Write using R code..... The purpose of this problem is to write a function $($say its name is check.prime$)$ to check whether or not a given natural number is a prime. The input of check.prime should be a positive integer and the output should be a list containing a logic variable called result and a character variable called report, which tells if the input is a prime. Specific requirements are implied from the following examples.

a$.$ If one feeds anything but a positive integer, assign NA to result and report will be $$Error$!$ The input must be a positive integer$.$

b$.$ We know $37$ is a prime number. Implementing check.prime$(37)$ will yield a T or TRUE for result and $$The input $37$ IS a prime number.$$ for report.

c$.$ Implementing check.prime$(51)$ will yield a F or FALSE for result and $$The input $51$ IS NOT a prime number.$$ for report.

Complete the following tasks and present your output.

$($i$).$ Implement your R function with $5,21,47\mathrm{.}5,63,87,$ and $111$ one by one and show your results.

$($ii$).$ Implement x$=$floor$(100*$runif$(1))$; check.prime$($x$)$ for three times and display your output.