Page "Fundamental theorem of arithmetic" Paragraph 45

Examples like this caused the notion of " prime " to be modified.

In it can be proven that if any of the factors above can be represented as a product, e. g. 2 = ab, then one of a or b must be a unit.

This is the traditional definition of " prime ".

It can also be proven that none of these factors obeys Euclid's lemma ; e. g.