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# Jan-Niclas Loosen
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# 1540907
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def sieve_of_eratosthenes(limit):
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primes = [True] * (limit + 1)
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primes[0] = primes[1] = False # 0 and 1 are not primes
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for num in range(2, int(limit ** 0.5) + 1): # only necessary to the square root of the limit
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if primes[num]:
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prime = num
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for i in range(1,limit):
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mult = prime * (i + 1)
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if mult >= len(primes): # more loops are unnecessary
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break
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primes[mult] = False
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return primes
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def prime_factorization(n):
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primes = sieve_of_eratosthenes(n)
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factors = []
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for i in range(2, n + 1):
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if primes[i] and n % i == 0:
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while n % i == 0:
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factors.append(i)
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n = n // i
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return factors
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# dialog for testing the functions
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num = int(input("insert positive integer: "))
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if num < 0 :
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print("invalid input")
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else:
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print(prime_factorization(num))
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