Contribution and Reservation

(10²¹⁷+17)/9 =: (1)₂₁₆3_<217>; = 3 · 29 · 59 · 6871 · [31504041998517249661722986237771142963524806047964519593430130699527373526574464354022362205392195913858334142435891960252597770533927384890712494059164660182107791602665023945103929582014105512650673318404891_<209>] SUBMIT/RESERVE

Status

Expression:	(10²¹⁷+17)/9
Composite Factor:	315040419985172496617229862377711429635248060479645195934301 306995273735265744643540223622053921959138583341424358919602 525977705339273848907124940591646601821077916026650239451039 29582014105512650673318404891 (209-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 217.00-digit and the GNFS difficulty is 208.50-digit. SNFS must be faster than GNFS. It will take about 71 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 11113_217.
Put the following polynomial file 11113_217.poly in there too.
And then, run "perl factMsieve.pl 11113_217".

11113_217.poly ^*1

n: 31504041998517249661722986237771142963524806047964519593430130699527373526574464354022362205392195913858334142435891960252597770533927384890712494059164660182107791602665023945103929582014105512650673318404891
m: 1000000000000000000000000000000000000
deg: 6
c6: 10
c0: 17
skew: 1.09
type: snfs
lss: 1
rlim: 29000000
alim: 29000000
lpbr: 29
lpba: 29
mfbr: 58
mfba: 58
rlambda: 2.6
alambda: 2.6

*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 209-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	118	Makoto Kamada	Feb 18, 2009
		786	Andreas Tete	May 12, 2009
		904 / 904
40	3e6	0 / 2104
40	3e6	/ 2104
45	11e6	0 / 4439 (610)
45	11e6	/ 4439 (610)
50	43e6	0 / 7548 (1266)
50	43e6	/ 7548 (1266)
55	11e7	0 / 17769 (3131)
55	11e7	/ 17769 (3131)

Command line to find prime factors up to about 40-digit

echo 31504041998517249661722986237771142963524806047964519593430130699527373526574464354022362205392195913858334142435891960252597770533927384890712494059164660182107791602665023945103929582014105512650673318404891 | ecm -n -c 2104 3e6

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

echo 31504041998517249661722986237771142963524806047964519593430130699527373526574464354022362205392195913858334142435891960252597770533927384890712494059164660182107791602665023945103929582014105512650673318404891 | ecm -n -c 4439 11e6

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

echo 31504041998517249661722986237771142963524806047964519593430130699527373526574464354022362205392195913858334142435891960252597770533927384890712494059164660182107791602665023945103929582014105512650673318404891 | ecm -n -c 7548 43e6

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

echo 31504041998517249661722986237771142963524806047964519593430130699527373526574464354022362205392195913858334142435891960252597770533927384890712494059164660182107791602665023945103929582014105512650673318404891 | ecm -n -c 17769 11e7

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