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25 April 2024

» arxiv » 1512.3936

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Large gaps between consecutive prime numbers containing perfect $k$-th powers of prime numbers
Helmut Maier ; Michael Th. Rassias ;
Date:	12 Dec 2015
Abstract:	Let $kgeq 2$ be a fixed natural number. We establish the existence of infinitely many pairs of consecutive primes $p_n$, $p_{n+1}$ satisfying $$ p_{n+1}-p_ngeq c:frac{log p_n: log_2 p_n: log_4 p_n}{log_3 p_n}:,$$ with $c$ being a fixed positive constant, for which the interval $(p_n, p_{n+1})$ contains the $k$-th power of a prime number.
Source:	arXiv, 1512.3936
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