Contribution and Reservation

(29·10¹⁸⁴-11)/9 =: 3(2)₁₈₃1_<185>; = 7 · 3547253 · 22124567 · 4554039086972747233_<19> · 1125483683198753328964583_<25> · [11443385985100041732346252855087611543625340410002691409085705234887286072280889361202027546977964371539046953753693747659880927_<128>] SUBMIT/RESERVE

Status

Expression:	(29·10¹⁸⁴-11)/9
Composite Factor:	114433859851000417323462528550876115436253404100026914090857 052348872860722808893612020275469779643715390469537536937476 59880927 (128-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 185.46-digit and the GNFS difficulty is 127.06-digit. GNFS must be faster than SNFS. It will take about 5 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 32221_184.
Put the following polynomial file 32221_184.poly in there too.
And then, run "perl factMsieve.pl 32221_184".

32221_184.poly

# Murphy_E = 1.112055e-10, selected by Jeff Gilchrist
n: 11443385985100041732346252855087611543625340410002691409085705234887286072280889361202027546977964371539046953753693747659880927
Y0: -3227033314991563294605080
Y1: 91285386449309
c0: 692885753005279709897547288723
c1: -32039882816401084018730525
c2: -91678353304982906035
c3: -348126874264955
c4: -27816283428
c5: 32700
skew: 161444.44
type: gnfs
# selected mechanically
rlim: 8100000
alim: 8100000
lpbr: 28
lpba: 28
mfbr: 53
mfba: 53
rlambda: 2.5
alambda: 2.5

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 128-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	Mar 17, 2009
		1836	Wataru Sakai	Dec 2, 2009
		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 11443385985100041732346252855087611543625340410002691409085705234887286072280889361202027546977964371539046953753693747659880927 | ecm -n -c 3962 11e6

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

echo 11443385985100041732346252855087611543625340410002691409085705234887286072280889361202027546977964371539046953753693747659880927 | ecm -n -c 7465 43e6

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

echo 11443385985100041732346252855087611543625340410002691409085705234887286072280889361202027546977964371539046953753693747659880927 | ecm -n -c 17751 11e7

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

echo 11443385985100041732346252855087611543625340410002691409085705234887286072280889361202027546977964371539046953753693747659880927 | 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