Contribution and Reservation

(67·10²⁰⁰+41)/9 =: 7(4)₁₉₉9_<201>; = 7 · 37019 · 1699219 · [1690675327011124131462652237169154370860204741924447467861558808620854905595729860342241688019225523720773829977244146577129384627603451568653082784603907517431654015880830658112333637627287_<190>] SUBMIT/RESERVE

Status

Expression:	(67·10²⁰⁰+41)/9
Composite Factor:	169067532701112413146265223716915437086020474192444746786155 880862085490559572986034224168801922552372077382997724414657 712938462760345156865308278460390751743165401588083065811233 3637627287 (190-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 201.83-digit and the GNFS difficulty is 189.23-digit. SNFS must be faster than GNFS. It will take about 22 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 74449_200.
Put the following polynomial file 74449_200.poly in there too.
And then, run "perl factMsieve.pl 74449_200".

74449_200.poly ^*1

n: 1690675327011124131462652237169154370860204741924447467861558808620854905595729860342241688019225523720773829977244146577129384627603451568653082784603907517431654015880830658112333637627287
m: 10000000000000000000000000000000000000000
deg: 5
c5: 67
c0: 41
skew: 0.91
type: snfs
lss: 1
rlim: 16200000
alim: 16200000
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 190-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	0 / 0
35	1e6	150	Lionel Debroux	Nov 3, 2009
		150 / 904
		/ 754
40	3e6	0 / 2310 (269)
40	3e6	/ 2310 (269)
45	11e6	0 / 4474 (670)
45	11e6	/ 4474 (670)
50	43e6	0 / 7553 (1276)
50	43e6	/ 7553 (1276)

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

echo 1690675327011124131462652237169154370860204741924447467861558808620854905595729860342241688019225523720773829977244146577129384627603451568653082784603907517431654015880830658112333637627287 | ecm -n -c 754 1e6

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

echo 1690675327011124131462652237169154370860204741924447467861558808620854905595729860342241688019225523720773829977244146577129384627603451568653082784603907517431654015880830658112333637627287 | ecm -n -c 2310 3e6

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

echo 1690675327011124131462652237169154370860204741924447467861558808620854905595729860342241688019225523720773829977244146577129384627603451568653082784603907517431654015880830658112333637627287 | ecm -n -c 4474 11e6

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

echo 1690675327011124131462652237169154370860204741924447467861558808620854905595729860342241688019225523720773829977244146577129384627603451568653082784603907517431654015880830658112333637627287 | ecm -n -c 7553 43e6

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers