THE FIRST OCCURRENCE OF CERTAIN LARGE PRIME GAPS

RICHARD P. BRENT

Abstract

The first occurrence of a string of 2r − 1 composite numbers between two primes (denoted by f(r) and f(r) + 2r) is tabulated for f(r) in the range 2.6 × 10^{12} < f(r) ≤ 4.444 × 10^{12}. This extends earlier computations in the range f(r) ≤ 2.6 × 10^{12}.

Comments

Only the Abstract is given here. The full paper appeared as [2]. It is an extension of [1], which covers the range f(r) ≤ 2.6 × 10^{12}.

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, 65A05. Key words and phrases. Distribution of primes, prime gap, maximal prime gap, successive composites, consec-

utive primes.

Copyright \begin{matrix}c \\ ◯ \end{matrix} 1980, American Mathematical Society. Comments \begin{matrix}c \\ ◯ \end{matrix} 2000, R. P. Brent.

rpb057a typeset using AMS-L^{A}TEX.