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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.

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    $\begingroup$ Well, for starters prime gaps do repeat so no sieving makes sense. $\endgroup$ – freakish Oct 26 '16 at 18:55
  • $\begingroup$ Prime gaps $\endgroup$ – Bumblebee Oct 26 '16 at 18:56
  • $\begingroup$ @bof Thanks, hope it's OK now. $\endgroup$ – Cloudscape Dec 25 '16 at 7:51
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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.

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  • $\begingroup$ Despite being unable to repay it in a proper way, I am quite grateful for this wonderful christmas present. The former being the case, I choose to pay it forward. $\endgroup$ – Cloudscape Dec 25 '16 at 9:19

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