[seqfan] Re: Prime numbers that differ by 30 with no primes between p and p+30

Chris Thompson cet1 at cam.ac.uk
Sun Dec 29 18:43:03 CET 2019


I was motivated by David Seal's posting to wonder what the situation was
for a similar but much better known series, namely prime pairs.

  A001359 is the lesser of each pair, primes p such that p+2 is also prime
  A006512 is the greater of each pair, primes p such hat p-2 is also prime
  A001097 is their union as a set, with 5 occurring once
  A077800 is their union as a multiset, with 5 occurring twice

It is probably not desirable that every sequence involving pairs should
have all four versions in OEIS, though!

The union version for (p,p+30) being consecutive primes would face the
same problem as for 5 with the prime pairs: should the p such that
(p-30,p,p+30) are consecutive primes, occur once or twice? [The smallest
such p is 69623, and there are undoubtedly infinitely many of them.]  

-- 
Chris Thompson
Email: cet1 at cam.ac.uk






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