Contribution and Reservation

(11·10¹⁹²+43)/9 =: 1(2)₁₉₁7_<193>; = 3 · 3203 · 29250110209_<11> · 2670433711978157_<16> · 453692740578735552721477164389_<30> · [3589226316010269059681018830007721984837214523215582227384325089871286371163106679189583897384898038294948828315383364247681736825979_<133>] (Makoto Kamada / GMP-ECM 6.1.3 B1=250000, sigma=2459156944 for P30 / Feb 1, 2008) SUBMIT/RESERVE

Status

Expression:	(11·10¹⁹²+43)/9
Composite Factor:	358922631601026905968101883000772198483721452321558222738432 508987128637116310667918958389738489803829494882831538336424 7681736825979 (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 193.94-digit and the GNFS difficulty is 132.56-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 12227_192.
Put the following polynomial file 12227_192.poly in there too.
And then, run "perl factMsieve.pl 12227_192".

12227_192.poly ^*1

# Murphy_E = 4.935274e-11, selected by Jeff Gilchrist
n: 3589226316010269059681018830007721984837214523215582227384325089871286371163106679189583897384898038294948828315383364247681736825979
Y0: -36440474323719319440392826
Y1: 505688140775389
c0: -502227190342180189471169239301725
c1: -5417889269507151383021670396
c2: 34162140871409488798295
c3: 219796156129478268
c4: -187174948702
c5: 55860
skew: 419466.24
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	2336	Wataru Sakai	May 2, 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 3589226316010269059681018830007721984837214523215582227384325089871286371163106679189583897384898038294948828315383364247681736825979 | ecm -n -c 3962 11e6

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

echo 3589226316010269059681018830007721984837214523215582227384325089871286371163106679189583897384898038294948828315383364247681736825979 | ecm -n -c 7465 43e6

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

echo 3589226316010269059681018830007721984837214523215582227384325089871286371163106679189583897384898038294948828315383364247681736825979 | ecm -n -c 17751 11e7

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

echo 3589226316010269059681018830007721984837214523215582227384325089871286371163106679189583897384898038294948828315383364247681736825979 | 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