Contribution and Reservation

(8·10²⁴⁴+1)/9 =: (8)₂₄₃9_<244>; = 3² · 59 · 4116617966651_<13> · 814959927820786541862220313297_<30> · [4989719550969023674916220069105323099035254845764663680168570115803888352756291458951569036847759837310694658793643565127294386108522380829831128949397387038248676240394807727475466179992759373354377_<199>] (Makoto Kamada / GMP-ECM 6.2.1 B1=250000, sigma=3168450891 for P30 / Oct 29, 2008) SUBMIT/RESERVE

Status

Expression:	(8·10²⁴⁴+1)/9
Composite Factor:	498971955096902367491622006910532309903525484576466368016857 011580388835275629145895156903684775983731069465879364356512 729438610852238082983112894939738703824867624039480772747546 6179992759373354377 (199-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 246.30-digit and the GNFS difficulty is 198.70-digit. SNFS must be faster than GNFS. It will take about 676 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 88889_244.
Put the following polynomial file 88889_244.poly in there too.
And then, run "perl factMsieve.pl 88889_244".

88889_244.poly ^*1

n: 4989719550969023674916220069105323099035254845764663680168570115803888352756291458951569036847759837310694658793643565127294386108522380829831128949397387038248676240394807727475466179992759373354377
m: 100000000000000000000000000000000000000000
deg: 6
c6: 2
c0: 25
skew: 1.52
type: snfs
lss: 1
rlim: 89000000
alim: 89000000
lpbr: 30
lpba: 30
mfbr: 61
mfba: 61
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 199-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	430	Makoto Kamada	Oct 31, 2008
30	25e4	430 / 430
35	1e6	0 / 825
35	1e6	/ 825
40	3e6	0 / 2336 (294)
40	3e6	/ 2336 (294)
45	11e6	0 / 4479 (677)
45	11e6	/ 4479 (677)
50	43e6	0 / 7553 (1277)
50	43e6	/ 7553 (1277)

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

echo 4989719550969023674916220069105323099035254845764663680168570115803888352756291458951569036847759837310694658793643565127294386108522380829831128949397387038248676240394807727475466179992759373354377 | ecm -n -c 825 1e6

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

echo 4989719550969023674916220069105323099035254845764663680168570115803888352756291458951569036847759837310694658793643565127294386108522380829831128949397387038248676240394807727475466179992759373354377 | ecm -n -c 2336 3e6

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

echo 4989719550969023674916220069105323099035254845764663680168570115803888352756291458951569036847759837310694658793643565127294386108522380829831128949397387038248676240394807727475466179992759373354377 | ecm -n -c 4479 11e6

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

echo 4989719550969023674916220069105323099035254845764663680168570115803888352756291458951569036847759837310694658793643565127294386108522380829831128949397387038248676240394807727475466179992759373354377 | ecm -n -c 7553 43e6

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers