Testing whether a number is prime

This lesson covers testing for a prime number in VB.NET, with the aim of understanding a basic mathematical algorithm built on a loop.

A prime is an integer of 2 or more divisible only by 1 and itself. An IsPrime() function settles it efficiently by testing divisibility from 2 up to the square root.

The sample code loops over For i As Integer = 2 To Math.Sqrt(n) and concludes the number is not prime the moment it finds an i where n Mod i = 0. Checking only as far as the square root works because any larger divisor is necessarily paired with a smaller one.

A common early stumble is why the square root is enough. Testing every number below n also gives the right answer, but stopping at the square root removes a great deal of wasted work.

Primality testing underpins mathematics used in real security work — cryptography, hash functions.

📖 Reference code

Module Program
    Function IsPrime(n As Integer) As Boolean
        If n < 2 Then Return False
        For i As Integer = 2 To Math.Sqrt(n)
            If n Mod i = 0 Then Return False
        Next
        Return True
    End Function

    Sub Main()
        Console.WriteLine(IsPrime(17))
        Console.WriteLine(IsPrime(18))
    End Sub
End Module

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🧪 This site can't compile or run VB.NET directly, so it checks on the spot whether what you typed matches the reference code (scoring happens entirely in your browser — nothing is sent anywhere).