An integer is said to be prime if it’s greater than 1 and divisible only by 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...

An integer is said to be prime if it’s greater than 1 and divisible only by 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 script 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? Display the results in a
.<p> <p>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. Why? Rewrite the program using the Math.sqrt method to calculate the square root, and run</p> <p>it both ways. Estimate the performance improvement.</p>