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Primes between consecutive powers
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abstract
This paper updates the explicit interval estimate for primes between consecutive powers. It is shown that there is least one prime between $n^{155}$ and $(n+1)^{155}$ for all $n\geq 1$. This result is in part obtained with a new explicit version of Goldston's 1983 estimate for the error in the truncated Riemann--von Mangoldt explicit formula.
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Cited by 1 Pith paper
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Effective short intervals containing primes
For every n ≥ 106 and every x ≥ 1, there is always a prime in the interval [x, x + x^(1−1/n)], making several classical prime-gap results fully explicit.
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