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On the incompatibility of two conjectures concerning primes; a discussion of the use of computers in attacking a theoretical problem

1974/05/01 by Ian Richards · 3 citations
Mathematics · #Analytic Number Theory Research #History and Theory of Mathematics #Mathematics and Applications

paper · pdf · doi:10.1090/s0002-9904-1974-13434-8

openalex publication_date 1974/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/07

Abstract

Introduction. This talk is about the interplay between computers and theoretical research, as experienced by someone who is not a computer expert. The story involves, among other things, a measure of good luck. Several instances of this will emerge in due course, but one example now may give the idea: The speaker and his co-worker, Douglas Hensley, used a computer to seek a certain combinatorial pattern. Our first attempts failed; however the desired patterns did exist, and we eventually found infinitely many of them by theoretical means. If, on the first day, the computer had given us the result we wanted, we probably would have stopped there and missed the further developments.

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