Contribution and Reservation

(2·10¹⁹⁴-17)/3 =: (6)₁₉₃1_<194>; = 702313 · 2657561 · 16564837 · 65459837 · 11225608146810247_<17> · 3000489897150321473_<19> · [977981542575426054595129013577787669570557340469645786029471421420693441351014495622657024768518898025558200275767775421764408951043_<132>] SUBMIT/RESERVE

Status

Expression:	(2·10¹⁹⁴-17)/3
Composite Factor:	977981542575426054595129013577787669570557340469645786029471 421420693441351014495622657024768518898025558200275767775421 764408951043 (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.

NFS

Use GGNFS and/or Msieve if GMP-ECM cannot find a factor. The SNFS difficulty of this composite number is 194.30-digit and the GNFS difficulty is 131.99-digit. GNFS must be faster than SNFS. It will take about 8 CPU-days to factor this composite number on 64-bit Opteron-2600MHz.

Steps of GNFS

Put factMsieve.pl to which $GGNFS_BIN_PATH and $NUM_CPUS were modified properly in the working directory 66661_194.
Put the following polynomial file 66661_194.poly in there too.
And then, run "perl factMsieve.pl 66661_194".

66661_194.poly

# Murphy_E = 5.632746e-11, selected by Jeff Gilchrist
n: 977981542575426054595129013577787669570557340469645786029471421420693441351014495622657024768518898025558200275767775421764408951043
Y0: -29805004952023129643143912
Y1: 374221497055369
c0: -213375862843122345507556033094021
c1: 4135176540994270660638105186
c2: 20197004305272516584742
c3: -45994152146252306
c4: 1387076259
c5: 41580
skew: 558640.92
type: gnfs
# selected mechanically
rlim: 11100000
alim: 11100000
lpbr: 28
lpba: 28
mfbr: 54
mfba: 54
rlambda: 2.6
alambda: 2.6

These parameters were not fully adjusted. The approximate expressions which were used for making the parameters are: d=log10(n); time=5*10^(d/20-5)[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	500	Erik Branger	Feb 3, 2009
		1850	Wataru Sakai	Nov 24, 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 977981542575426054595129013577787669570557340469645786029471421420693441351014495622657024768518898025558200275767775421764408951043 | ecm -n -c 3961 11e6

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

echo 977981542575426054595129013577787669570557340469645786029471421420693441351014495622657024768518898025558200275767775421764408951043 | ecm -n -c 7465 43e6

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

echo 977981542575426054595129013577787669570557340469645786029471421420693441351014495622657024768518898025558200275767775421764408951043 | ecm -n -c 17751 11e7

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

echo 977981542575426054595129013577787669570557340469645786029471421420693441351014495622657024768518898025558200275767775421764408951043 | ecm -n -c 42014 26e7

Contribution and Reservation

Status

How to factor it

ECM, P-1, P+1

NFS

Steps of GNFS

See also

Efforts by ECM

Submit polynomial for GNFS

Submit factors

Make reservation