Contribution and Reservation

(19·10¹⁸⁵+71)/9 =: 2(1)₁₈₄9_<186>; = 3 · 17 · 12326868841128266538371_<23> · 111808313062155714683573643800539_<33> · [3003406009090687751119109429703408159141068851531342602648036716692608662865742661191418683186041717439507344403574306740703995301_<130>] (Makoto Kamada / GMP-ECM 6.2 B1=250000, sigma=1213718395 for P33 / Jun 7, 2008) SUBMIT/RESERVE

Status

Expression:	(19·10¹⁸⁵+71)/9
Composite Factor:	300340600909068775111910942970340815914106885153134260264803 671669260866286574266119141868318604171743950734440357430674 0703995301 (130-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 186.28-digit and the GNFS difficulty is 129.48-digit. GNFS may be faster than SNFS. It will take about 6 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 21119_185.
Put the following polynomial file 21119_185.poly in there too.
And then, run "perl factMsieve.pl 21119_185".

21119_185.poly ^*1

# Murphy_E = 8.102623e-11, selected by Jeff Gilchrist
n: 3003406009090687751119109429703408159141068851531342602648036716692608662865742661191418683186041717439507344403574306740703995301
Y0: -9939412265920851657312027
Y1: 170919812075287
c0: 6577617220589017959902166770372
c1: 252045022072535910677562280
c2: -3532397779409443746341
c3: -8200413504267160
c4: 39675206412
c5: 30960
skew: 283645.66
type: gnfs
# selected mechanically
rlim: 9500000
alim: 9500000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

*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 130-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	2504	Max Dettweiler	Apr 21, 2009
40	3e6	2504 / 2008
45	11e6	0 / 3870
45	11e6	/ 3870
50	43e6	0 / 7452 (1103)
50	43e6	/ 7452 (1103)
55	11e7	0 / 17749 (3091)
55	11e7	/ 17749 (3091)
60	26e7	0 / 42014 (7634)
60	26e7	/ 42014 (7634)

Command line to find prime factors up to about 45-digit

echo 3003406009090687751119109429703408159141068851531342602648036716692608662865742661191418683186041717439507344403574306740703995301 | ecm -n -c 3870 11e6

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

echo 3003406009090687751119109429703408159141068851531342602648036716692608662865742661191418683186041717439507344403574306740703995301 | ecm -n -c 7452 43e6

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

echo 3003406009090687751119109429703408159141068851531342602648036716692608662865742661191418683186041717439507344403574306740703995301 | ecm -n -c 17749 11e7

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

echo 3003406009090687751119109429703408159141068851531342602648036716692608662865742661191418683186041717439507344403574306740703995301 | 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