A TEST OF NON-PRIMALITY IN THREE ACTS

Abstract

The article aims to show the movement of elaboration of a non-primality test, which verifies if a natural number is prime or not, showing how inventive thinking, systematization and articulating reasoning happen when creating and demonstrating the test. In this sense, it was thematized how the ideas around the sieve emerged, understood as evidence of inventive thinking; yet, how they were organized and systematized from the point of view of Mathematics; and, finally, how the articulating reasoning was mobilized in the Test demonstration. To carry out the task, the theoretical-methodological framework was assumed, concerning the Theory of Numbers; the determination of algebraic-geometric relationships, manifested, respectively, with geometric (visual) and symbolic resources; in addition to this, the axiomatic method was used in the demonstration of the test. As a result, a sieve was evidenced that allows to verify the primality of a natural number and, still, a perspective of the modus operandi that can be practiced by the mathematician when elaborating and demonstrating propositions, understanding that the initial ideas presented in different languages, the systematization and articulating reasoning are part of the mathematics development process.