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 | References | Similar Articles | Additional Information

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 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 . 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.

**[1]**M. F. Jones, M. Lal, and W. J. Blundon,*Statistics on certain large primes*, Math. Comp.**21**(1967), 103–107. MR**0220655**, 10.1090/S0025-5718-1967-0220655-3**[2]**G. H. Hardy and J. E. Littlewood,*Some problems of ‘Partitio numerorum’; III: On the expression of a number as a sum of primes*, Acta Math.**44**(1923), no. 1, 1–70. MR**1555183**, 10.1007/BF02403921**[3]**Cherwell,*Note on the distribution of the intervals between prime numbers*, Quart. J. Math., Oxford Ser.**17**(1946), 46–62. MR**0017308****[4]**Daniel Shanks,*On maximal gaps between successive primes*, Math. Comp.**18**(1964), 646–651. MR**0167472**, 10.1090/S0025-5718-1964-0167472-8**[5]**L. J. Lander and T. R. Parkin,*On first appearance of prime differences*, Math. Comp.**21**(1967), 483–488. MR**0230677**, 10.1090/S0025-5718-1967-0230677-4

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DOI:
https://doi.org/10.1090/S0025-5718-1971-0299567-6

Keywords:
Consecutive primes,
interval between primes,
maximum interval between primes

Article copyright:
© Copyright 1971
American Mathematical Society