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