UNI_Python/ha_03/loosen_janniclas_1540907_04.py

# Jan-Niclas Loosen
# 1540907

def sieve_of_eratosthenes(limit):
    primes = [True] * (limit + 1)
    primes[0] = primes[1] = False   # 0 and 1 are not primes

    for num in range(2, int(limit ** 0.5) + 1):  # only necessary to the square root of the limit
        if primes[num]:
            prime = num
            for i in range(1,limit):
                mult = prime * (i + 1)
                if mult >= len(primes):  # more loops are unnecessary
                    break
                primes[mult] = False

    return primes

def prime_factorization(n):
    primes = sieve_of_eratosthenes(n)
    factors = []
    for i in range(2, n + 1):
        if primes[i] and n % i == 0:
            while n % i == 0:
                factors.append(i)
                n = n // i
    return factors

# dialog for testing the functions
num = int(input("insert positive integer: "))
if num < 0 :
    print("invalid input")
else:
    print(prime_factorization(num))