József Sándor and Antoine Verroken
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 17, 2011, Number 2, Page 1—3
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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
- P. Dusart, The kth prime is greater than k(ln k + ln ln k − 1) for k ≥ 2; Math. Comp., 68(1999), no. 225, 411-415.
- J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math., 6(1962), 64-94.
- J. Sándor, On a limit for the sequence of primes, Octogon Math. Mag., 8(2000), no. 1, 180-181.
- J. Sándor, Geometric theorems, diophantine equations, and arithmetic functions, American Research Press, 2002, USA.
Related papers
- Sándor, J. (2012). On certain bounds and limits for prime numbers. Notes on Number Theory and Discrete Mathematics, 18(1), 1-5.
Cite this paper
Sándor, J., & Verroken, A. (2011). On a limit involving the product of prime numbers. Notes on Number Theory and Discrete Mathematics, 17(2), 1-3.