Thread: Superprime gaps
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Old 2019-01-11, 14:47   #5
Bobby Jacobs
 
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May 2018

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The maximal gaps between superprimes are in A280080, A280081, and A280082 in OEIS. The first few maximal gaps are 2 between 3 and 5, 6 between 5 and 11, 14 between 17 and 31, 18 between 41 and 59, and 26 between 83 and 109. An interesting thing is that many maximal superprime gaps correspond to maximal prime gaps. There are a lot of maximal prime gaps starting with a prime n, where p(n) is the start of a maximal superprime gap. For example, p(2)=3, so the maximal prime gap between 2 and 3 corresponds to the maximal superprime gap between 3 and 5. Also, p(3)=5, so the prime gap between 3 and 5 corresponds to the superprime gap between 5 and 11. However, there are maximal superprime gaps not corresponding to a maximal prime gap. For example, the maximal superprime gap between 41 and 59 corresponds to the prime gap between 13 and 17, which is not maximal. It would be fun to see which maximal superprime gaps correspond to maximal prime gaps.
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