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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## Details

### Authors and affiliations

József Sándor

*Babeș-Bolyai University of Cluj, Romania*

Antoine Verroken

*Univ. of Gent, Gent, Belgium*

### Abstract

Let p_{k} denote the _{k}th prime number. The aim of this note is to prove that the limit of the sequence is *e*.

### Keywords

- Arithmetic functions
- Estimates
- Primes

### AMS Classification

- 11A25
- 11N37

### References

- 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. - 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

## Cite this paper

APASándor, J., & Verroken, A. (2011). On a limit involving the product of prime numbers. Notes on Number Theory and Discrete Mathematics, 17(2), 1-3.

ChicagoSándor, József, and Antoine Verroken. “On a Limit Involving the Product of Prime Numbers.” Notes on Number Theory and Discrete Mathematics 17, no. 2 (2011): 1-3.

MLASándor, József, and Antoine Verroken. “On a Limit Involving the Product of Prime Numbers.” Notes on Number Theory and Discrete Mathematics 17.2 (2011): 1-3. Print.