A natural partial order on the prime numbers

Lucian M. Ionescu
Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132
Volume 21, 2015, Number 1, Pages 1–9
Full paper (PDF, 229 Kb)

Details

Authors and affiliations

Lucian M. Ionescu
Department of Mathematics, Illinois State University
IL 61790-4520, United States

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 [1], independently of [2], who investigated Pratt trees  [3] used 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.

Keywords

• Prime numbers
• Pratt tress
• Rooted trees
• Prime Number Theorem
• Finite fields

AMS Classification

• 11NXX
• 11TXX

References

1. Ionescu, L. M. (2011) Prime Numbers and Multiplicative Number Theory, Discrete Mathematics Seminar, 10/2011,
   http://my.ilstu.edu/~lmiones/presentations_drafts.htm
2. Ford, K., S. V. Konyagin, & F. Luca. (2010) Prime chains and Pratt trees, 0904.0473.
3. Pratt, V. R. (1975) Every prime has a succint certificat, SIAM J. Comput., 4(3), 214–220.
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