Contribution and Reservation

(8·10²²³+7)/3 =: 2(6)₂₂₂9_<224>; = 11293537 · 12113953 · [194918413957663848108395761008525922287298241582897600515495310611246768408304255228909571790361332828475736718482741069900554990356353159442674468356356220923202738486839940558741869392570996667556838656739629_<210>] SUBMIT/RESERVE

Status

Expression:	(8·10²²³+7)/3
Composite Factor:	194918413957663848108395761008525922287298241582897600515495 310611246768408304255228909571790361332828475736718482741069 900554990356353159442674468356356220923202738486839940558741 869392570996667556838656739629 (210-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 224.51-digit and the GNFS difficulty is 209.29-digit. SNFS must be faster than GNFS. It will take about 127 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 26669_223.
Put the following polynomial file 26669_223.poly in there too.
And then, run "perl factMsieve.pl 26669_223".

26669_223.poly ^*1

n: 194918413957663848108395761008525922287298241582897600515495310611246768408304255228909571790361332828475736718482741069900554990356353159442674468356356220923202738486839940558741869392570996667556838656739629
m: 20000000000000000000000000000000000000
deg: 6
c6: 5
c0: 28
skew: 1.33
type: snfs
lss: 1
rlim: 39000000
alim: 39000000
lpbr: 29
lpba: 29
mfbr: 59
mfba: 59
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 210-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	700	Serge Batalov	Oct 16, 2009
40	3e6	700 / 0
45	11e6	0 / 1514
45	11e6	/ 1514
50	43e6	800	Dmitry Domanov	Oct 30, 2009
		800 / 7526 (1232)
		/ 6726 (432)
55	11e7	0 / 17478 (2790)
55	11e7	/ 17478 (2790)
60	26e7	0 / 41923 (7518)
60	26e7	/ 41923 (7518)

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

echo 194918413957663848108395761008525922287298241582897600515495310611246768408304255228909571790361332828475736718482741069900554990356353159442674468356356220923202738486839940558741869392570996667556838656739629 | ecm -n -c 1514 11e6

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

echo 194918413957663848108395761008525922287298241582897600515495310611246768408304255228909571790361332828475736718482741069900554990356353159442674468356356220923202738486839940558741869392570996667556838656739629 | ecm -n -c 6726 43e6

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

echo 194918413957663848108395761008525922287298241582897600515495310611246768408304255228909571790361332828475736718482741069900554990356353159442674468356356220923202738486839940558741869392570996667556838656739629 | ecm -n -c 17478 11e7

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

echo 194918413957663848108395761008525922287298241582897600515495310611246768408304255228909571790361332828475736718482741069900554990356353159442674468356356220923202738486839940558741869392570996667556838656739629 | ecm -n -c 41923 26e7

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