"Germain Primes"
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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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