Contribution and Reservation

(4·10²³⁷-1)/3 =: 1(3)₂₃₇_<238>; = 202801370044879324554086001001_<30> · [6574577543723056377491832231829230492879349865822238907247684637847112489290720141885240127649246691529378767571799036688532079804021184163805147918235262881269406241522989634379010640767433147359127695000333_<208>] (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=1213199094 for P30 / Jul 9, 2008) SUBMIT/RESERVE

Status

Expression:	(4·10²³⁷-1)/3
Composite Factor:	657457754372305637749183223182923049287934986582223890724768 463784711248929072014188524012764924669152937876757179903668 853207980402118416380514791823526288126940624152298963437901 0640767433147359127695000333 (208-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 237.90-digit and the GNFS difficulty is 207.82-digit. SNFS must be faster than GNFS. It will take about 355 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 13333_237.
Put the following polynomial file 13333_237.poly in there too.
And then, run "perl factMsieve.pl 13333_237".

13333_237.poly ^*1

n: 6574577543723056377491832231829230492879349865822238907247684637847112489290720141885240127649246691529378767571799036688532079804021184163805147918235262881269406241522989634379010640767433147359127695000333
m: 2000000000000000000000000000000000000000
deg: 6
c6: 125
c0: -2
skew: 0.50
type: snfs
lss: 1
rlim: 65000000
alim: 65000000
lpbr: 30
lpba: 30
mfbr: 60
mfba: 60
rlambda: 2.7
alambda: 2.7

*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 208-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	500	suberi	Jul 25, 2008
40	3e6	500 / 0
45	11e6	700	Dmitry Domanov	Jul 11, 2009
		700 / 4368
		/ 3668
50	43e6	0 / 7377 (1046)
50	43e6	/ 7377 (1046)
55	11e7	0 / 17722 (3060)
55	11e7	/ 17722 (3060)
60	26e7	0 / 42006 (7623)
60	26e7	/ 42006 (7623)

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

echo 6574577543723056377491832231829230492879349865822238907247684637847112489290720141885240127649246691529378767571799036688532079804021184163805147918235262881269406241522989634379010640767433147359127695000333 | ecm -n -c 3668 11e6

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

echo 6574577543723056377491832231829230492879349865822238907247684637847112489290720141885240127649246691529378767571799036688532079804021184163805147918235262881269406241522989634379010640767433147359127695000333 | ecm -n -c 7377 43e6

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

echo 6574577543723056377491832231829230492879349865822238907247684637847112489290720141885240127649246691529378767571799036688532079804021184163805147918235262881269406241522989634379010640767433147359127695000333 | ecm -n -c 17722 11e7

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

echo 6574577543723056377491832231829230492879349865822238907247684637847112489290720141885240127649246691529378767571799036688532079804021184163805147918235262881269406241522989634379010640767433147359127695000333 | ecm -n -c 42006 26e7

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers