The sieve of Eratosthenes (SoE) is a well-known method of extracting the set of prime numbers from the set positive integers . Applying the SoE again to the index of the prime numbers will result in the set of prime-indexed primes . More generally, the application of the SoE -times will yield the set of -th order primes. In this paper, we give an upper bound for the -th -order prime as well as some results relating to number-theoretic functions over .
"Arithmetic functions of higher-order primes." Involve 13 (2) 181 - 191, 2020. https://doi.org/10.2140/involve.2020.13.181