#!/usr/bin/env python3

'''

sievePrime Generation

'''

import random, numpy as np, math

def sieve(n):

primality = [True]*(n+1)

primality[0] = primality[1] = False

nPrimes = []

for prime in range(n+1):

# if a number in range 0 to n is prime, then added to nPrimes

# and all multiples would then not be prime

if primality[prime]:

nPrimes.append(prime)

for multiple in range(2*prime,n+1,prime):

primality[multiple] = False

return nPrimes

# determines if p is prime by iterating over odd numbers (no even number is prime aside from 2)

def isPrime(p):

if p < 2:

return False

elif p == 2:

return True

elif p%2 == 0:

return False

for factor in range(3,math.ceil(math.sqrt(p)),2):

if p%factor == 0:

return False

return True