Contribution and Reservation

(16·10²¹²-61)/9 =: 1(7)₂₁₁1_<213>; = 3 · 3263041518593_<13> · [18160743257968542497498161945925583293582042729670566183879188236617129256810547762687279554248596135573240889074193941052472459596557021410997855885245751482132544729194788086311670988697618637827449_<200>] SUBMIT/RESERVE

Status

Expression:	(16·10²¹²-61)/9
Composite Factor:	181607432579685424974981619459255832935820427296705661838791 882366171292568105477626872795542485961355732408890741939410 524724595965570214109978558852457514821325447291947880863116 70988697618637827449 (200-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 213.20-digit and the GNFS difficulty is 199.26-digit. SNFS must be faster than GNFS. It will take about 53 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_212.
Put the following polynomial file 17771_212.poly in there too.
And then, run "perl factMsieve.pl 17771_212".

17771_212.poly ^*1

n: 18160743257968542497498161945925583293582042729670566183879188236617129256810547762687279554248596135573240889074193941052472459596557021410997855885245751482132544729194788086311670988697618637827449
m: 200000000000000000000000000000000000
deg: 6
c6: 25
c0: -61
skew: 1.16
type: snfs
lss: 1
rlim: 25000000
alim: 25000000
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 200-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 18160743257968542497498161945925583293582042729670566183879188236617129256810547762687279554248596135573240889074193941052472459596557021410997855885245751482132544729194788086311670988697618637827449 | ecm -n -c 204 5e4

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

echo 18160743257968542497498161945925583293582042729670566183879188236617129256810547762687279554248596135573240889074193941052472459596557021410997855885245751482132544729194788086311670988697618637827449 | ecm -n -c 430 25e4

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

echo 18160743257968542497498161945925583293582042729670566183879188236617129256810547762687279554248596135573240889074193941052472459596557021410997855885245751482132544729194788086311670988697618637827449 | ecm -n -c 904 1e6

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

echo 18160743257968542497498161945925583293582042729670566183879188236617129256810547762687279554248596135573240889074193941052472459596557021410997855885245751482132544729194788086311670988697618637827449 | ecm -n -c 2350 3e6

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