Formulas giving prime numbers under Cramér's conjecture

2006/11/24 by Bakir Farhi, Farhi, Bakir
Mathematics · #11A41 #Analytic Number Theory Research #FOS: Mathematics #History and Theory of Mathematics #Mathematics and Applications #Number Theory (math.NT) #math.NT #msc:11A41

paper · pdf · doi:10.48550/arxiv.math/0611761

9 pages

arxiv created 2006/11/24 · openalex publication_date 2006/11/24 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Under Cramér's conjecture concerning the prime numbers, we prove that for any x>1, there exists a real A=A(x)>1 for which the formula [A^nx] (where [] denotes the integer part) gives a prime number for any positive integer n. Under the same conjecture, we also prove that for any ε>0, there exists a positive real number B for which the formula [B.n!^2+ε] gives a prime number for any sufficiently large positive integer n.

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