Remote Access Mathematics of Computation
Green Open Access

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
DOI: https://doi.org/10.1090/S0025-5718-1971-0299567-6
MathSciNet review: 0299567
Full-text PDF Free Access

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 $ (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.


References [Enhancements On Off] (What's this?)

  • [1] M. F. Jones, M. Lal & W. J. Blundon, ``Statistics on certain large primes,'' Math. Comp., v. 21, 1967, pp. 103-107. MR 36 #3707. MR 0220655 (36:3707)
  • [2] G. H. Hardy & J. E. Littlewood, ``Some problems of 'Partitio Numerorum'. III: On the expression of a number as a sum of primes,'' Acta Math., v. 44, 1923, pp. 1-70. MR 1555183
  • [3] Lord Cherwell, ``Note on the distribution of the intervals between prime numbers,'' Quart. J. Math. Oxford Ser., v. 17, 1946, pp. 46-62. MR 8, 136; 708. MR 0017308 (8:136e)
  • [4] D. Shanks, ``On maximal gaps between successive primes,'' Math. Comp., v. 18, 1964, pp. 646-651. MR 29 #4745. MR 0167472 (29:4745)
  • [5] L. J. Lander & T. R. Parkin, ``On first appearance of prime differences,'' Math. Comp., v. 21, 1967, pp. 483-488. MR 37 #6237. MR 0230677 (37:6237)

Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 10H15

Retrieve articles in all journals with MSC: 10H15


Additional Information

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

American Mathematical Society