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import PIL, 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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