Note On Prime Gaps And Very Short Intervals

Details Note On Prime Gaps And Very Short Intervals Note On Prime Gaps And Very Short Intervals

2010-08-13

arxiv.org/abs/1008.2381v2

Mathematics

Number Theory

12 Pages, 1 Table, Improved

Scientific paper

Assuming the Riemann hypothesis, this article discusses a new elementary argument that seems to prove that the maximal prime gap of a finite sequence of primes p_1, p_2, ..., p_n <= x, satisfies max {p_(n+1) - p_n : p_n <= x} <= c1((logx)^2)/loglogx, c1 > 0 constant. Equivalently, it shows that the very short intervals (x, x + y] contain prime numbers for all y > c2((logx)^2)/loglogx, c2 > 0 constant, and sufficiently large x > 0.

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