Unusually Large Gaps between Consecutive Primes

  title={Unusually Large Gaps between Consecutive Primes},
  author={Helmut Maier and Carl Pomerance},
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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Topics in multiplicative number theory, Lecture

H. L. Montgomery
Notes in Math., • 1971
View 9 Excerpts
Highly Influenced

deBruijn, On the number of positive integers :<:; x and free of prime factors > y, Nederl

N G.
Akad. Wetensch. Proc. Ser. A • 1951
View 5 Excerpts
Highly Influenced

The exceptional set in Goldbach's

H. L. Montgomery, R. C. Vaughan
Acta Arith • 1975
View 9 Excerpts
Highly Influenced

The number of k -twin primes lying on an interval of a given length, Dokl

A. F. Lavrik
Akad. Nauk SSSR • 1961
View 3 Excerpts
Highly Influenced

A large sieve density estimate near a = I

P. X. Gallagher
Invent. Math • 1970
View 3 Excerpts
Highly Influenced

On the problem of Jacobsthal

H. Iwaniec
Demonstratio Math • 1978
View 2 Excerpts

On the order of magnitude of the difference between consecutive prime numbers

H. Cramer
Acta Arith • 1936
View 1 Excerpt

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