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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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Large intervals between consecutive primes
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by J. H. Cadwell PDF
Math. Comp. 25 (1971), 909-913 Request permission

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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Additional Information
  • © Copyright 1971 American Mathematical Society
  • Journal: Math. Comp. 25 (1971), 909-913
  • MSC: Primary 10H15
  • DOI: https://doi.org/10.1090/S0025-5718-1971-0299567-6
  • MathSciNet review: 0299567