Minimal Elements for the Prime Numbers. Issue 3 (2nd July 2016)

• Record Type: Journal Article
• Authors: Bright, Curtis; Devillers, Raymond; Shallit, Jeffrey
• Is Part Of: Experimental mathematics. Volume 25:Issue 3(2016)
• Page Start: 321
• Page End: 331
• Publication Date: 2016-07-02
• Subjects: prime number -- minimal element -- heuristic algorithm; Mathematics -- Periodicals; Mathematics -- Research -- Periodicals; 510.724
• DOI: 10.1080/10586458.2015.1064048
• Languages: English
• ISSNs: 1058-6458

Abstract

ABSTRACT: We say a string of symbols s is minimal for a language L if s is a member of L, and it is not possible to obtain another member of L by striking out one or more symbols from s . Although the set M ( L ) of minimal strings is necessarily finite, determining it explicitly for a given L can be a difficult computational problem. We use some number-theoretic heuristics to compute M ( L ), where L is the language of base- b representations of the prime numbers, for 2 ≤ b ≤ 30.