Contribution and Reservation

(23·10¹⁹³-41)/9 =: 2(5)₁₉₂1_<194>; = 3² · 7 · 29 · 12097 · 19421 · 41175707 · 173256341 · 3380474941_<10> · 278067141973787440159_<21> · [8878506420470077733153707056339101035098915749128617822704389752681314283286225003432565978064250243007097561544332709347944489658825733_<136>] SUBMIT/RESERVE

Status

Expression:	(23·10¹⁹³-41)/9
Composite Factor:	887850642047007773315370705633910103509891574912861782270438 975268131428328622500343256597806425024300709756154433270934 7944489658825733 (136-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 195.76-digit and the GNFS difficulty is 135.95-digit. GNFS may be faster than SNFS. It will take about 12 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 25551_193.
Put the following polynomial file 25551_193.poly in there too.
And then, run "perl factMsieve.pl 25551_193".

25551_193.poly ^*1

# Murphy_E = 3.360045e-11, selected by Jeff Gilchrist
n: 8878506420470077733153707056339101035098915749128617822704389752681314283286225003432565978064250243007097561544332709347944489658825733
Y0: -159756089071199763246465116
Y1: 1611877542885731
c0: 493649908345385467696609776986175
c1: 5416388019236452918466699430
c2: -3827736040868393143187
c3: -66724789855703336
c4: 38268326586
c5: 85320
skew: 466725.38
type: gnfs
# selected mechanically
rlim: 14200000
alim: 14200000
lpbr: 28
lpba: 28
mfbr: 55
mfba: 55
rlambda: 2.6
alambda: 2.6

*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 136-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	May 7, 2009
		1192	Wataru Sakai	Aug 17, 2009
		644	Wataru Sakai	Aug 21, 2009
		2336 / 2336
45	11e6	0 / 3962
45	11e6	/ 3962
50	43e6	0 / 7465 (1130)
50	43e6	/ 7465 (1130)
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 8878506420470077733153707056339101035098915749128617822704389752681314283286225003432565978064250243007097561544332709347944489658825733 | ecm -n -c 3962 11e6

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

echo 8878506420470077733153707056339101035098915749128617822704389752681314283286225003432565978064250243007097561544332709347944489658825733 | ecm -n -c 7465 43e6

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

echo 8878506420470077733153707056339101035098915749128617822704389752681314283286225003432565978064250243007097561544332709347944489658825733 | ecm -n -c 17751 11e7

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

echo 8878506420470077733153707056339101035098915749128617822704389752681314283286225003432565978064250243007097561544332709347944489658825733 | 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