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# Prime Number Sieve
# http://inventwithpython.com/hacking (BSD Licensed)
import math
def isPrime(num):
# Returns True if num is a prime number, otherwise False.
# Note: Generally, isPrime() is slower than primeSieve().
# all numbers less than 2 are not prime
if num < 2:
return False
# see if num is divisible by any number up to the square root of num
for i in range(2, int(math.sqrt(num)) + 1):
if num % i == 0:
return False
return True
def primeSieve(sieveSize):
# Returns a list of prime numbers calculated using
# the Sieve of Eratosthenes algorithm.
sieve = [True] * sieveSize
sieve[0] = False # zero and one are not prime numbers
sieve[1] = False
# create the sieve
for i in range(2, int(math.sqrt(sieveSize)) + 1):
pointer = i * 2
while pointer < sieveSize:
sieve[pointer] = False
pointer += i
# compile the list of primes
primes = []
for i in range(sieveSize):
if sieve[i] == True:
primes.append(i)
return primes
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