Dressler & Parker (1975) used a computer-aided proof (based on calculations involving the subset sum problem) to show that every integer greater than 96 may be represented as a sum of distinct super-prime numbers.
Their proof relies on a result resembling Bertrand's postulate, stating that (after the larger gap between super-primes 5 and 11) each super-prime number is less than twice its predecessor in the sequence.
Broughan & Barnett (2009) show that there are super-primes up to x.
This can be used to show that the set of all super-primes is small.
A variation on this theme is the sequence of prime numbers with palindromic prime indices, beginning with This number theory-related article is a stub.