def prime_factorization(n):
limit = int(n ** 0.5)
prime = 2
while prime <= limit:
if n % prime == 0:
n = n / prime
limit = int(n ** 0.5)
else:
prime = next_prime(prime)
return n
def nth_prime(n):
prime = 2
while n > 1:
prime = next_prime(prime)
n = n - 1
return prime