Lucian M. Ionescu

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 21, 2015, Number 1, Pages 1—9

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## 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

- Ionescu, L. M. (2011) Prime Numbers and Multiplicative Number Theory, Discrete Mathematics Seminar, 10/2011,

http://my.ilstu.edu/~lmiones/presentations_drafts.htm - Ford, K., S. V. Konyagin, & F. Luca. (2010) Prime chains and Pratt trees, 0904.0473.
- Pratt, V. R. (1975) Every prime has a succint certificat, SIAM J. Comput., 4(3), 214–220.
- Manin, Y. Lectures on zeta functions and motives, MPI / 92–50.
- Shai Haran, M. J. (2001) The mystery of the real prime.
- Tretkoff, P. (2006) Noncommutative geometry and number theory, Clay Mathematics Proceedings, Vol. 6.
- Ionescu, L. M. (2011) Remarks on physics as number theory, 2011, http://www.gsjournal.net/old/files/4606_Ionescu2.pdf
- Ionescu, L. M. (2004) From Lie theory to deformation theory, http://arxiv.org/abs/0704.2213.
- Ionescu, L. M. (2013–2014) p-adic math-physics, Outlines for presentations in the Math-Physics seminar.
- Ionescu, L. M. p-adic numbers and algebraic quantum groups. (work in progress)
- Ionescu, L. M. The quantum group of rationals,

http://my.ilstu.edu/~lmiones/presentations_drafts.htm - Formal groups. Wikipedia, The Free Encyclopedia.
- Ionescu, L. M. Real numbers and p-adic numbers: a Haar analysis point of view. (work in progress)
- Ionescu, L. M. (2012, 2013) ISU Summer Research Academy, http://cemast2012.webs.com/prime-numbers.
- Gracia-Bondia, J. M., Varilly, J. C., & Figueroa, H. (2001) Elements of Noncommutative Geometry, Birkhauser Basel.

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## Cite this paper

Ionescu, L. M. (2015). A natural partial order on the prime numbers. Notes on Number Theory and Discrete Mathematics, 20(1), 1-9.