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Chains of large gaps between consecutive primes
 Adv. in Math
, 1981
"... ABSTRACT. 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 ..."
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ABSTRACT. 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 = coe Y where Co = 1.31256... is the solution of the equation 4 / Co e4/co = 3. The principal new tool used is a result of independent interest, namely, a mean value theorem for generalized twin primes lying in a residue class with a large modulus. 1.