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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



Large intervals between consecutive primes

Author: J. H. Cadwell
Journal: Math. Comp. 25 (1971), 909-913
MSC: Primary 10H15
MathSciNet review: 0299567
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Abstract: Some results in number theory, including the Prime Number Theorem, can be obtained by assuming a random distribution of prime numbers. In addition, conjectural formulae, such as Cherwell’s for the density of prime pairs $(p,p + 2)$ obtained in this way, have been found to agree well with the available evidence. Recently, primes have been determined over ranges of 150,000 numbers with starting points up to ${10^{15}}$. Statistical arguments are used to obtain a formula for the largest interval between consecutive primes in such a range, and it is found to agree well with recorded values. The same method is applied to predict the maximum interval between consecutive primes occurring below a given integer.

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Keywords: Consecutive primes, interval between primes, maximum interval between primes
Article copyright: © Copyright 1971 American Mathematical Society