Finding the Prime Numbers up to any limit using Sieve of Eratosthenes algorithm. Code example in Python

primesieve.py

import time
start_time = time.clock()

# using Sieve of Eratosthenes algorithm
limit = 10000000
# set objects is more faster
not_primenums = set()
primes = set()

print "Generate prime numbers under ", limit

for i in range(2,limit+1):
    if i not in not_primenums:
        primes.add(i)
        for j in range(i*i, limit+1, i):
            # store multiple of the prime in here (not prime)
            not_primenums.add(j) 

print "\nExecution time for generating primes: ", time.clock() - start_time, " seconds"
print "\nNumber of prime numbers generated: ", len(primes)

'''
References
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
http://www.onlinemathlearning.com/sieve-eratosthenes.html
https://www.quora.com/What-is-Sieve-of-Eratosthenes-can-someone-explain
https://rosettacode.org/wiki/Sieve_of_Eratosthenes#Python
https://iamrafiul.wordpress.com/2013/04/28/sieve-of-eratosthenes-in-python/
'''

primesieve_old.py

# limit, to find prime numbers under 100
lim = 100 
# create array/list from 1 to the limit
nums = range(1,lim+1)
primenum = [] # we will store the primes in this list

# iterate through the numbers
# check for the multiples for each prime
# if true, break the loop, and store the prime number into the list
for i in range(1,len(nums)):
    for j in range(2,nums[i]):
        if nums[i]%j == 0:
            break
    else:
        primenum.append(nums[i])
            

print primenum

'''
References
https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes
http://www.onlinemathlearning.com/sieve-eratosthenes.html
https://www.quora.com/What-is-Sieve-of-Eratosthenes-can-someone-explain
'''