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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: [email protected] 

Original: 17 February 2020        Revised: 5 September 2020        Accepted: 26 September 2020        Published online: 20 December 2020  

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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