Steely's refinement of the Goldbach Conjecture

In number theory, the Goldbach Conjecture (not yet proven) states that every even number greater than two is the sum of two primes. For example, the even number 8 is the sum of primes 3 and 5.

Steely's refinement of the Goldbach Conjecture is as follows:

Every even number n greater than four is the sum of two primes p1 and p2 such that the remainder given by dividing the product of p1 and p2 by n is prime.

For example, 8 is the sum of primes 3 and 5, and (3 x 5) ÷ 8 gives 1 with a remainder of 7, which is prime.

Is this anything?