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import PIL
import math
# Problem 7 - 10,001st prime
# returns a list of every prime up to a certain number
def listprimes(number):
primes = []
if (number <= 1):
return [1]
a = [1] * number
a[0] = 0
a[1] = 0 # 1 and 0 are not prime
# Sieve of eratosthenes
for i in range(2, int(math.ceil(math.sqrt(number)))):
if(a[i] == 1):
j = i**2 # cross out all the multiples of i, starting with its square
while(j < number):
a[j] = 0
j += i
for k in range(2, number):
# is prime
if(a[k] == 1):
primes.append(k)
return primes
out_list = listprimes(1000000)
# print(out_list)
# return 10,001th prime factor
print(out_list[10000])
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