• WHY THE NUMBER 1 SHOULD NOT BE CONSIDERED A PRIME NUMBER

Eberto R. Morgado, Marco V. José*

Abstract


This is a pedagogical note about the historically polemic question about whether the number 1 is or is not a prime. A number theoretical argument is given for not considering 1 as a prime number. In order to avoid this inclusion a correct definition of prime number is proposed and also a consequent formulation of the so-called Fundamental Theorem of Arithmetic, which is here interpreted in terms of a generator set of a monoid. Finally, the generalized concept of a prime element in an integral domain is given.


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