	(22·10¹⁹⁰-1)/3
Composite Factor:	670752157077959693893106497149303332418671300954297387115460 837220646970944236104759291441812250373486996554773011372297 935912680264642214701667733772371108875270587517912131467422 7872801 (187-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 192.55-digit and the GNFS difficulty is 186.83-digit. SNFS must be faster than GNFS. It will take about 11 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 73333_190.
Put the following polynomial file 73333_190.poly in there too.
And then, run "perl factMsieve.pl 73333_190".

73333_190.poly ^*1

n: 6707521570779596938931064971493033324186713009542973871154608372206469709442361047592914418122503734869965547730113722979359126802646422147016677337723711088752705875179121314674227872801
m: 200000000000000000000000000000000000000
deg: 5
c5: 11
c0: -16
skew: 1.08
type: snfs
lss: 1
rlim: 11300000
alim: 11300000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

*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 187-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	2345	Dmitry Domanov	Jul 6, 2009
40	3e6	2345 / 2009
45	11e6	0 / 3905
45	11e6	/ 3905
50	43e6	0 / 7458 (1113)
50	43e6	/ 7458 (1113)
55	11e7	0 / 17750 (3094)
55	11e7	/ 17750 (3094)
60	26e7	0 / 42014 (7635)
60	26e7	/ 42014 (7635)

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

echo 6707521570779596938931064971493033324186713009542973871154608372206469709442361047592914418122503734869965547730113722979359126802646422147016677337723711088752705875179121314674227872801 | ecm -n -c 3905 11e6

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

echo 6707521570779596938931064971493033324186713009542973871154608372206469709442361047592914418122503734869965547730113722979359126802646422147016677337723711088752705875179121314674227872801 | ecm -n -c 7458 43e6

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

echo 6707521570779596938931064971493033324186713009542973871154608372206469709442361047592914418122503734869965547730113722979359126802646422147016677337723711088752705875179121314674227872801 | ecm -n -c 17750 11e7

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

echo 6707521570779596938931064971493033324186713009542973871154608372206469709442361047592914418122503734869965547730113722979359126802646422147016677337723711088752705875179121314674227872801 | ecm -n -c 42014 26e7

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