Contribution and Reservation

(43·10¹⁸⁸+11)/9 =: 4(7)₁₈₇9_<189>; = 8387 · 200015330041_<12> · 73294994688491_<14> · 86021662446856582196340817_<26> · [45172473400715363806431220689349008576670945631260308299011341083624453308210514912851237384219906104953017455002980766454772198286171_<134>] SUBMIT/RESERVE

Status

Expression:	(43·10¹⁸⁸+11)/9
Composite Factor:	451724734007153638064312206893490085766709456312603082990113 410836244533082105149128512373842199061049530174550029807664 54772198286171 (134-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 191.03-digit and the GNFS difficulty is 133.65-digit. GNFS may be faster than SNFS. It will take about 10 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 47779_188.
Put the following polynomial file 47779_188.poly in there too.
And then, run "perl factMsieve.pl 47779_188".

47779_188.poly ^*1

# Murphy_E = 4.386016e-11, selected by Jeff Gilchrist
n: 45172473400715363806431220689349008576670945631260308299011341083624453308210514912851237384219906104953017455002980766454772198286171
Y0: -58768192366281592916768010
Y1: 778591583690333
c0: -160479757071797757880642248277163
c1: -3073609234866309378307360717
c2: -15721653443221957192531
c3: -242303433292223363
c4: 74774497254
c5: 64440
skew: 594418.12
type: gnfs
# selected mechanically
rlim: 12300000
alim: 12300000
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 134-digit composite number so far are as follows. According to the reports, unknown prime factors of this composite number are probably 35-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
35	1e6	118	Makoto Kamada	Feb 19, 2009
35	1e6	118 / 0
40	3e6	500	Erik Branger	May 11, 2009
		500 / 2318
		/ 1818
45	11e6	0 / 4365 (527)
45	11e6	/ 4365 (527)
50	43e6	0 / 7534 (1244)
50	43e6	/ 7534 (1244)
55	11e7	0 / 17765 (3125)
55	11e7	/ 17765 (3125)

Command line to find prime factors up to about 40-digit

echo 45172473400715363806431220689349008576670945631260308299011341083624453308210514912851237384219906104953017455002980766454772198286171 | ecm -n -c 1818 3e6

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

echo 45172473400715363806431220689349008576670945631260308299011341083624453308210514912851237384219906104953017455002980766454772198286171 | ecm -n -c 4365 11e6

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

echo 45172473400715363806431220689349008576670945631260308299011341083624453308210514912851237384219906104953017455002980766454772198286171 | ecm -n -c 7534 43e6

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

echo 45172473400715363806431220689349008576670945631260308299011341083624453308210514912851237384219906104953017455002980766454772198286171 | ecm -n -c 17765 11e7

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