On a limit involving the product of prime numbers

József Sándor and Antoine Verroken
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 17, 2011, Number 2, Page 1–3
Full paper (PDF, 142 Kb)

Details

Authors and affiliations

József Sándor
Babeș-Bolyai University of Cluj, Romania

Antoine Verroken
Univ. of Gent, Gent, Belgium

Abstract

Let denote the -th prime number. The aim of this note is to prove that the limit of the sequence is .

Keywords

• Arithmetic functions
• Estimates
• Primes

AMS Classification

• 11A25
• 11N37

References

1. P. Dusart, The k^th prime is greater than k(ln k + ln ln k − 1) for k ≥ 2; Math. Comp., 68(1999), no. 225, 411-415.
2. J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math., 6(1962), 64-94.
3. J. Sándor, On a limit for the sequence of primes, Octogon Math. Mag., 8(2000), no. 1, 180-181.
4. J. Sándor, Geometric theorems, diophantine equations, and arithmetic functions, American Research Press, 2002, USA.