Skip to main content
edited tags
Link
GH from MO
  • 105.3k
  • 8
  • 293
  • 398
Source Link
Sylvain JULIEN
  • 7k
  • 3
  • 31
  • 66

Which even numbers are known to be both prime gaps and the sum of 2 primes?

Goldbach's conjecture asserts that every even integer greater than $3$ is the sum of two primes, while de Polignac's one says every even positive integer is a prime gap infinitely often. My question is thus: which even positive integers are known to be both prime gaps (at least once) and the sum of 2 primes? Can we prove that the set of such integers has asymptotic density $1$ among all even positive integers?
Thanks in advance.