A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself. 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. Unless you want to use some other more advanced method, you can write your function based on the so-called “trial division” method. The idea is as follows. For a positive integer n, one only needs to test whether n is a multiple of each integer m between 2 and √n. If n is a multiple of any of these integers then it is a composite number and not a prime; if it is not a multiple of any of these integers then it is a prime. Of course, you can use other methods. For example, you can check how many factors n has. If n has exactly 2 factors (must be positive integers less than or equal to n), then n 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.

1. If one feeds anything but a positive integer, assign NA to result and report will be “Error! The input must be a positive integer”.
2. 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.
3. 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, 47.5, 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.