In this tutorial, we will learn how to check if a number is prime in Swift. We will understand what a prime number is, write an algorithm to determine primality, and implement it step by step with a complete Swift program and output.

What is a Prime Number?

A prime number is a natural number greater than 1 that has no divisors other than 1 and itself. For example, 2, 3, 5, and 7 are prime numbers, while 4, 6, and 8 are not because they have divisors other than 1 and themselves.

Prime numbers play a crucial role in mathematics and computer science, particularly in cryptography and number theory.

Algorithm to Check if a Number is Prime

The algorithm to check if a number n is prime is as follows:

  1. Check if n is less than 2. If yes, it is not a prime number.
  2. Iterate through numbers from 2 to the square root of n (inclusive).
  3. For each number in this range, check if it divides n without a remainder.
  4. If any number divides n, it is not a prime number; otherwise, it is prime.

This approach is efficient because it reduces the number of iterations by only testing divisors up to the square root of the number.

Step-by-Step Implementation in Swift

Let’s convert the algorithm into Swift code step by step.

1. Handle Base Cases

First, write a function that handles base cases for numbers less than 2, as these are not prime numbers:

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func isPrime(_ n: Int) -> Bool {
    if n < 2 {
        return false // Numbers less than 2 are not prime
    }
    return true
}

2. Check Divisors Up to Square Root

Next, extend the function to iterate through possible divisors up to the square root of the number:

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func isPrime(_ n: Int) -> Bool {
    if n < 2 {
        return false
    }
    
    for i in 2...Int(Double(n).squareRoot()) {
        if n % i == 0 {
            return false // Found a divisor, not prime
        }
    }
    
    return true // No divisors found, number is prime
}

Explanation:

if n < 2: Eliminates numbers less than 2 as non-prime.

for i in 2...Int(Double(n).squareRoot()): Iterates through possible divisors up to the square root of n.

if n % i == 0: Checks if i divides n without a remainder. If true, n is not prime.

return true: If no divisors are found, the number is prime.

3. Test the Function

Let’s test the function with some example inputs:

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// Test cases
let number1 = 7
print("\(number1) is prime: \(isPrime(number1))")

let number2 = 10
print("\(number2) is prime: \(isPrime(number2))")

let number3 = 1
print("\(number3) is prime: \(isPrime(number3))")

The function will determine whether each number is prime or not.

Complete Swift Program

Here’s the complete program combining the isPrime function and test cases:

main.swift

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import Foundation

// Function to check if a number is prime
func isPrime(_ n: Int) -> Bool {
    if n < 2 {
        return false // Numbers less than 2 are not prime
    }
    
    for i in 2...Int(Double(n).squareRoot()) {
        if n % i == 0 {
            return false // Found a divisor, not prime
        }
    }
    
    return true // No divisors found, number is prime
}

// Test cases
let number1 = 7
print("\(number1) is prime: \(isPrime(number1))")

let number2 = 10
print("\(number2) is prime: \(isPrime(number2))")

let number3 = 1
print("\(number3) is prime: \(isPrime(number3))")

let number4 = 29
print("\(number4) is prime: \(isPrime(number4))")

Output

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7 is prime: true
10 is prime: false
1 is prime: false
29 is prime: true

Screenshot from Xcode

Swift Program to Check Prime Number