Contribution and Reservation

(31·10¹⁹⁵-13)/9 =: 3(4)₁₉₄3_<196>; = 11 · 409 · 433 · 1231 · 9857 · 29106199 · 226024859 · 5027043972621015155274153602261603_<34> · [4406138049467862108822304886904684665095340472558491300911579282015207482952828657413786426677152881312064869462756319604850096004769_<133>] (Philippe STROHL / gmp-ecm 6.1.1 B1=2131945, sigma=463069574 for P34 / Mar 9, 2007) SUBMIT/RESERVE

Status

Expression:	(31·10¹⁹⁵-13)/9
Composite Factor:	440613804946786210882230488690468466509534047255849130091157 928201520748295282865741378642667715288131206486946275631960 4850096004769 (133-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 196.49-digit and the GNFS difficulty is 132.64-digit. GNFS must be faster than SNFS. It will take about 9 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 34443_195.
Put the following polynomial file 34443_195.poly in there too.
And then, run "perl factMsieve.pl 34443_195".

34443_195.poly ^*1

# Murphy_E = 5.888409e-11, selected by Jeff Gilchrist
n: 4406138049467862108822304886904684665095340472558491300911579282015207482952828657413786426677152881312064869462756319604850096004769
Y0: -38466040709390593600672691
Y1: 566409709858601
c0: 12743911080891267181702715527560
c1: 675273985806067991417123394
c2: -2011637548804946253551
c3: -43264121121620890
c4: 23974124896
c5: 52320
skew: 303202.29
type: gnfs
# selected mechanically
rlim: 11500000
alim: 11500000
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 133-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	Feb 2, 2009
		1850	Wataru Sakai	Aug 31, 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 4406138049467862108822304886904684665095340472558491300911579282015207482952828657413786426677152881312064869462756319604850096004769 | ecm -n -c 3961 11e6

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

echo 4406138049467862108822304886904684665095340472558491300911579282015207482952828657413786426677152881312064869462756319604850096004769 | ecm -n -c 7465 43e6

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

echo 4406138049467862108822304886904684665095340472558491300911579282015207482952828657413786426677152881312064869462756319604850096004769 | ecm -n -c 17751 11e7

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

echo 4406138049467862108822304886904684665095340472558491300911579282015207482952828657413786426677152881312064869462756319604850096004769 | 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