THE FIRST OCCURRENCE OF LARGE GAPS BETWEEN SUCCESSIVE PRIMES

RICHARD P. BRENT

Abstract

A table of the first occurrence of a string of 2r − 1 composite numbers between two primes is given for r = 158(1)267, 269, 270, 273, 275, 276, 281, 282, 291, 294 and 301. All such strings between primes less than 2.6 × 10^{12} have been accounted for. The computation supports some conjectures on the distribution of these strings.

Comments

Only the Abstract is given here. The full paper appeared as [1] and an extension to 4.444×10^{12} appeared as [2].

References

[1] R. P. Brent, “The first occurrence of large gaps between successive primes”, Mathematics of Computation 27 (1973), 959-963. MR 48#8360, Zbl 269.10002. rpb019

[2] R. P. Brent, “The first occurrence of certain large prime gaps”, Mathematics of Computation 35 (1980), 1435-1436. MR 81g:10002, Zbl 443.10003. rpb057

Computer Centre, Australian National University, Canberra, Australia

1991 Mathematics Subject Classification. Primary 10-04, 10A20, 10A25, 10A40, 65A05. Key words and phrases. Prime, distribution of primes, prime gap, maximal prime gap, successive composites,

successive primes.

Copyright \begin{matrix}c \\ ◯ \end{matrix} 1973, American Mathematical Society. Comments \begin{matrix}c \\ ◯ \end{matrix} 2000, R. P. Brent.

rpb019a typeset using AMS-L^{A}TEX.