Jackson Lawrence Capper
Abstract
We derive a generalised proof of Polignac’s Conjecture by regarding a prime in terms of its whole indivisibility and the consequent probability of prime intervals by applying the second Borel–Cantelli lemma. The specific case of the Twin Prime Conjecture is proven as an example.
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We derive a generalised proof of Polignac’s Conjecture by regarding a prime in terms of its whole indivisibility and the consequent probability of prime intervals by applying the second Borel–Cantelli lemma. The specific case of the Twin Prime Conjecture is proven as an example.
Key concepts: Twin prime, Conjecture, Lemma (botany), Mathematics, Prime (order theory), Combinatorics, Number theory, Discrete mathematics