# Explicit Estimates in the Theory of Prime Numbers

@article{Dudek2016ExplicitEI,
title={Explicit Estimates in the Theory of Prime Numbers},
author={A. Dudek},
journal={The Bulletin of the Center for Children's Books},
year={2016}
}
• A. Dudek
• Published 2016
• Mathematics
• The Bulletin of the Center for Children's Books
It is the purpose of this thesis to enunciate and prove a collection of explicit results in the theory of prime numbers. First, the problem of primes in short intervals is considered. We prove that there is a prime between consecutive cubes $n^3$ and $(n+1)^3$ for all $n \geq \exp(\exp(33.3))$. To prove this, we first derive an explicit version of the Riemann--von Mangoldt explicit formula. We then assume the Riemann hypothesis and show that there will be a prime in the interval \$(x-4/ \pi… Expand
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