Mangammal primes

devarajkandadai · 2011-12-22, 05:19

I wanted to check whether the exponent in M_47 (12978189 ) is a Mangammal prime A123239-0EIS or not. So I tried to run the following program in pari:

{p(n) = if (Mod(3,12978189)^n = = 2, print(“integer”))}

for (n = 1, 12978188, print p(n)))

However this will take at least some hours .

Two questions: a) Is pari capable of this?

b) If so is there a shorter cut?

A.K. Devaraj

axn · 2011-12-22, 05:30

1. 12978189 = 3^2*7^2*29429 is not a prime.
2. 47th mersenne prime has an exponent 43112609
3.

Code:

? p=43112609; s=Mod(3,p); z=znorder(s); for(i=2,z, if((s*=3)==2, return(i)))
%7 = 30763196
? ##
  ***   last result computed in 18,347 ms.
? Mod(3,p)^%
%8 = Mod(2, 43112609)

4. Alternately,

Code:

? znlog(2, Mod(3,p))
%9 = 30763196
? ##
  ***   last result computed in 32 ms.

devarajkandadai · 2011-12-23, 11:03

Quote:

Originally Posted by axn

1. 12978189 = 3^2*7^2*29429 is not a prime.
2. 47th mersenne prime has an exponent 43112609
3.

Code:

? p=43112609; s=Mod(3,p); z=znorder(s); for(i=2,z, if((s*=3)==2, return(i)))
%7 = 30763196
? ##
  ***   last result computed in 18,347 ms.
? Mod(3,p)^%
%8 = Mod(2, 43112609)

4. Alternately,

Code:

? znlog(2, Mod(3,p))
%9 = 30763196
? ##
  ***   last result computed in 32 ms.

Thank you very much.
A.K. Devaraj

Christenson · 2011-12-24, 04:22

Small correction: 2^43112609-1 is the 47th KNOWN Mersenne Prime. There's a distinct nonzero (O(1:1000) or better) probability that it's actually the 48th Mersenne Prime.

2011-12-22, 05:19	#1
devarajkandadai May 2004 2²·79 Posts	Mangammal primes I wanted to check whether the exponent in M_47 (12978189 ) is a Mangammal prime A123239-0EIS or not. So I tried to run the following program in pari: {p(n) = if (Mod(3,12978189)^n = = 2, print(“integer”))} for (n = 1, 12978188, print p(n))) However this will take at least some hours . Two questions: a) Is pari capable of this? b) If so is there a shorter cut? A.K. Devaraj

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2011-12-24, 04:22	#4
Christenson Dec 2010 Monticello 5×359 Posts	Small correction: 2^43112609-1 is the 47th KNOWN Mersenne Prime. There's a distinct nonzero (O(1:1000) or better) probability that it's actually the 48th Mersenne Prime.