A prime gap $g(n)$ between two consecutive primes is defined as
where $p_n$ is the $n$th prime number. An interesting property of prime gaps is that the “spikes” of its plot occurs at multiples of $6$. From its graph, it seems very improbable that a continuous function could approximate. Some formulas for prime numbers are known (they are not exact) are known (there is a whole wikipedia article on them) and some approximations for the prime counting function are known, but my question is:
What are some approximations for $g(n)$?
An approximation in terms of continuous functions isn’t necessary (such a formula is highly improbable); an approximation in terms of other discontinuous functions might also help.