Contribution and Reservation

(16·10²²⁷-7)/9 =: 1(7)₂₂₇_<228>; = 3 · 6978529417_<10> · 998945248363_<12> · [8500620332853352373100619494859864036219623065828944278551768110817378446210927884562453439711314210424131541144585190430418520177440149893041637577056204111557942429485079430082059275669583801816757447529_<205>] RESERVED

Status

Expression:	(16·10²²⁷-7)/9
Composite Factor:	850062033285335237310061949485986403621962306582894427855176 811081737844621092788456245343971131421042413154114458519043 041852017744014989304163757705620411155794242948507943008205 9275669583801816757447529 (205-digit)
Status:	Not factored. Reserved by Lionel Debroux 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 228.90-digit and the GNFS difficulty is 204.93-digit. SNFS must be faster than GNFS. It will take about 178 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 17777_227.
Put the following polynomial file 17777_227.poly in there too.
And then, run "perl factMsieve.pl 17777_227".

17777_227.poly ^*1

n: 8500620332853352373100619494859864036219623065828944278551768110817378446210927884562453439711314210424131541144585190430418520177440149893041637577056204111557942429485079430082059275669583801816757447529
m: 100000000000000000000000000000000000000
deg: 6
c6: 8
c0: -35
skew: 1.28
type: snfs
lss: 1
rlim: 46000000
alim: 46000000
lpbr: 30
lpba: 30
mfbr: 59
mfba: 59
rlambda: 2.7
alambda: 2.7

*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 205-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 45-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
45	11e6	4500	Dmitry Domanov	Sep 2, 2009
45	11e6	4500 / 3861
50	43e6	0 / 6440
50	43e6	/ 6440
55	11e7	0 / 17467 (2671)
55	11e7	/ 17467 (2671)
60	26e7	0 / 41942 (7513)
60	26e7	/ 41942 (7513)
65	85e7	0 / 69396 (13587)
65	85e7	/ 69396 (13587)

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

echo 8500620332853352373100619494859864036219623065828944278551768110817378446210927884562453439711314210424131541144585190430418520177440149893041637577056204111557942429485079430082059275669583801816757447529 | ecm -n -c 6440 43e6

Command line to find prime factors up to about 55-digit

echo 8500620332853352373100619494859864036219623065828944278551768110817378446210927884562453439711314210424131541144585190430418520177440149893041637577056204111557942429485079430082059275669583801816757447529 | ecm -n -c 17467 11e7

Command line to find prime factors up to about 60-digit

echo 8500620332853352373100619494859864036219623065828944278551768110817378446210927884562453439711314210424131541144585190430418520177440149893041637577056204111557942429485079430082059275669583801816757447529 | ecm -n -c 41942 26e7

Command line to find prime factors up to about 65-digit

echo 8500620332853352373100619494859864036219623065828944278551768110817378446210927884562453439711314210424131541144585190430418520177440149893041637577056204111557942429485079430082059275669583801816757447529 | ecm -n -c 69396 85e7

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