# A program to find primes using an efficient seive that stops seiving when it gets to the squareroute of the biggest number
# It prints a message to show which times tables were 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 seive3(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 seiveall3(numbers, MAX):
	"""Seive all the timestable numbers out of a list of numbers"""
	for timestable in range(2, int(math.sqrt(MAX))+1):
		numbers = seive3(numbers,timestable,MAX)
	return numbers

def primes3(MAX):
	"""primes up to MAX"""
	numberlist = createlistupto(MAX)
	return seiveall3(numberlist, MAX)

print(primes3(100))