A Note on Oppermann's Conjecture

A prime gap is the difference between consecutive prime numbers. The nᵗʰ prime gap, denoted gₙ, is calculated by subtracting the nᵗʰ prime from the (n+1)ᵗʰ prime: gₙ=pₙ₊₁-pₙ. 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 gₙ<√ pₙ. 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.