Contribution and Reservation

(14·10²⁰¹+1)/3 =: 4(6)₂₀₀7_<202>; = 13 · 523 · [686375447369711232043928028631661518850811393832426337206451929205275285581212923469137618277197627102024807569740648134529587684463401480609893611805657694759033191155562092464578124233955973917733_<198>] SUBMIT/RESERVE

Status

Expression:	(14·10²⁰¹+1)/3
Composite Factor:	686375447369711232043928028631661518850811393832426337206451 929205275285581212923469137618277197627102024807569740648134 529587684463401480609893611805657694759033191155562092464578 124233955973917733 (198-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 203.05-digit and the GNFS difficulty is 197.84-digit. SNFS must be faster than GNFS. It will take about 24 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 46667_201.
Put the following polynomial file 46667_201.poly in there too.
And then, run "perl factMsieve.pl 46667_201".

46667_201.poly ^*1

n: 686375447369711232043928028631661518850811393832426337206451929205275285581212923469137618277197627102024807569740648134529587684463401480609893611805657694759033191155562092464578124233955973917733
m: 20000000000000000000000000000000000000000
deg: 5
c5: 35
c0: 8
skew: 0.74
type: snfs
lss: 1
rlim: 17000000
alim: 17000000
lpbr: 29
lpba: 29
mfbr: 56
mfba: 56
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 198-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	Feb 12, 2009
35	1e6	118 / 62
40	3e6	300	Serge Batalov	Feb 17, 2009
		300 / 2318
		/ 2018
45	11e6	0 / 4409 (585)
45	11e6	/ 4409 (585)
50	43e6	0 / 7541 (1257)
50	43e6	/ 7541 (1257)
55	11e7	0 / 17767 (3129)
55	11e7	/ 17767 (3129)

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

echo 686375447369711232043928028631661518850811393832426337206451929205275285581212923469137618277197627102024807569740648134529587684463401480609893611805657694759033191155562092464578124233955973917733 | ecm -n -c 2018 3e6

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

echo 686375447369711232043928028631661518850811393832426337206451929205275285581212923469137618277197627102024807569740648134529587684463401480609893611805657694759033191155562092464578124233955973917733 | ecm -n -c 4409 11e6

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

echo 686375447369711232043928028631661518850811393832426337206451929205275285581212923469137618277197627102024807569740648134529587684463401480609893611805657694759033191155562092464578124233955973917733 | ecm -n -c 7541 43e6

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

echo 686375447369711232043928028631661518850811393832426337206451929205275285581212923469137618277197627102024807569740648134529587684463401480609893611805657694759033191155562092464578124233955973917733 | ecm -n -c 17767 11e7

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers