Contribution and Reservation

(2·10¹⁹⁹+7)/9 =: (2)₁₉₈3_<199>; = 3 · 17 · 14249 · 1631921 · 282992363 · 16423844282900437_<17> · 26596092569686884031_<20> · [15158855823514284233452836685887209937313207494030862868357940871398349544767238556786074785640147324163997293289052269686919580129313606190117_<143>] SUBMIT/RESERVE

Status

Expression:	(2·10¹⁹⁹+7)/9
Composite Factor:	151588558235142842334528366858872099373132074940308628683579 408713983495447672385567860747856401473241639972932890522696 86919580129313606190117 (143-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 199.30-digit and the GNFS difficulty is 142.18-digit. SNFS must be faster than GNFS. It will take about 18 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 22223_199.
Put the following polynomial file 22223_199.poly in there too.
And then, run "perl factMsieve.pl 22223_199".

22223_199.poly

n: 15158855823514284233452836685887209937313207494030862868357940871398349544767238556786074785640147324163997293289052269686919580129313606190117
m: 2000000000000000000000000000000000000000
deg: 5
c5: 625
c0: 7
skew: 0.41
type: snfs
lss: 1
rlim: 14700000
alim: 14700000
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 143-digit composite number are not reported yet. Please report your efforts by ECM. (Anonymous reports are not acceptable)

Level	B1	Reported runs Total / Required runs (Required runs for lower level)
20	11e3	0 / 74
20	11e3	/ 74
25	5e4	0 / 214 (21)
25	5e4	/ 214 (21)
30	25e4	0 / 430 (50)
30	25e4	/ 430 (50)
35	1e6	0 / 904 (118)
35	1e6	/ 904 (118)
40	3e6	0 / 2350 (322)
40	3e6	/ 2350 (322)

Command line to find prime factors up to about 20-digit

echo 15158855823514284233452836685887209937313207494030862868357940871398349544767238556786074785640147324163997293289052269686919580129313606190117 | ecm -n -c 74 11e3

Command line to find prime factors up to about 25-digit

echo 15158855823514284233452836685887209937313207494030862868357940871398349544767238556786074785640147324163997293289052269686919580129313606190117 | ecm -n -c 214 5e4

Command line to find prime factors up to about 30-digit

echo 15158855823514284233452836685887209937313207494030862868357940871398349544767238556786074785640147324163997293289052269686919580129313606190117 | ecm -n -c 430 25e4

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

echo 15158855823514284233452836685887209937313207494030862868357940871398349544767238556786074785640147324163997293289052269686919580129313606190117 | ecm -n -c 904 1e6

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

echo 15158855823514284233452836685887209937313207494030862868357940871398349544767238556786074785640147324163997293289052269686919580129313606190117 | ecm -n -c 2350 3e6

Submit factors

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