2020/04/02 by Christian Elsholtz, Elsholtz, Christian
Mathematics · #11A41 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11A41
paper · pdf · doi:10.48550/arxiv.2004.01285
arxiv created 2020/04/02 · arxiv updated 2020/04/06
Mills proved that there exists a real constant A>1 such that for all n∈ ℕ the values \lfloor A3n\rfloor 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: \lfloor A^1010n\rfloor is prime, where A=1.00536773279814724017… can be computed to millions of digits. Similarly, \lfloor A^313n\rfloor is prime, with A=3.8249998073439146171615551375… .