The use of the invariant's properties in the primality test and prime search

The purpose of this article is to delve into the properties of invariants. The properties, explained in [2], reveal new ways to develop algorithms that allow us to test the primality of a number. In this article, some of these are shown, indicating the advantages and disadvantages of these new algorithms. The information provided by these algorithms also gives additional information regarding the factorization of a compound number.