Quote:
Originally Posted by SethTro
Just regular primes. I don't think it would be very hard to store other prime gaps.
There are ~100k prime gaps, can you tell me the relative magnitude of other records? How many twin prime gaps? How many other categories might be worth recording (quad primes, quint primes, ...)?

The current first occurence list for twin prime gaps has 4757 entries (at 54.6*10
^{15}) and for quadruplet prime gaps 134776 entries (at 5.5*10
^{15}).
The number of entries would increase dramatically if the search is continued outside the range for first occurence gaps.
A. Kourbatov has listed maximal gaps for tuplets up to septuplets here
https://arxiv.org/abs/1309.4053
and has even results for gaps in decuplets in the OEIS, for example A
202281.
The probabilistic models for studying prime gaps in arithmetic progressions are similar to those for the usual prime gaps, that's why I think they are also quite relevant. My search lists on average a little over 200 entries per common difference q (for even q <= 2690). If this is too much data, one idea would be only to list the maximal gaps for each q, or only the top CSG value as I do in the other thread.
Quote:
Originally Posted by kruoli

Here's some data as well. Though the site looked different some weeks ago. I'm not sure if the search for narrow admissible tuplets is still active, but here seems to be a contact address if any new results are found.
http://math.mit.edu/~primegaps/