Contribution and Reservation

(41·10²⁰⁵+31)/9 =: 4(5)₂₀₄9_<206>; = 7 · 19 · 61 · 91643911 · [61271181704394077921259815891547181780419896377632854522469730802601441655871101329759022905501460761090481682638669009884922663637145266319765005235366848039936495415654681141554572186805984113_<194>] SUBMIT/RESERVE

Status

Expression:	(41·10²⁰⁵+31)/9
Composite Factor:	612711817043940779212598158915471817804198963776328545224697 308026014416558711013297590229055014607610904816826386690098 849226636371452663197650052353668480399364954156546811415545 72186805984113 (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 206.61-digit and the GNFS difficulty is 193.79-digit. SNFS must be faster than GNFS. It will take about 32 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 45559_205.
Put the following polynomial file 45559_205.poly in there too.
And then, run "perl factMsieve.pl 45559_205".

45559_205.poly ^*1

n: 61271181704394077921259815891547181780419896377632854522469730802601441655871101329759022905501460761090481682638669009884922663637145266319765005235366848039936495415654681141554572186805984113
m: 100000000000000000000000000000000000000000
deg: 5
c5: 41
c0: 31
skew: 0.95
type: snfs
lss: 1
rlim: 19400000
alim: 19400000
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 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 3, 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 61271181704394077921259815891547181780419896377632854522469730802601441655871101329759022905501460761090481682638669009884922663637145266319765005235366848039936495415654681141554572186805984113 | ecm -n -c 825 1e6

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

echo 61271181704394077921259815891547181780419896377632854522469730802601441655871101329759022905501460761090481682638669009884922663637145266319765005235366848039936495415654681141554572186805984113 | ecm -n -c 2336 3e6

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

echo 61271181704394077921259815891547181780419896377632854522469730802601441655871101329759022905501460761090481682638669009884922663637145266319765005235366848039936495415654681141554572186805984113 | ecm -n -c 4479 11e6

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

echo 61271181704394077921259815891547181780419896377632854522469730802601441655871101329759022905501460761090481682638669009884922663637145266319765005235366848039936495415654681141554572186805984113 | ecm -n -c 7553 43e6

Submit factors

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