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math.NT2021
On the sum of a prime and a square-free number with divisibility conditions
Shehzad Hathi, Daniel R. Johnston
Every integer greater than two can be expressed as the sum of a prime and a square-free number. Expanding on recent work, we provide explicit and asymptotic results when divisibili…
math.NT2021
Improving bounds on prime counting functions by partial verification of the Riemann hypothesis
Daniel R. Johnston
Using a recent verification of the Riemann hypothesis up to height , we provide strong estimates on and other prime counting functions for finite ranges of $…