Contribution and Reservation

(10²¹⁶+17)/9 =: (1)₂₁₅3_<216>; = 79 · 149027 · [9437684184074970622612613916033320197020717519381723718836023606554951100196618105912089085472075369496896969660591714296535264751626530602441262755726203985898325544365387795339703638030005361454008131150061_<208>] RESERVED

Status

Expression:	(10²¹⁶+17)/9
Composite Factor:	943768418407497062261261391603332019702071751938172371883602 360655495110019661810591208908547207536949689696966059171429 653526475162653060244126275572620398589832554436538779533970 3638030005361454008131150061 (208-digit)
Status:	Not factored. Reserved by Sinkiti Sibata 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 216.00-digit and the GNFS difficulty is 207.97-digit. SNFS must be faster than GNFS. It will take about 66 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_216.
Put the following polynomial file 11113_216.poly in there too.
And then, run "perl factMsieve.pl 11113_216".

11113_216.poly ^*1

n: 9437684184074970622612613916033320197020717519381723718836023606554951100196618105912089085472075369496896969660591714296535264751626530602441262755726203985898325544365387795339703638030005361454008131150061
m: 1000000000000000000000000000000000000
deg: 6
c6: 1
c0: 17
skew: 1.60
type: snfs
lss: 1
rlim: 28000000
alim: 28000000
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 208-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 9437684184074970622612613916033320197020717519381723718836023606554951100196618105912089085472075369496896969660591714296535264751626530602441262755726203985898325544365387795339703638030005361454008131150061 | ecm -n -c 2104 3e6

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

echo 9437684184074970622612613916033320197020717519381723718836023606554951100196618105912089085472075369496896969660591714296535264751626530602441262755726203985898325544365387795339703638030005361454008131150061 | ecm -n -c 4439 11e6

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

echo 9437684184074970622612613916033320197020717519381723718836023606554951100196618105912089085472075369496896969660591714296535264751626530602441262755726203985898325544365387795339703638030005361454008131150061 | ecm -n -c 7548 43e6

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

echo 9437684184074970622612613916033320197020717519381723718836023606554951100196618105912089085472075369496896969660591714296535264751626530602441262755726203985898325544365387795339703638030005361454008131150061 | ecm -n -c 17769 11e7

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