Super-prime
Super-prime numbers are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers. The subsequence begins
That is, if p denotes the ith prime number, the numbers in this sequence are those of the form p. used a computer-aided proof 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 each super-prime number is less than twice its predecessor in the sequence.
show that there are
super-primes up to x.
This can be used to show that the set of all super-primes is small.
One can also define "higher-order" primeness much the same way and obtain analogous sequences of primes.
A variation on this theme is the sequence of prime numbers with palindromic prime indices, beginning with
