Contribution and Reservation

(16·10²¹⁷-61)/9 =: 1(7)₂₁₆1_<218>; = 11² · 17 · 357140913977385032759873377_<27> · [24199343030304673917570818401198090307706604729662034881244790117480409070719630603838594427982130442667613637004200332400246256214237608195295430110631679470541689001223915098825589372339_<188>] (Tetsuya Kobayashi / GMP-ECM 4c) SUBMIT/RESERVE

Status

Expression:	(16·10²¹⁷-61)/9
Composite Factor:	241993430303046739175708184011980903077066047296620348812447 901174804090707196306038385944279821304426676136370042003324 002462562142376081952954301106316794705416890012239150988255 89372339 (188-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 218.51-digit and the GNFS difficulty is 187.38-digit. SNFS must be faster than GNFS. It will take about 80 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 17771_217.
Put the following polynomial file 17771_217.poly in there too.
And then, run "perl factMsieve.pl 17771_217".

17771_217.poly ^*1

n: 24199343030304673917570818401198090307706604729662034881244790117480409070719630603838594427982130442667613637004200332400246256214237608195295430110631679470541689001223915098825589372339
m: 2000000000000000000000000000000000000
deg: 6
c6: 5
c0: -122
skew: 1.70
type: snfs
lss: 1
rlim: 31000000
alim: 31000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
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 188-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 20-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
20	11e3	74	Max Dettweiler	Mar 7, 2009
20	11e3	74 / 74
25	5e4	0 / 204
25	5e4	/ 204
30	25e4	0 / 430 (48)
30	25e4	/ 430 (48)
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 25-digit

echo 24199343030304673917570818401198090307706604729662034881244790117480409070719630603838594427982130442667613637004200332400246256214237608195295430110631679470541689001223915098825589372339 | ecm -n -c 204 5e4

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

echo 24199343030304673917570818401198090307706604729662034881244790117480409070719630603838594427982130442667613637004200332400246256214237608195295430110631679470541689001223915098825589372339 | ecm -n -c 430 25e4

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

echo 24199343030304673917570818401198090307706604729662034881244790117480409070719630603838594427982130442667613637004200332400246256214237608195295430110631679470541689001223915098825589372339 | ecm -n -c 904 1e6

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

echo 24199343030304673917570818401198090307706604729662034881244790117480409070719630603838594427982130442667613637004200332400246256214237608195295430110631679470541689001223915098825589372339 | ecm -n -c 2350 3e6

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