A prime gap is the difference between consecutive prime numbers. The $n^{\text{th}}$ prime gap, denoted $g_{n}$, is calculated by subtracting the $n^{\text{th}}$ prime from the $(n+1)^{\text{th}}$ prime: $g_{n}=p_{n+1}-p_{n}$. 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 $g_{n}<{\sqrt {p_{n}}}$. We examine the ratio of Chebyshev functions for consecutive primes, $\frac{\theta(p_{n+1})}{\theta(p_{n})}$, and compare it to the square root of their ratio, $\sqrt {\frac{p_{n+1}}{p_{n}}}$. Assuming this inequality holds for primes larger than $10^{8}$, we demonstrate the truth of Oppermann's conjecture. For sufficiently large $n$, this inequality guarantees that $g_{n}<{\sqrt {p_{n}}}$ for all primes beyond a certain point. Our proof also validates Andrica's, Legendre's, and Brocard's conjectures for primes exceeding a specific threshold.