#This program builds a list of all prime numbers less than or equal to
# a value 'n' entered by the user

def main():
    print "Hello! This program builds and displays a list of all prime",
    print " numbers less than or equal to a value entered by the user"

    while True: # making sure that the user enters a proper value
        n=input("Please, enter a whole number, greater than 1:")
        if (n > 1) and type(n) == int:
            break;
        print "The number you entered is either less than 2 or a decimal number"

    primes = [2] # list of primes initially consists of one value
    counter = 0 # used for counting number of iterations of for and while loops
    for k in range(3,n+1):
        d=2 # divisor

        # checks whether the current k is prime:
        while k%d > 0 and d**2 < k: 
            d+=1 # increasing the divisor
            counter +=1 # adding 1 for each iteration of while loop

        if k%d != 0:
            #print k, ",",primes
            primes.append(k)

        k+=1 #skipping even numbers that are clearly not prime
        counter +=1 # adding 1 for each iteration of for loop

    print "the list of all prime numbers less than or equal to",n,"is",
    print primes
    print "Complexity (number of iterations of for and while loops:",counter

main()