Contribution and Reservation

(64·10³¹¹-1)/9 =: 7(1)₃₁₁_<312>; = 3 · 2111 · 50727232006475081_<17> · [2213537130543906475153324390303948098474796612383675216242904740392606439266488277705446256616344515156530174687546526087603891644677021627828079184471715487448011802462213795266282909773272464079806943098656533110678191611718627938061182856538554550949617235427081834863299907369480803426107_<292>] SUBMIT/RESERVE

Status

Expression:	(64·10³¹¹-1)/9
Composite Factor:	221353713054390647515332439030394809847479661238367521624290 474039260643926648827770544625661634451515653017468754652608 760389164467702162782807918447171548744801180246221379526628 290977327246407980694309865653311067819161171862793806118285 6538554550949617235427081834863299907369480803426107 (292-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 313.81-digit and the GNFS difficulty is 291.35-digit. SNFS must be faster than GNFS. It will take about 120225 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 71111_311.
Put the following polynomial file 71111_311.poly in there too.
And then, run "perl factMsieve.pl 71111_311".

71111_311.poly ^*1

n: 2213537130543906475153324390303948098474796612383675216242904740392606439266488277705446256616344515156530174687546526087603891644677021627828079184471715487448011802462213795266282909773272464079806943098656533110678191611718627938061182856538554550949617235427081834863299907369480803426107
m: 20000000000000000000000000000000000000000000000000000
deg: 6
c6: 1
c0: -10
skew: 1.47
type: snfs
lss: 1
rlim: 1190000000
alim: 1190000000
lpbr: 33
lpba: 33
mfbr: 70
mfba: 70
rlambda: 3.0
alambda: 3.0

*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 292-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 40-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
40	3e6	600	Serge Batalov	Feb 16, 2009
40	3e6	600 / 0
45	11e6	600	Serge Batalov	Feb 16, 2009
		500	Serge Batalov	Aug 20, 2009
		1100 / 4311
		/ 3211
50	43e6	0 / 7279 (916)
50	43e6	/ 7279 (916)
55	11e7	0 / 17695 (3020)
55	11e7	/ 17695 (3020)
60	26e7	0 / 41999 (7612)
60	26e7	/ 41999 (7612)

Command line to find prime factors up to about 45-digit

echo 2213537130543906475153324390303948098474796612383675216242904740392606439266488277705446256616344515156530174687546526087603891644677021627828079184471715487448011802462213795266282909773272464079806943098656533110678191611718627938061182856538554550949617235427081834863299907369480803426107 | ecm -n -c 3211 11e6

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

echo 2213537130543906475153324390303948098474796612383675216242904740392606439266488277705446256616344515156530174687546526087603891644677021627828079184471715487448011802462213795266282909773272464079806943098656533110678191611718627938061182856538554550949617235427081834863299907369480803426107 | ecm -n -c 7279 43e6

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

echo 2213537130543906475153324390303948098474796612383675216242904740392606439266488277705446256616344515156530174687546526087603891644677021627828079184471715487448011802462213795266282909773272464079806943098656533110678191611718627938061182856538554550949617235427081834863299907369480803426107 | ecm -n -c 17695 11e7

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

echo 2213537130543906475153324390303948098474796612383675216242904740392606439266488277705446256616344515156530174687546526087603891644677021627828079184471715487448011802462213795266282909773272464079806943098656533110678191611718627938061182856538554550949617235427081834863299907369480803426107 | ecm -n -c 41999 26e7

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