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
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Authors and affiliations

József Sándor
Babeș-Bolyai University of Cluj, Romania

Antoine Verroken
Univ. of Gent, Gent, Belgium

Abstract

Let pk denote the kth prime number. The aim of this note is to prove that the limit of the sequence (p_n / sqrt{n}{p_1 \dots p_n}) is e.

Keywords

  • Arithmetic functions
  • Estimates
  • Primes

AMS Classification

  • 11A25
  • 11N37

References

  1. 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.
  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.

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Cite this paper

APA

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.

Chicago

Sándor, 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.

MLA

Sándor, 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.

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