The distribution of small gaps between successive primes

Author:
Richard P. Brent

Journal:
Math. Comp. **28** (1974), 315-324

MSC:
Primary 10-04; Secondary 10A25, 10H15

MathSciNet review:
0330017

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Abstract | References | Similar Articles | Additional Information

Abstract: For and large *N*, a well-known conjecture of Hardy and Littlewood implies that the number of primes such that is the least prime greater than *p* is asymptotic to

**[1]**Paul T. Bateman and Roger A. Horn,*A heuristic asymptotic formula concerning the distribution of prime numbers*, Math. Comp.**16**(1962), 363–367. MR**0148632**, 10.1090/S0025-5718-1962-0148632-7**[2]**Richard P. Brent,*The first occurrence of large gaps between successive primes*, Math. Comp.**27**(1973), 959–963. MR**0330021**, 10.1090/S0025-5718-1973-0330021-0**[3]**F. Gruenberger & G. Armerding,*Statistics on the First Six Million Prime Numbers*, Paper P-2460, The RAND Corporation, Santa Monica, Calif., 1961, 145 pp. (Copy deposited in the UMT File and reviewed in*Math. Comp.*, v. 19, 1965, pp. 503-505.)**[4]**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**[5]**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**[6]**D. H. Lehmer, "Tables concerning the distribution of primes up to 37 millions", 1957. Copy deposited in the UMT File and reviewed in*MTAC*, v. 13, 1959, pp. 56-57.**[7]**C. L. Liu,*Introduction to combinatorial mathematics*, McGraw-Hill Book Co., New York-Toronto, Ont.-London, 1968. MR**0234840****[8]**B. H. Mayoh,*The second Goldbach conjecture revisited*, Nordisk Tidskr. Informationsbehandling (BIT)**8**(1968), 128–133. MR**0238761****[9]**Hans Riesel,*Primes forming arithmetic series and clusters of large primes*, Nordisk Tidskr. Informationsbehandling (BIT)**10**(1970), 333–342. MR**0282931****[10]**John W. Wrench Jr.,*Evaluation of Artin’s constant and the twin-prime constant*, Math. Comp.**15**(1961), 396–398. MR**0124305**, 10.1090/S0025-5718-1961-0124305-0

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0330017-X

Keywords:
Prime,
distribution of primes,
Hardy-Littlewood conjecture,
prime gap,
twin primes

Article copyright:
© Copyright 1974
American Mathematical Society