A Note on Oppermann's Conjecture

A prime gap is the difference between consecutive prime numbers. The n^th prime gap, denoted g₍, is calculated by subtracting the n^th prime from the (n+1) ^th prime: g₍=p₍+₁-p₍. Oppermann's conjecture is a prominent unsolved problem in pure mathematics concerning prime gaps. Despite verification for numerous primes, a general proof remains elusive. If true, the conjecture implies that prime gaps grow at a rate bounded by g₍ {p₍}. This note presents a proof of Oppermann's conjecture using the square root function on inequalities involving prime numbers. This proof simultaneously establishes Andrica's, Legendre's, and Brocard's conjectures.