This is a function designed to return all the prime factors of a given number, in sorted order from least to greatest, in a list. It relies on another function that checks if a given number is prime. Here is the prime checking function:
def isPrime(x): if x <= 1 or isinstance(x,float): return False else: for divisor in range(2,x,1): if x % divisor == 0: return False return True
Here is the prime factorization function:
def allPrimeFactors(y): primeFactors =  restart = True while restart: restart = False for i in range(2,y,1): if y % i == 0 and isPrime(i): primeFactors.append(i) y = y / i if isPrime(y) and y == i: primeFactors.append(y) else: pass restart = True else: pass primeFactors.sort() return primeFactors
The while loop is designed to restart the for loop at the first iterable value, which is, in this case, 2. This is so that, if y factors into 2, or any other prime, more than once, it will appear in the final list more than once, how ever many times it, or any other prime, is part of the factorization of y. I found that, if a number's prime factorization was 2 primes of the same value, it would return an incomplete list, therefore I added the if statement to the end of the function so that if the final value of y was prime AND equal to the current value of i, it would append the final value of y to the end of the list, therefore making it complete.
This is a looping function I made to test the prime factorization function with a large set of numbers:
def primeFactorsTester(d,e): for f in range(d,e+1,1): if f == 1: print "1 is undefined" elif isPrime(f): print str(f) + " is prime" else: print "the prime factors of " + str(f) + " are "+ str(allPrimeFactors(f))
It is meant to produce an output that is human readable, and is primarily a testing function.
Does my prime factorization function seem complete or incomplete? Any general feedback to give? I would love to know.