# A program to find primes Eratosthenes efficient seive
# It prints a message if any times tables are still making no difference

import math

def createlistupto(n):
        """create a list of numbers from 2 up to the given number"""
        return list(range(2, n+1))

def seive(numbers,n, MAX):
        """Seive the n times table out of a list of numbers, but noting when a particular timestable removed no new values from the list"""
        removed = False
        for i in range(2, int(MAX/n)+1):
                if n*i in numbers:
                        numbers.remove(n*i)
                        removed = True
        if removed == False:
                print(n, 'no change')
        return numbers

def seiveall(numbers, MAX):
        """Seive all the timestable numbers out of a list of numbers"""
        for timestable in range(2, int(math.sqrt(MAX))+1):
                if timestable in numbers:
                        numbers = seive(numbers,timestable,MAX)
        return numbers

def EratosthenesPrimes(MAX):
        """primes up to MAX"""
        numberlist = createlistupto(MAX)
        return seiveall(numberlist, MAX)

print(EratosthenesPrimes(100))