Unconditional Prime-Representing Functions, Following Mills

Abstract

Mills proved that there exists a real constant A > 1 such that for all n∈N the values ⌊A3n⌋ are prime numbers. No explicit value of A is known, but assuming the Riemann hypothesis one can choose A=1.3063778838…. Here we give a first unconditional variant: ⌊A1010n⌋ is prime, where A=1.00536773279814724017… can be computed to millions of digits. Similarly, ⌊A313n⌋ is prime, with A=3.8249998073439146171615551375….

Locations

• American Mathematical Monthly - View
• arXiv (Cornell University) - View - PDF