Portion of Primes in Short in Intervals and Landau's Inequality
Mehdi Hassani*1
1 Department of Mathematics University of Zanjan University Blvd., 45371-38791, Zanjan, Iran
*Corresponding author’s e-mail: mehdi.hassani@znu.ac.ir
Original: 17 February 2020 Revised: 5 September 2020 Accepted: 26 September 2020 Published online: 20 December 2020
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Abstract
In this paper, we study Landau’s inequality concerning primes counting function, asserting that $\pi(2x)<2\pi(x)$ for $x$ sufficiently large. We give some variants of this inequality to study portion of primes in intervals with similar length.
Key Words: Landau’s inequality, prime numbers
References
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