Contribution and Reservation

(64·10²⁸¹-1)/9 =: 7(1)₂₈₁_<282>; = 3² · 71 · 117760681 · [9450097687028652230921847297053650039945085766965806213080332525434209517752501247204213643897166067907967058913938128060643253747223255107157311223733961202013596578973884463752723623173149371292342943426594720350815615678085454449712821767002085409791144023422470128529_<271>] SUBMIT/RESERVE

Status

Expression:	(64·10²⁸¹-1)/9
Composite Factor:	945009768702865223092184729705365003994508576696580621308033 252543420951775250124720421364389716606790796705891393812806 064325374722325510715731122373396120201359657897388446375272 362317314937129234294342659472035081561567808545444971282176 7002085409791144023422470128529 (271-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 283.81-digit and the GNFS difficulty is 270.98-digit. SNFS must be faster than GNFS. It will take about 12022 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_281.
Put the following polynomial file 71111_281.poly in there too.
And then, run "perl factMsieve.pl 71111_281".

71111_281.poly ^*1

n: 9450097687028652230921847297053650039945085766965806213080332525434209517752501247204213643897166067907967058913938128060643253747223255107157311223733961202013596578973884463752723623173149371292342943426594720350815615678085454449712821767002085409791144023422470128529
m: 200000000000000000000000000000000000000000000000
deg: 6
c6: 1
c0: -10
skew: 1.47
type: snfs
lss: 1
rlim: 380000000
alim: 380000000
lpbr: 32
lpba: 32
mfbr: 66
mfba: 66
rlambda: 2.9
alambda: 2.9

*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 271-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	450	Serge Batalov	Jan 27, 2009
40	3e6	450 / 438
45	11e6	550	Serge Batalov	Jan 27, 2009
		550 / 4379
		/ 3829
50	43e6	0 / 7413 (1092)
50	43e6	/ 7413 (1092)
55	11e7	0 / 17732 (3075)
55	11e7	/ 17732 (3075)
60	26e7	0 / 42008 (7627)
60	26e7	/ 42008 (7627)

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

echo 9450097687028652230921847297053650039945085766965806213080332525434209517752501247204213643897166067907967058913938128060643253747223255107157311223733961202013596578973884463752723623173149371292342943426594720350815615678085454449712821767002085409791144023422470128529 | ecm -n -c 3829 11e6

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

echo 9450097687028652230921847297053650039945085766965806213080332525434209517752501247204213643897166067907967058913938128060643253747223255107157311223733961202013596578973884463752723623173149371292342943426594720350815615678085454449712821767002085409791144023422470128529 | ecm -n -c 7413 43e6

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

echo 9450097687028652230921847297053650039945085766965806213080332525434209517752501247204213643897166067907967058913938128060643253747223255107157311223733961202013596578973884463752723623173149371292342943426594720350815615678085454449712821767002085409791144023422470128529 | ecm -n -c 17732 11e7

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

echo 9450097687028652230921847297053650039945085766965806213080332525434209517752501247204213643897166067907967058913938128060643253747223255107157311223733961202013596578973884463752723623173149371292342943426594720350815615678085454449712821767002085409791144023422470128529 | ecm -n -c 42008 26e7

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