# Super Primes

Super-prime numbers (also known as higher-order primes or prime-indexed primes) are the subsequence of prime numbers that occupy prime-numbered positions within the sequence of all prime numbers.

That is, if p(i) denotes the ith prime number, the numbers in this sequence are those of the form p(p(i)). 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.

First 20: 3, 5, 11, 17, 31, 41, 59, 67, 83, 109, 127, 157, 179, 191, 211, 241, 277, 283, 331, 353

Checkout list of first: 10, 50, 100, 500, 1000 super primes. You can also check all super primes.

## External#

- OEIS: A006450
- Wikipedia: Super-prime

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