This is a small object illustrating numerical programming in the Python language. Module prime.py defines a class Prime. The purpose of a Prime object is to work with prime numbers---to test numbers for primality, and to find the set of prime factors in a given number.
We could just provide simple functions for primality testing and factoring. However, the process of testing a number for primes involves generating primes. For efficiency's sake, we provide an object that remembers all the primes it has already generated, rather than discarding them.
p = Prime()where p is the name of the variable to which you want to assign the Prime object. You will need to do this only once when your program starts up.
f = p.factor(n)where p is a Prime object. This method returns the smallest prime factor of n other than 1 (except that the value 1 will be returned for n=1). If n is prime, this method returns None.
L = p.factorize(n)The value returned is a list containing the prime factors of n in ascending order. The value 1 will not be included unless n is 1. If n is prime, the returned value will be a one-element list [n].