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New Bounds And Computations On Prime-Indexed Primes, Jonathan Bayless, Dominic Klyve, Tomas Oliveira E Silva

Mathematics Faculty Scholarship

In a 2009 article, Barnett and Broughan considered the set of prime-index primes. If the prime numbers are listed in increasing order (2, 3, 5, 7, 11, 13, 17, . . .), then the prime-index primes are those which occur in a prime-numbered position in the list (3, 5, 11, 17, . . .). Barnett and Broughan established a prime-indexed prime number theorem analogous to the standard prime number theorem and gave an asymptotic for the size of the n-th prime-indexed prime.

We give explicit upper and lower bounds for π²(x), the number of prime-indexed primes up to …