Abstract
This work proposes to present some forms found by important mathematicians to work with the primality problem of whole number. Therefore, classics and moderns algorithm are presented with a lot examples of application. Different activites to work with the primality problem under the view of factorization are also suggested, indicating that factorizing perfectly a number can be a resourceful tool to solve other problems. Finally, this work presents, in the school supplies of the State Education Department of São Paulo, ways to work with mathematical concepts in the elementary school.