On the Riemann hypothesis and the difference between primes
A Lean 4 proof of Theorems 1, 2 and 3 of A. W. Dudek, On the Riemann hypothesis and the difference between primes, Int. J. Number Theory 11, 2015, arXiv 1402.6417. Each theorem is conditional on the Riemann hypothesis, the paper's own hypothesis, stated with Mathlib's RiemannHypothesis. Theorem 2: for every real x at least 2 there is a prime in the interval from x - (4/pi) sqrt(x) log x to x. Theorem 1: there is c > 0 such that the interval from x to x + c sqrt(x) log x holds more than sqrt(x) primes for every real x at least 2. Theorem 3: for every epsilon > 0 and all large x there is a…
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