Note On The Maximal Primes Gaps

2013/12/06 by Carella, N. A.
#11A41 #11N05 #11N13 #11P32 #11Y55 #FOS: Mathematics #General Mathematics (math.GM)

paper · doi:10.48550/arxiv.1312.2481

Abstract

This note presents a result on the maximal prime gap of the form p_(n+1) - p_n <= C(log p_n)^(1+e), where C > 0 is a constant, for any arbitrarily small real number e > 0, and all sufficiently large integer n > n₀. Equivalently, the result shows that any short interval [x, x + y], y => C(log x)^(1+e), contains prime numbers for all sufficiently large real numbers x => x₀ unconditionally. An application demonstrates that a prime p => x > 2 can be determined in deterministic polynomial time O(log(x)⁸).

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• Note On Prime Gaps And Very Short Intervals
• On Maximal Prime Gaps
• On the Maximal Gap between Primes
• On the gaps between consecutive primes
• The existence of small prime gaps in subsets of the integers