$1.$ boolean isPrime$($int n$)\{//$ tests if n is a prime number

$2//$ Input: a positive integer n

$3.//$ Output: returns true if n is a prime number, false otherwise

$4.$ for $($int x $=2$; x$*$x $<=$ n; x$++)\{$

$5.$ if $($n $\%$ x $==0)\{//$ find that x divides n

$6.$ return false;

$7.\}$

$8.\}$

$9.$ return true; $//$ found no divisor of n

$10.\}$

Note: when giving the big$-$Oh$,$ give the nearest possible upper limit$.$

possible. For example, if you can prove that f$($n$)$ is O$($n$),$ and f$($n$)$ is O$($n$2),$

choose the nearest upper bound, i$.$e$.$ that f$($n$)$ is O$($n$).$

$($a$)(5$ pts$)$ Give a big$-$Oh for T$($n$),$ the worst$-$case execution time of this algorithm for an integer input n$.$

algorithm for an integer input n$.$ Explain how you obtained this worst$-$case

case.

$($b$)(5$ pts$)$ Give a big$-$Oh for B$($n$),$ the best execution time for this algorithm

for an integer input of input n$.$ Explain the type of inputs $($not just one

but an infinite sequence of inputs$)$ that will give this best case.