# A program to find primes using a simple seive

import math

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

def seiveOneTimesTable(numbers,n, MAX):
	"""Seive the n times table out of a list of numbers"""
	for i in range(2, int(MAX/n)+1):
		if n*i in numbers:
			numbers.remove(n*i)
	return numbers

def seiveAll(numbers, MAX):
	"""Seive all the timestable numbers out of a list of numbers"""
	for timestable in range(2, MAX):
		numbers = seiveOneTimesTable(numbers,timestable,MAX)
	return numbers



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

print(primes(100))


print (createlistupto(100))

print(seiveOneTimesTable(createlistupto(100),2, 100))
print(seiveOneTimesTable(createlistupto(100),3, 100))

l = createlistupto(100)
print(seiveOneTimesTable(l,2, 100))
print(seiveOneTimesTable(l,3, 100))