Contribution and Reservation

5·10¹⁹⁷-1 =: 4(9)₁₉₇_<198>; = 6526969 · [76605235906590026703053132319151508150260863809832711017931906831486406630704083319531623330829363522333260660499536614928001036928473231602601452527199072034814321931052529895576338726290871_<191>] SUBMIT/RESERVE

Status

Expression:	5·10¹⁹⁷-1
Composite Factor:	766052359065900267030531323191515081502608638098327110179319 068314864066307040833195316233308293635223332606604995366149 280010369284732316026014525271990720348143219310525298955763 38726290871 (191-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 199.10-digit and the GNFS difficulty is 190.88-digit. SNFS must be faster than GNFS. It will take about 18 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 49999_197.
Put the following polynomial file 49999_197.poly in there too.
And then, run "perl factMsieve.pl 49999_197".

49999_197.poly ^*1

n: 76605235906590026703053132319151508150260863809832711017931906831486406630704083319531623330829363522333260660499536614928001036928473231602601452527199072034814321931052529895576338726290871
m: 5000000000000000000000000000000000000000
deg: 5
c5: 4
c0: -25
skew: 1.44
type: snfs
lss: 1
rlim: 14600000
alim: 14600000
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 191-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 30-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
30	25e4	203	Luigi Morelli	Feb 24, 2009
		200	Luigi Morelli	Jun 10, 2009
		403 / 0
35	1e6	28	Luigi Morelli	Jun 10, 2009
		14	Luigi Morelli	Jun 10, 2009
		86	Luigi Morelli	Jun 10, 2009
		128 / 828
		/ 700
40	3e6	0 / 2302 (250)
40	3e6	/ 2302 (250)
45	11e6	0 / 4473 (667)
45	11e6	/ 4473 (667)
50	43e6	0 / 7553 (1275)
50	43e6	/ 7553 (1275)

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

echo 76605235906590026703053132319151508150260863809832711017931906831486406630704083319531623330829363522333260660499536614928001036928473231602601452527199072034814321931052529895576338726290871 | ecm -n -c 700 1e6

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

echo 76605235906590026703053132319151508150260863809832711017931906831486406630704083319531623330829363522333260660499536614928001036928473231602601452527199072034814321931052529895576338726290871 | ecm -n -c 2302 3e6

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

echo 76605235906590026703053132319151508150260863809832711017931906831486406630704083319531623330829363522333260660499536614928001036928473231602601452527199072034814321931052529895576338726290871 | ecm -n -c 4473 11e6

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

echo 76605235906590026703053132319151508150260863809832711017931906831486406630704083319531623330829363522333260660499536614928001036928473231602601452527199072034814321931052529895576338726290871 | ecm -n -c 7553 43e6

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers