Contribution and Reservation

(8·10¹⁸⁴-53)/9 =: (8)₁₈₃3_<184>; = 3² · 7 · 6637 · 59377 · 90065296430573975747_<20> · 67475797886411273729109827_<26> · [58913028362753951237802316734583805710571858745928990357031746550974040556656806255122874946114335569783560475087229302800294761_<128>] (Makoto Kamada / GMP-ECM 6.0.1 B1=11000000, sigma=2608337868 for P26 / May 8, 2005) SUBMIT/RESERVE

Status

Expression:	(8·10¹⁸⁴-53)/9
Composite Factor:	589130283627539512378023167345838057105718587459289903570317 465509740405566568062551228749461143355697835604750872293028 00294761 (128-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.

GNFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 185.60-digit and the GNFS difficulty is 127.77-digit. GNFS must be faster than SNFS. It will take about 5 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 88883_184.
Put the following polynomial file 88883_184.poly in there too.
And then, run "perl factMsieve.pl 88883_184".

88883_184.poly ^*1

# Murphy_E = 1.128412e-10, selected by Jeff Gilchrist
n: 58913028362753951237802316734583805710571858745928990357031746550974040556656806255122874946114335569783560475087229302800294761
Y0: -4808383122407966507368468
Y1: 100275273605957
c0: 1812698404909927660048151473497
c1: 64346144917825815351806367
c2: -33684984705782716903
c3: -5334350758962991
c4: 3578478950
c5: 22920
skew: 209591.21
type: gnfs
# selected mechanically
rlim: 8500000
alim: 8500000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

*1 These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=10^(d/21-4)[hours]; rlim=round(3*10^(d/37+3)); lpbr=floor(d/18+21); mfbr=floor(d/5+28); rlambda=floor(d/26+21)/10;

Efforts by ECM

The efforts by ECM to find small factors of this 128-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	500	Erik Branger	Jan 31, 2009
		1850	Wataru Sakai	Nov 27, 2009
		2350 / 2350
45	11e6	0 / 3961
45	11e6	/ 3961
50	43e6	0 / 7465 (1129)
50	43e6	/ 7465 (1129)
55	11e7	0 / 17751 (3097)
55	11e7	/ 17751 (3097)
60	26e7	0 / 42014 (7636)
60	26e7	/ 42014 (7636)

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

echo 58913028362753951237802316734583805710571858745928990357031746550974040556656806255122874946114335569783560475087229302800294761 | ecm -n -c 3961 11e6

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

echo 58913028362753951237802316734583805710571858745928990357031746550974040556656806255122874946114335569783560475087229302800294761 | ecm -n -c 7465 43e6

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

echo 58913028362753951237802316734583805710571858745928990357031746550974040556656806255122874946114335569783560475087229302800294761 | ecm -n -c 17751 11e7

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

echo 58913028362753951237802316734583805710571858745928990357031746550974040556656806255122874946114335569783560475087229302800294761 | ecm -n -c 42014 26e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation