2020/07/28 by Christian Elsholtz · 1 citation
Mathematics · #Advanced Mathematical Theories #Analytic Number Theory Research #Combinatorics #Computer science #Constant (computer programming) #Discrete mathematics #History and Theory of Mathematics #Mathematics #Prime (order theory) #Prime number #Pure mathematics #Riemann hypothesis #Statistics #Value (mathematics)
paper · open access · doi:10.1080/00029890.2020.1751560
published in American Mathematical Monthly 127(7), 639-642 (Taylor & Francis)
openalex publication_date 2020/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
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….