TRANSCENDENCE OF THE MINIMUM OF PRIME-REPRESENTING CONSTANTS (Analytic Number Theory and Related Topics)

Abstract

Let (ck) k∈ℕ be a sequence of integers satisfying that Ck ≥ 2 for every k∈ℕ and lim⁻ k→∞ ck = ∞. We investigate the set of A > 1 such that lA[c1…ck]| is a prime number for every k∈ℕ. Let W(ck) be the set of all such A > 1. We show that the minimum of W(ck) exists, and is transcendental.