Question: (Prime Numbers) An integer is said to be prime if it's divisible by only 1 and itself. For example, 2, 3, 5 and 7 are prime, but 4, 6, 8 and 9 are not.
a) Write a function that determines whether a number is prime.
b) Use this function in a program that determines and prints all the prime numbers between 1 and 10,000. How many of these 10,000 numbers do you really have to test before being sure that you have found all the primes?
c) Initially you might think that n/2 is the upper limit for which you must test to see whether a number is prime, but you need go only as high as the square root of n. Rewrite the program, and run it both ways. Estimate the performance improvement.