How to resolve the algorithm Emirp primes step by step in the Visual Basic .NET programming language

Published on 12 May 2024 09:40 PM

How to resolve the algorithm Emirp primes step by step in the Visual Basic .NET programming language

Table of Contents

Problem Statement

An   emirp   (prime spelled backwards)   are primes that when reversed   (in their decimal representation)   are a different prime. (This rules out palindromic primes.)

In each list, the numbers should be in order. Invoke the (same) program once per task requirement, this will show what limit is used as the upper bound for calculating surplus (regular) primes. The specific method of how to determine if a range or if specific values are to be shown will be left to the programmer.

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Emirp primes step by step in the Visual Basic .NET programming language

Source code in the visual programming language

Imports System.Runtime.CompilerServices

Module Module1
    
    Function ToHashSet(Of T)(source As IEnumerable(Of T)) As HashSet(Of T)
        Return New HashSet(Of T)(source)
    End Function

    
    Function Reverse(number As Integer) As Integer
        If number < 0 Then
            Return -Reverse(-number)
        End If
        If number < 10 Then
            Return number
        End If

        Dim rev = 0
        While number > 0
            rev = rev * 10 + number Mod 10
            number = number \ 10
        End While

        Return rev
    End Function

    
    Function Delimit(Of T)(source As IEnumerable(Of T), Optional seperator As String = " ") As String
        Return String.Join(If(seperator, " "), source)
    End Function

    Iterator Function Primes(bound As Integer) As IEnumerable(Of Integer)
        If bound < 2 Then
            Return
        End If
        Yield 2

        Dim composite As New BitArray((bound - 1) / 2)
        Dim limit As Integer = Int((Int(Math.Sqrt(bound)) - 1) / 2)
        For i = 0 To limit - 1
            If composite(i) Then
                Continue For
            End If
            Dim prime = 2 * i + 3
            Yield prime

            For j As Integer = Int((prime * prime - 2) / 2) To composite.Count - 1 Step prime
                composite(j) = True
            Next
        Next
        For i = limit To composite.Count - 1
            If Not composite(i) Then
                Yield 2 * i + 3
            End If
        Next
    End Function

    Iterator Function FindEmirpPrimes(limit As Integer) As IEnumerable(Of Integer)
        Dim ps = Primes(limit).ToHashSet()

        For Each p In ps
            Dim rev = p.Reverse()
            If rev <> p AndAlso ps.Contains(rev) Then
                Yield p
            End If
        Next
    End Function

    Sub Main()
        Dim limit = 1_000_000
        Console.WriteLine("First 20:")
        Console.WriteLine(FindEmirpPrimes(limit).Take(20).Delimit())
        Console.WriteLine()

        Console.WriteLine("Between 7700 and 8000:")
        Console.WriteLine(FindEmirpPrimes(limit).SkipWhile(Function(p) p < 7700).TakeWhile(Function(p) p < 8000).Delimit())
        Console.WriteLine()

        Console.WriteLine("10000th:")
        Console.WriteLine(FindEmirpPrimes(limit).ElementAt(9999))
    End Sub

End Module


  

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