Contribution and Reservation

8·10²⁰⁰+3 =: 8(0)₁₉₉3_<201>; = 11 · 607472219 · 147010366511382569644373_<24> · 7546527715304377195290179372975899421_<37> · [107913492600146389511828126361061001602717552095077467114432068529999855181951097623769940565256091764288088215600992621367406387499_<132>] (Serge Batalov / GMP-ECM 6.2.1 B1=3000000, sigma=4043050459 for P37 / Oct 21, 2008) SUBMIT/RESERVE

Status

Expression:	8·10²⁰⁰+3
Composite Factor:	107913492600146389511828126361061001602717552095077467114432 068529999855181951097623769940565256091764288088215600992621 367406387499 (132-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 200.90-digit and the GNFS difficulty is 131.03-digit. GNFS must be faster than SNFS. It will take about 7 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 80003_200.
Put the following polynomial file 80003_200.poly in there too.
And then, run "perl factMsieve.pl 80003_200".

80003_200.poly ^*1

# Murphy_E = 6.430191e-11, selected by Jeff Gilchrist
n: 107913492600146389511828126361061001602717552095077467114432068529999855181951097623769940565256091764288088215600992621367406387499
Y0: -19033392627987988289967557
Y1: 304612724316973
c0: -116499866917249617995354782911840
c1: 4921936071381268461321224052
c2: -23815585880767150741301
c3: -205976711597598856
c4: 68183070720
c5: 43200
skew: 482533.17
type: gnfs
# selected mechanically
rlim: 10400000
alim: 10400000
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 132-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	2336	Wataru Sakai	Apr 20, 2009
40	3e6	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 107913492600146389511828126361061001602717552095077467114432068529999855181951097623769940565256091764288088215600992621367406387499 | ecm -n -c 3962 11e6

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

echo 107913492600146389511828126361061001602717552095077467114432068529999855181951097623769940565256091764288088215600992621367406387499 | ecm -n -c 7465 43e6

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

echo 107913492600146389511828126361061001602717552095077467114432068529999855181951097623769940565256091764288088215600992621367406387499 | ecm -n -c 17751 11e7

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

echo 107913492600146389511828126361061001602717552095077467114432068529999855181951097623769940565256091764288088215600992621367406387499 | 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