An explicit lower bound for large gaps between some consecutive primes
Abstract
The main purpose of this paper is to clarify the numerical value of the constant cLG such that the above in- equality holds. We see that cLG is determined by several factors related to analytic number theory, for example, the ratio of integrals of functions in the multidimensional sieve of Maynard [14], the distribution of primes in arithmetic progressions to large moduli, and the coefficient of upper bound sieve of Selberg. We prove that the above inequality is valid at least for some cLG ≥ 2.0 × 10−17 .
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