An Explicit Result for Primes Between Cubes

@article{Dudek2014AnER,
  title={An Explicit Result for Primes Between Cubes},
  author={A. Dudek},
  journal={arXiv: Number Theory},
  year={2014}
}
  • A. Dudek
  • Published 2014
  • Mathematics
  • arXiv: Number Theory
We prove that there is a prime between $n^3$ and $(n+1)^3$ for all $n \geq \exp(\exp(33.217))$. Our new tool which we derive is a version of Landau's explicit formula for the Riemann zeta-function with explicit bounds on the error term. We use this along with other recent explicit estimates regarding the zeroes of the Riemann zeta-function to obtain the result. Furthermore, we show that there is a prime between any two consecutive $m$th powers for $m \geq 4.971 \times 10^9$. 
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