In prime numbers, one has the sieve of Eratosthenes, which is a method of computing the next prime, once you have all previous primes: You just cross out the multiples of the previous primes on the number line, and the first remaining number is the next prime.
I wonder whether there is such a method for prime gaps. Of course, one could add up the prime gaps and then apply the sieve of Eratosthenes, get the next prime, and then compute the next prime gap from it, but I wonder whether there is a more "direct" way.
A "more direct way" to apply a sieve process to prime gaps is described in the paper by Fred Holt and Helgi Rudd "Eratosthenes sieve and the gaps between primes"; see arXiv:1408.6002.