Proof there exists a non-trivial lower bound on the number of twin primes leading to a rigorous proof of the Twin Prime Conjecture.

Proof of the existence of a non-trivial lower bound on the number of twin primes, with derivation and calculation of that lower bound, and a generalization to a simple, non-trivial, lower bound that requires no prior knowledge about specific primes, proving Polignac’s 1846 twin prime conjecture. Includes an extrapolation showing how this method also proves part of Polignac’s 1849 generalized conjecture on the infinitude of all even prime gap sizes.