Contribution and Reservation

5·10¹⁹²-7 =: 4(9)₁₉₁3_<193>; = 405074911 · 39130784437_<11> · 1055724654930419_<16> · 2150492628020236856777894383_<28> · [138940060255352917497510962318998533818910635413057695065614809172817655873731032561767948732767643562656642737775501722271172720487_<132>] SUBMIT/RESERVE

Status

Expression:	5·10¹⁹²-7
Composite Factor:	138940060255352917497510962318998533818910635413057695065614 809172817655873731032561767948732767643562656642737775501722 271172720487 (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 193.60-digit and the GNFS difficulty is 131.14-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 49993_192.
Put the following polynomial file 49993_192.poly in there too.
And then, run "perl factMsieve.pl 49993_192".

49993_192.poly ^*1

# Murphy_E = 6.379343e-11, selected by Jeff Gilchrist
n: 138940060255352917497510962318998533818910635413057695065614809172817655873731032561767948732767643562656642737775501722271172720487
Y0: -20847899238197746041629994
Y1: 298372122554021
c0: 2262453481553201622105382465225
c1: 6332147537710657091035043227
c2: 33123365142104146596121
c3: -5679059463558243
c4: -71462470810
c5: 35280
skew: 621920.21
type: gnfs
# selected mechanically
rlim: 10500000
alim: 10500000
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 138940060255352917497510962318998533818910635413057695065614809172817655873731032561767948732767643562656642737775501722271172720487 | ecm -n -c 3962 11e6

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

echo 138940060255352917497510962318998533818910635413057695065614809172817655873731032561767948732767643562656642737775501722271172720487 | ecm -n -c 7465 43e6

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

echo 138940060255352917497510962318998533818910635413057695065614809172817655873731032561767948732767643562656642737775501722271172720487 | ecm -n -c 17751 11e7

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

echo 138940060255352917497510962318998533818910635413057695065614809172817655873731032561767948732767643562656642737775501722271172720487 | 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