Contribution and Reservation

(73·10²¹³-1)/9 =: 8(1)₂₁₃_<214>; = 313 · 6829 · [3794712696843573573475228557365113688292838290709612833780719563818048620458190245373920332761995151812679673798179400812785873771325310686903817496567734348070697888731018444227054191044446846029740255034843_<208>] SUBMIT/RESERVE

Status

Expression:	(73·10²¹³-1)/9
Composite Factor:	379471269684357357347522855736511368829283829070961283378071 956381804862045819024537392033276199515181267967379817940081 278587377132531068690381749656773434807069788873101844422705 4191044446846029740255034843 (208-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 216.96-digit and the GNFS difficulty is 207.58-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 81111_213.
Put the following polynomial file 81111_213.poly in there too.
And then, run "perl factMsieve.pl 81111_213".

81111_213.poly ^*1

n: 3794712696843573573475228557365113688292838290709612833780719563818048620458190245373920332761995151812679673798179400812785873771325310686903817496567734348070697888731018444227054191044446846029740255034843
m: 500000000000000000000000000000000000
deg: 6
c6: 584
c0: -125
skew: 0.77
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 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	May 26, 2009
		239	Dmitry Domanov	Jun 2, 2009
		357 / 0
40	3e6	326	Dmitry Domanov	Jun 2, 2009
		326 / 1366
		/ 1040
45	11e6	257	Dmitry Domanov	Jun 2, 2009
		257 / 4392 (559)
		/ 4135 (302)
50	43e6	0 / 7481 (1179)
50	43e6	/ 7481 (1179)
55	11e7	0 / 17751 (3104)
55	11e7	/ 17751 (3104)

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

echo 3794712696843573573475228557365113688292838290709612833780719563818048620458190245373920332761995151812679673798179400812785873771325310686903817496567734348070697888731018444227054191044446846029740255034843 | ecm -n -c 1040 3e6

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

echo 3794712696843573573475228557365113688292838290709612833780719563818048620458190245373920332761995151812679673798179400812785873771325310686903817496567734348070697888731018444227054191044446846029740255034843 | ecm -n -c 4135 11e6

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

echo 3794712696843573573475228557365113688292838290709612833780719563818048620458190245373920332761995151812679673798179400812785873771325310686903817496567734348070697888731018444227054191044446846029740255034843 | ecm -n -c 7481 43e6

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

echo 3794712696843573573475228557365113688292838290709612833780719563818048620458190245373920332761995151812679673798179400812785873771325310686903817496567734348070697888731018444227054191044446846029740255034843 | ecm -n -c 17751 11e7

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