Abstract
The sieve of Eratosthenes (SoE) is a well-known method of extracting the set of prime numbers ℙ from the set positive integers ℕ. Applying the SoE again to the index of the prime numbers will result in the set of prime-indexed primes ℙ2={3,5,11,17,31,…}. More generally, the application of the SoE k-times will yield the set ℙk of k-th order primes. In this paper, we give an upper bound for the n-th k-order prime as well as some results relating to number-theoretic functions over ℙk.
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