The first occurrence of large gaps between successive primes

Author:
Richard P. Brent

Journal:
Math. Comp. **27** (1973), 959-963

MSC:
Primary 10A20

DOI:
https://doi.org/10.1090/S0025-5718-1973-0330021-0

MathSciNet review:
0330021

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A table of the first occurrence of a string of composite numbers between two primes is given for and 301. All such strings between primes less than have been accounted for. The computation supports some conjectures on the distribution of these strings.

**[1]**K. I. Appel & J. B. Rosser,*Table for Estimating Functions of Primes*, IDA-CRD Technical Report Number 4, 1961, p. 102. (Reviewed in RMT**55**,*Math. Comp.*, v. 16, 1962, pp. 500-501.)**[2]**R. P. Brent,*Empirical Evidence for a Proposed Distribution of Small Prime Gaps*, Technical Report CS 123, Computer Science Dept., Stanford Univ., Calif., 1969.**[3]**J. H. Cadwell, "Large intervals between consecutive primes,"*Math. Comp.*, v. 25, 1971, pp. 909-913. MR**0299567 (45:8615)****[4]**H. Cramér, "On the order of magnitude of the difference between consecutive prime numbers,"*Acta Arith.*, v. 2, 1937, pp. 23-46.**[5]**J. W. L. Glaisher, "On long successions of composite numbers,"*Messenger Math.*, v. 7, 1877, pp. 102, 171.**[6]**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.)**[7]**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****[8]**S. M. Johnson, "An elementary remark on maximal gaps between successive primes,"*Math. Comp.*, v. 19, 1965, pp. 675-676.**[9]**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)****[10]**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)****[11]**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.**[12]**K. Pracher,*Primzahlverteilung*, Springer-Verlag, Berlin, 1957, pp. 154-164. MR**19**, 393. MR**0087685 (19:393b)****[13]**D. Shanks, "On maximal gaps between successive primes,"*Math. Comp.*, v. 18, 1964, pp. 646-651. MR**29**#4745. MR**0167472 (29:4745)****[14]**S. Weintraub, "Distribution of primes between and ," 1971. Copy deposited in the UMT File and reviewed in*Math. Comp.*, v. 26, 1972, p. 596.**[15]**A. E. Western, "Note on the magnitude of the difference between successive primes,"*J. London Math. Soc.*, v. 9, 1934, pp. 276-278.

Retrieve articles in *Mathematics of Computation*
with MSC:
10A20

Retrieve articles in all journals with MSC: 10A20

Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1973-0330021-0

Keywords:
Prime,
distribution of primes,
prime gap,
maximal prime gap,
successive composites,
consecutive primes

Article copyright:
© Copyright 1973
American Mathematical Society