Some data in the attachment, just to show off.

The interested reader might also like to check, for instance, the differences p(n+42)-p(n) for p in the range [327076775000..327076783000]. Makes for a nice graph.

And this related result, 100 primes in the range p+[1..8349] while there are no primes in q+[1..8349], with q < p, still appears to be unmatched:

https://www.mersenneforum.org/showpo...2&postcount=86
Excuse my being a bit cocky today