Unusually Large Gaps between Consecutive Primes

@inproceedings{Maier1981UnusuallyLG,
  title={Unusually Large Gaps between Consecutive Primes},
  author={Helmut Maier and Carl Pomerance},
  year={1981}
}
Let G(x) denote the largest gap between consecutive grimes below x, In a series of papers from 1935 to 1963, Erdos, Rankin, and Schonhage showed that G(x) :::: (c + o( I)) logx loglogx log log log 10gx(loglog logx) -2, where c = eY and y is Euler's constant. Here, this result is shown with c = coeY where Co = 1.31256... is the solution of the equation 4/ Co e -4/co = 3 . The principal new tool used is a result of independent interest, namely, a mean value theorem for generalized twin primes… CONTINUE READING

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