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Subject: "Germain Primes"     Previous Topic | Next Topic
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neat_maths
Member since Aug-22-03
Feb-17-08, 07:21 PM (EST)
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"Germain Primes"
 
   A pair of primes n and p are known as a Sophie Germain Prime Pair if the larger prime, p is equal to 1 plus 2*n
For example, (2,5), (3,7), (5,11), (11,23), (23,47), (29,59), (41,83), ........
This leaves out upper Germain partners for 7, 13, 17, 19, 31, 37, 43...........
A "True Sophie Germain Prime Pair" is a pair of primes (n, p) where none of the integers (i,j,k) chosen from 1,2,3,....(p-1) raised to the power n can be added together in mod p to give 0.
ie
mod(i^n,p) plus mod(j^n,p) plus mod(k^n,p) cannot equal 0 (mod p)

It is my contention that for ALL primes n there exists a prime p
where
p is equal to 1 plus 2^q * n^r where q and r are positive integers
For example
(7, 29), (13, 53), (17, 137), ....(31, 15377) I would like to check the last pair.

CAN ANYONE PLEASE FIND A COUNTER EXAMPLE ?


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