1. Introduction

A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In this guide, we will create a Swift program to determine if a given number is prime.

2. Program Overview

To check for primality, we will iterate from 2 to the square root of the given number. If the number is divisible by any number in this range, then it is not prime.

3. Code Program

// Define the number to be checked let number = 29 var isPrime = true if number <= 1 { isPrime = false } else { for i in 2...Int(sqrt(Double(number))) { if number % i == 0 { isPrime = false break } } } print("\(number) is \(isPrime ? "a prime number" : "not a prime number")") 

Output:

29 is a prime number 

4. Step By Step Explanation

1. let number = 29: Here, we define the number that we want to check for primality. In our example, we've chosen 29.

2. var isPrime = true: We assume that the number is prime until proven otherwise.

3. The first if condition checks if the number is less than or equal to 1. If it is, we immediately know it's not a prime.

4. for i in 2...Int(sqrt(Double(number))): The loop starts from 2 (as all numbers are divisible by 1) and iterates up to the square root of the number. This is an optimization, as if a number is not divisible by any integer up to its square root, it won't be divisible by any larger number.

5. Inside the loop, if number % i == 0 checks if our number is divisible by i. If it is, we set isPrime to false and break out of the loop.

6. The final print statement outputs whether the number is prime or not.

By using this efficient approach, we can quickly determine if larger numbers are prime.