Contribution and Reservation

(86·10¹⁹⁸+31)/9 =: 9(5)₁₉₇9_<199>; = 13 · 79 · 571 · [16294813341965794913100328871017647093374775212102574713140232216248088912080576715128578393115403468104702891552522446579064992241963578060587526547756213676539997229881731865814864772944091927_<194>] SUBMIT/RESERVE

Status

Expression:	(86·10¹⁹⁸+31)/9
Composite Factor:	162948133419657949131003288710176470933747752121025747131402 322162480889120805767151285783931154034681047028915525224465 790649922419635780605875265477562136765399972298817318658148 64772944091927 (194-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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 199.93-digit and the GNFS difficulty is 193.21-digit. SNFS must be faster than GNFS. It will take about 19 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of SNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 95559_198.
Put the following polynomial file 95559_198.poly in there too.
And then, run "perl factMsieve.pl 95559_198".

95559_198.poly

n: 16294813341965794913100328871017647093374775212102574713140232216248088912080576715128578393115403468104702891552522446579064992241963578060587526547756213676539997229881731865814864772944091927
m: 1000000000000000000000000000000000000000
deg: 5
c5: 86000
c0: 31
skew: 0.20
type: snfs
lss: 1
rlim: 15000000
alim: 15000000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.5
alambda: 2.5

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 194-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	0 / 0
45	11e6	750	Dmitry Domanov	Dec 18, 2009
		750 / 4479
		/ 3729
50	43e6	0 / 7385 (1063)
50	43e6	/ 7385 (1063)
55	11e7	0 / 17723 (3064)
55	11e7	/ 17723 (3064)
60	26e7	0 / 42006 (7623)
60	26e7	/ 42006 (7623)

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

echo 16294813341965794913100328871017647093374775212102574713140232216248088912080576715128578393115403468104702891552522446579064992241963578060587526547756213676539997229881731865814864772944091927 | ecm -n -c 3729 11e6

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

echo 16294813341965794913100328871017647093374775212102574713140232216248088912080576715128578393115403468104702891552522446579064992241963578060587526547756213676539997229881731865814864772944091927 | ecm -n -c 7385 43e6

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

echo 16294813341965794913100328871017647093374775212102574713140232216248088912080576715128578393115403468104702891552522446579064992241963578060587526547756213676539997229881731865814864772944091927 | ecm -n -c 17723 11e7

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

echo 16294813341965794913100328871017647093374775212102574713140232216248088912080576715128578393115403468104702891552522446579064992241963578060587526547756213676539997229881731865814864772944091927 | ecm -n -c 42006 26e7

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers