Suppose you have a number k in mind, and you discover that whenever that number divides a product mn, then your chosen number divides one or the other (or both)

Suppose you have a number k in mind, and you discover that whenever that number divides a product mn, then your chosen number divides one or the other (or both) of the multiplicands. In shorthand, your number k satisfies k|mn => k|m or k|n Alternative formulation: k|mn and not(k|m) => k|n This is an interesting property to have, and has arisen several times in different contexts and different places. 17 is a number like that, and so are 37, 41, 43, 101, 103 and 257. Such numbers as k are called "prime."