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This paper proposes, and demonstrates the efficacy of, an elementary methodfor establishing a lower bound for cardinalities of selected sets of twinprimes, and shows that the proof employed may be modified for selected sets ofGoldbach pairs. Our sieve method is centred on the restrictive properties ofintervals, specifically regarding divisibility distributions. We implicitly usethe Chinese Remainder Theorem by way of the use of the midpoint in ourintervals, and consider the sieve of Eratosthenes in such a way as to find aset of primes whose distribution is mirror-symmetrical about that midpoint.Bounds are established through the use of the formulae closely associated withthe Prime Number theorem and the Mertens theorem. We show that the Goldbachconjecture is true if the Riemann hypothesis is true.

Goldbach and Twin Prime Pairs: A Sieve Method to Connect the Two