Contribution and Reservation

(88·10²⁰⁰-7)/9 =: 9(7)₂₀₀_<201>; = 157 · 857 · 252509 · 24774025606639_<14> · 20683264482894007536309560322300919_<35> · [56165180484430952300766307618116484534228422042636160492389602943693696922297926733979303491972770778598171625374154176211273951939843834033017_<143>] (Wataru Sakai / GMP-ECM 6.0.1 B1=11000000, sigma=976504838 for P35 / May 29, 2005) SUBMIT/RESERVE

Status

Expression:	(88·10²⁰⁰-7)/9
Composite Factor:	561651804844309523007663076181164845342284220426361604923896 029436936969222979267339793034919727707785981716253741541762 11273951939843834033017 (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.

SNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 202.55-digit and the GNFS difficulty is 142.75-digit. SNFS may be faster than GNFS. It will take about 24 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 97777_200.
Put the following polynomial file 97777_200.poly in there too.
And then, run "perl factMsieve.pl 97777_200".

97777_200.poly ^*1

n: 56165180484430952300766307618116484534228422042636160492389602943693696922297926733979303491972770778598171625374154176211273951939843834033017
m: 20000000000000000000000000000000000000000
deg: 5
c5: 11
c0: -28
skew: 1.21
type: snfs
lss: 1
rlim: 16600000
alim: 16600000
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 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 56165180484430952300766307618116484534228422042636160492389602943693696922297926733979303491972770778598171625374154176211273951939843834033017 | ecm -n -c 74 11e3

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

echo 56165180484430952300766307618116484534228422042636160492389602943693696922297926733979303491972770778598171625374154176211273951939843834033017 | ecm -n -c 214 5e4

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

echo 56165180484430952300766307618116484534228422042636160492389602943693696922297926733979303491972770778598171625374154176211273951939843834033017 | ecm -n -c 430 25e4

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

echo 56165180484430952300766307618116484534228422042636160492389602943693696922297926733979303491972770778598171625374154176211273951939843834033017 | ecm -n -c 904 1e6

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

echo 56165180484430952300766307618116484534228422042636160492389602943693696922297926733979303491972770778598171625374154176211273951939843834033017 | ecm -n -c 2350 3e6

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