Contribution and Reservation

(10²⁰⁸+53)/9 =: (1)₂₀₇7_<208>; = 23 · 31 · 41299 · 766247 · [49244716049126759875870702658166783116648633642743870825537726369336365249964507265898228199963978986421135544657988706362766587710012978586765580033840342222167519112916898351613317165455429953_<194>] SUBMIT/RESERVE

Status

Expression:	(10²⁰⁸+53)/9
Composite Factor:	492447160491267598758707026581667831166486336427438708255377 263693363652499645072658982281999639789864211355446579887063 627665877100129785867655800338403422221675191129168983516133 17165455429953 (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.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 208.60-digit and the GNFS difficulty is 193.69-digit. SNFS must be faster than GNFS. It will take about 37 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 11117_208.
Put the following polynomial file 11117_208.poly in there too.
And then, run "perl factMsieve.pl 11117_208".

11117_208.poly ^*1

n: 49244716049126759875870702658166783116648633642743870825537726369336365249964507265898228199963978986421135544657988706362766587710012978586765580033840342222167519112916898351613317165455429953
m: 200000000000000000000000000000000000000000
deg: 5
c5: 125
c0: 212
skew: 1.11
type: snfs
lss: 1
rlim: 21000000
alim: 21000000
lpbr: 29
lpba: 29
mfbr: 57
mfba: 57
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 194-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	Feb 1, 2009
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 49244716049126759875870702658166783116648633642743870825537726369336365249964507265898228199963978986421135544657988706362766587710012978586765580033840342222167519112916898351613317165455429953 | ecm -n -c 825 1e6

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

echo 49244716049126759875870702658166783116648633642743870825537726369336365249964507265898228199963978986421135544657988706362766587710012978586765580033840342222167519112916898351613317165455429953 | ecm -n -c 2336 3e6

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

echo 49244716049126759875870702658166783116648633642743870825537726369336365249964507265898228199963978986421135544657988706362766587710012978586765580033840342222167519112916898351613317165455429953 | ecm -n -c 4479 11e6

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

echo 49244716049126759875870702658166783116648633642743870825537726369336365249964507265898228199963978986421135544657988706362766587710012978586765580033840342222167519112916898351613317165455429953 | ecm -n -c 7553 43e6

Submit factors

Make reservation

Back to Factorizations of near-repdigit numbers