Contribution and Reservation

(16·10²⁴⁸-7)/9 =: 1(7)₂₄₈_<249>; = 3² · 31 · 100271 · [6354742010362590418595633709985644200910077695816301184999324868237105321917309388252380056419067687776797916276917431101420447282408678852273699485068502986933288128876042619046390653292937350453310159495644144074853840635883128684625874553_<241>] SUBMIT/RESERVE

Status

Expression:	(16·10²⁴⁸-7)/9
Composite Factor:	635474201036259041859563370998564420091007769581630118499932 486823710532191730938825238005641906768777679791627691743110 142044728240867885227369948506850298693328812887604261904639 065329293735045331015949564414407485384063588312868462587455 3 (241-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 249.20-digit and the GNFS difficulty is 240.80-digit. SNFS must be faster than GNFS. It will take about 844 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_248.
Put the following polynomial file 17777_248.poly in there too.
And then, run "perl factMsieve.pl 17777_248".

17777_248.poly ^*1

n: 6354742010362590418595633709985644200910077695816301184999324868237105321917309388252380056419067687776797916276917431101420447282408678852273699485068502986933288128876042619046390653292937350453310159495644144074853840635883128684625874553
m: 200000000000000000000000000000000000000000
deg: 6
c6: 25
c0: -7
skew: 0.81
type: snfs
lss: 1
rlim: 100000000
alim: 100000000
lpbr: 30
lpba: 30
mfbr: 62
mfba: 62
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 241-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 / 3858
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 6354742010362590418595633709985644200910077695816301184999324868237105321917309388252380056419067687776797916276917431101420447282408678852273699485068502986933288128876042619046390653292937350453310159495644144074853840635883128684625874553 | ecm -n -c 6440 43e6

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

echo 6354742010362590418595633709985644200910077695816301184999324868237105321917309388252380056419067687776797916276917431101420447282408678852273699485068502986933288128876042619046390653292937350453310159495644144074853840635883128684625874553 | ecm -n -c 17467 11e7

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

echo 6354742010362590418595633709985644200910077695816301184999324868237105321917309388252380056419067687776797916276917431101420447282408678852273699485068502986933288128876042619046390653292937350453310159495644144074853840635883128684625874553 | ecm -n -c 41942 26e7

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

echo 6354742010362590418595633709985644200910077695816301184999324868237105321917309388252380056419067687776797916276917431101420447282408678852273699485068502986933288128876042619046390653292937350453310159495644144074853840635883128684625874553 | ecm -n -c 69396 85e7

Submit factors

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