Contribution and Reservation

(64·10³⁰⁵-1)/9 =: 7(1)₃₀₅_<306>; = 3 · 641 · 1373 · 16729 · 208147 · [77347718160625654521404297311876678719873682046606519017463906169699423062890796169458658673057407214915110219867006145166103976725415263809839326792267070757717202978081579603896213153786034195456859939988052261946093483227482032225105928601989735709336730398090723933416039552883034931843_<290>] SUBMIT/RESERVE

Status

Expression:	(64·10³⁰⁵-1)/9
Composite Factor:	773477181606256545214042973118766787198736820466065190174639 061696994230628907961694586586730574072149151102198670061451 661039767254152638098393267922670707577172029780815796038962 131537860341954568599399880522619460934832274820322251059286 01989735709336730398090723933416039552883034931843 (290-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 307.81-digit and the GNFS difficulty is 289.89-digit. SNFS must be faster than GNFS. It will take about 75857 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_305.
Put the following polynomial file 71111_305.poly in there too.
And then, run "perl factMsieve.pl 71111_305".

71111_305.poly ^*1

n: 77347718160625654521404297311876678719873682046606519017463906169699423062890796169458658673057407214915110219867006145166103976725415263809839326792267070757717202978081579603896213153786034195456859939988052261946093483227482032225105928601989735709336730398090723933416039552883034931843
m: 2000000000000000000000000000000000000000000000000000
deg: 6
c6: 1
c0: -10
skew: 1.47
type: snfs
lss: 1
rlim: 940000000
alim: 940000000
lpbr: 33
lpba: 33
mfbr: 69
mfba: 69
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 290-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 77347718160625654521404297311876678719873682046606519017463906169699423062890796169458658673057407214915110219867006145166103976725415263809839326792267070757717202978081579603896213153786034195456859939988052261946093483227482032225105928601989735709336730398090723933416039552883034931843 | ecm -n -c 3211 11e6

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

echo 77347718160625654521404297311876678719873682046606519017463906169699423062890796169458658673057407214915110219867006145166103976725415263809839326792267070757717202978081579603896213153786034195456859939988052261946093483227482032225105928601989735709336730398090723933416039552883034931843 | ecm -n -c 7279 43e6

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

echo 77347718160625654521404297311876678719873682046606519017463906169699423062890796169458658673057407214915110219867006145166103976725415263809839326792267070757717202978081579603896213153786034195456859939988052261946093483227482032225105928601989735709336730398090723933416039552883034931843 | ecm -n -c 17695 11e7

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

echo 77347718160625654521404297311876678719873682046606519017463906169699423062890796169458658673057407214915110219867006145166103976725415263809839326792267070757717202978081579603896213153786034195456859939988052261946093483227482032225105928601989735709336730398090723933416039552883034931843 | ecm -n -c 41999 26e7

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