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A Natural Partial Order on The Prime Numbers

2014/07/14 by Lucian M. Ionescu, Ionescu, Lucian M.
Chemistry · Computer Science · Mathematics · #Advanced Graph Theory Research #Graph theory and applications #Synthesis and Properties of Aromatic Compounds #math.NT

paper · pdf · doi:10.48550/arxiv.1407.6659

10 pages, conference: Number Theory at Illinois, June 5-7, 2014; submitted to IJNT

arxiv created 2014/07/14 · arxiv updated 2014/07/25

Abstract

A natural partial order on the set of prime numbers was derived by the author from the internal symmetries of the primary finite fields, independently of Ford a.a., who investigated Pratt trees for primality tests. It leads to a correspondence with the Hopf algebra of rooted trees, and as an application, to an alternative approach to the Prime Number Theorem.

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