Contribution and Reservation

(23·10²⁰²-41)/9 =: 2(5)₂₀₁1_<203>; = 3³ · 251 · 73583 · 17408653 · [2943778858838999694997289577641754228968297409433717737831660631316624690061751952606116072502137285043408479838250140971844700591905787300444100988111730401766295523842215486140510215037_<187>] SUBMIT/RESERVE

Status

Expression:	(23·10²⁰²-41)/9
Composite Factor:	294377885883899969499728957764175422896829740943371773783166 063131662469006175195260611607250213728504340847983825014097 184470059190578730044410098811173040176629552384221548614051 0215037 (187-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 204.26-digit and the GNFS difficulty is 186.47-digit. SNFS must be faster than GNFS. It will take about 27 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 25551_202.
Put the following polynomial file 25551_202.poly in there too.
And then, run "perl factMsieve.pl 25551_202".

25551_202.poly ^*1

n: 2943778858838999694997289577641754228968297409433717737831660631316624690061751952606116072502137285043408479838250140971844700591905787300444100988111730401766295523842215486140510215037
m: 20000000000000000000000000000000000000000
deg: 5
c5: 575
c0: -328
skew: 0.89
type: snfs
lss: 1
rlim: 17800000
alim: 17800000
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 187-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	Jul 28, 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 2943778858838999694997289577641754228968297409433717737831660631316624690061751952606116072502137285043408479838250140971844700591905787300444100988111730401766295523842215486140510215037 | ecm -n -c 825 1e6

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

echo 2943778858838999694997289577641754228968297409433717737831660631316624690061751952606116072502137285043408479838250140971844700591905787300444100988111730401766295523842215486140510215037 | ecm -n -c 2336 3e6

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

echo 2943778858838999694997289577641754228968297409433717737831660631316624690061751952606116072502137285043408479838250140971844700591905787300444100988111730401766295523842215486140510215037 | ecm -n -c 4479 11e6

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

echo 2943778858838999694997289577641754228968297409433717737831660631316624690061751952606116072502137285043408479838250140971844700591905787300444100988111730401766295523842215486140510215037 | ecm -n -c 7553 43e6

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers