Assignment 3

1. Write a function isprime() that determines if an integer number is prime. You can use the % (modulus) operator (division rest on integers) or work with plain division. Use your function to implement a program primes_simple that prints all primes between 0 and 10000.
2. The Sieve of Erathostenes is a more efficient (and ancient) algorithm for finding all primes up to a given number. It starts with a list of all numbers from 2 to the desired limit. It traverses this list, starting at two. Whenever it encounteres a new number, it strikes all multiples of it from the list. What remains at the end is a list of prime numbers.

   Example:

      Initial list:            2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 
      Striking multiples of 2: 2 3   5   7   9    11    13    15
      Striking multiples of 3: 2 3   5   7        11    13
      (There are no multiples of any remainig number, so we skip the rest)
   

   Use the Sieve algorithm in a second program, primes_sieve, that prints all primes between 0 and 10000. Hint: Use an array!