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The following is proven using arguments that do not revolve around theRiemann Hypothesis or Sieve Theory. If $p_n$ is the $n^{\rm th}$ prime and$g_n=p_{n+1}-p_n$, then $g_n=O({p_n}^{2/3})$.

The gap $g_n$ between two consecutive primes satisfies $g_n=O({p_n}^{2/3})$