Prime Representing Polynomial with 10 Unknowns – Introduction

Prime-representing Functions

We construct prime-representing functions. In particular we show that there exist real numbers α > 1 such that ⌊ α n⌋ is prime for all n ∈ N. Indeed the set consisting of such numbers α has the cardinality of the continuum.

Representing numbers: prime and irrational

This article draws an analogy between prime and irrational numbers with respect to how these numbers are defined and how they are perceived by learners. Excerpts are presented from two research studies: a study on understanding prime numbers by pre-service elementary school teachers and a study on understanding irrational numbers by pre-service secondary school teachers. Considering the results...

Polynomial inequalities representing polyhedra

Our main result is that every ro-dimensional polytope can be described by at most (2n — 1) polynomial inequalities and, moreover, these polynomials can explicitly be constructed. For an n-dimensional pointed polyhedral cone we prove the bound 2n — 2 and for arbitrary polyhedra we get a constructible representation by 2n polynomial inequalities. 1. I N T R O D U C T I O N By a striking result of...

Prime Polynomial Sequences

Let F(x) be a polynomial with integral coefficients of degree d >_ 2 such that F(n) >_ 1 for all it 3 1 . Let OF = {F(n)Í„ , . Then F(tr) is called prime in OF if F(u) is not the product of strictly smaller terms of &F . It is proved that if F(x) is not of the form a(bx+c)d, then almost all terms of (! r are prime in O F. Let 0 = be a sequence of positive integers . Then a,, E & is called compo...

Prime: an Introduction and Assessment