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- W2023704174 abstract "We prove some results concerning the distribution of primes assuming the Riemann hypothesis. First, we prove the explicit result that there exists a prime in the interval [Formula: see text] for all x ≥ 2; this improves a result of Ramaré and Saouter. We then show that the constant 4/π may be reduced to (1 + ϵ) provided that x is taken to be sufficiently large. From this, we get an immediate estimate for a well-known theorem of Cramér, in that we show the number of primes in the interval [Formula: see text] is greater than [Formula: see text] for c = 3 + ϵ and all sufficiently large values of x." @default.
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- W2023704174 date "2015-03-31" @default.
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- W2023704174 title "On the Riemann hypothesis and the difference between primes" @default.
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- W2023704174 doi "https://doi.org/10.1142/s1793042115500426" @default.
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