Contribution and Reservation

(22·10¹⁹⁵-31)/9 =: 2(4)₁₉₄1_<196>; = 18307 · 61409 · 226017649145596719973_<21> · 52333261226040013874068864421239_<32> · [183827640054939547309364653857658843651474314964103416379471945088898934302542172912689307063113308104017719598958720895076627555187681_<135>] (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=1438106012 for P32 / Oct 22, 2008) SUBMIT/RESERVE

Status

Expression:	(22·10¹⁹⁵-31)/9
Composite Factor:	183827640054939547309364653857658843651474314964103416379471 945088898934302542172912689307063113308104017719598958720895 076627555187681 (135-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 196.34-digit and the GNFS difficulty is 134.26-digit. GNFS must be faster than SNFS. It will take about 10 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 24441_195.
Put the following polynomial file 24441_195.poly in there too.
And then, run "perl factMsieve.pl 24441_195".

24441_195.poly ^*1

# Murphy_E = 4.06359e-11, selected by Jeff Gilchrist
n: 183827640054939547309364653857658843651474314964103416379471945088898934302542172912689307063113308104017719598958720895076627555187681
Y0: -75510382215782957492637817
Y1: 909236376496921
c0: 371466108605451523065574033098000
c1: 3038975702613473268869049660
c2: -28855679247068108217716
c3: -46237944257002279
c4: 166578971992
c5: 74880
skew: 428761.67
type: gnfs
# selected mechanically
rlim: 12800000
alim: 12800000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
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 135-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 10, 2009
		1836	Wataru Sakai	Jul 26, 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 183827640054939547309364653857658843651474314964103416379471945088898934302542172912689307063113308104017719598958720895076627555187681 | ecm -n -c 3962 11e6

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

echo 183827640054939547309364653857658843651474314964103416379471945088898934302542172912689307063113308104017719598958720895076627555187681 | ecm -n -c 7465 43e6

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

echo 183827640054939547309364653857658843651474314964103416379471945088898934302542172912689307063113308104017719598958720895076627555187681 | ecm -n -c 17751 11e7

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

echo 183827640054939547309364653857658843651474314964103416379471945088898934302542172912689307063113308104017719598958720895076627555187681 | 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