[AdamSpeight2008]

Nobody!

Beach_Coder: Unable to run as its missing a manifest.

[xnn]

I might give it a go later today

[xnn]

xnn, on 10 December 2011 - 09:36 AM, said:

I might give it a go later today

I tried taking a much different approach creating a prime factorization tree using Fermat's method to find the primes. Then find the composite factors using a mixture of Non repetitious varaiations and permutations. My head started spinning.

[Beach_Coder]

AdamSpeight2008, on 10 December 2011 - 10:53 AM, said:

Nobody!

Beach_Coder: Unable to run as its missing a manifest.

Ah yes. Maybe someday I will get a code signing certificate.

[AdamSpeight2008]

Beach_Coder: The .Manifest has nothing to do with Code Signing. For these challenge you need to is zip up the .exe and .exe.manifest the bin (Debug or Release) folder of your project, if want you can include a copy of the project. No need to create a Click Once application.

[Beach_Coder]

I'll give that a go in a bit. I just figured out the coolest frickin thing!

[cfoley]

My resubmission, now that the problem has been clarified. I know its late but I wanted to post my answer even if it won't count.

This is actually a really short submission. Most of the code here is a test method.

Spoiler

Module Module1

    Public Function factorsOf(ByVal n As Integer) As List(Of Integer)
        Dim result As New List(Of Integer)
        For i = 1 To n / 2
            If (n Mod i) = 0 Then result.Add(i)
        Next
        Return result
    End Function

    Public Function isPerfect(ByVal n As Integer)
        Return n = factorsOf(n).Sum(Function(x) x)
    End Function

    Sub Main()
        Console.WriteLine("Testing part 1")
        For Each n In {1, 2, 7, 6, 16}
            Console.WriteLine("Factors of " & n & " are " & String.Join(" ", factorsOf(n)))
        Next

        Console.WriteLine("")
        Console.WriteLine("Testing part 2")
        Console.WriteLine("These are perfect.")
        For Each n In {6, 28, 496, 8128, 33550336}
            Console.WriteLine(n & " is perfect: " & isPerfect(n))
        Next
        Console.WriteLine("")
        Console.WriteLine("Testing part 2")
        Console.WriteLine("These are not perfect.")
        For Each n In {5, 30, 1}
            Console.WriteLine(n & " is perfect: " & isPerfect(n))
        Next
        Console.ReadLine()

    End Sub

End Module

This post has been edited by cfoley: 12 December 2011 - 07:23 AM

[Beach_Coder]

Perhaps I have properly submitted it now.

Attaching the right file would help ...

Attached File(s)

•  DIC_Challenge_Factors_And_Perfect.zip (56.28K)
  Number of downloads: 41

This post has been edited by Beach_Coder: 15 December 2011 - 07:03 AM

[AdamSpeight2008]

Beach_Coder: Crashes on option 3 because your assuming the user as write access to the location you're trying to save the file to. (Something to do with F: drive) Are you on a non pre-Vista OS? What'a wrong with just listing them? in the console.

This post has been edited by AdamSpeight2008: 15 December 2011 - 07:40 AM

[Beach_Coder]

AdamSpeight2008, on 15 December 2011 - 09:37 AM, said:

Beach_Coder: Crashes on option 3 because your assuming the user as write access to the location you're trying to save the file to. (Something to do with F: drive) Are you on a non pre-Vista OS? What'a wrong with just listing them? in the console.

I originally attached the wrong set of files. I endeavored to attached the correct files directly, but not soon enough it would appear. In any event, maybe I'll just try it this way:

Spoiler

Imports System.Console


Module Module1

    Sub Main()

        Launch_Defaults()          ' mod_Launch
        Intro()
        Commence_Application()

    End Sub

    Sub Commence_Application()

Begin:

        Display_Main_Menu()        ' mod_Main_Menu
        Main_Menu_Selection()      ' mod_Main_Menu

        GoTo Begin

    End Sub

    Sub Intro()
        Clear()
        WriteLine()
        WriteLine("SUBMITTED BY BEACH_CODER FOR THE DIC CHALLENGE: FACTORS + PERFECT.")
        WriteLine()
        WriteLine("THE CODE RELATED TO THE USER DISPLAY GOT A LITTLE UGLY. I'LL BE CLEANING THAT UP EVENUTALLY.")
        WriteLine()
        WriteLine("THANK YOU TO DIC REGULAR DBASNETT FOR REMINDING ME THE SIMPLE SOLUTION IS OFTEN THE BEST.")
        WriteLine()
        WriteLine("THANKS TO ANY OF YOU WHO INDULGE MY SUBMISSION BY TESTING IT.")
        WriteLine()
        WriteLine("AND THANK YOU TO EUCLID.")
        WriteLine()
        WriteLine("Press any key to reach the Main Menu ...")
        WriteLine()
        ReadKey(True)



    End Sub

End Module

'=====================================================================================================================

Imports System.Console

Module mod_Launch

    Public strSubTitle As String = "(Put forth by DIC Mentor AdamSpeight2008)"
    Public strTitle As String = "DIC CHALLENGE: FACTORS + PERFECT"
    Public Const Default_Cursor_Left As Integer = 0
    Public Const Default_Cursor_Top As Integer = 2
    Public Footer_Spot As Integer = Console.WindowHeight - 5
    Public SpotX As Integer
    Public SpotY As Integer
    Public Const SubMenuFooterString As String = "PRESS [ F10 ] TO RETURN TO THE MAIN MENU"
    Public Const Max_Int_Value = Int32.MaxValue

    Sub Launch_Defaults()

        CursorSize = 100
        ForegroundColor = ConsoleColor.Green
        BackgroundColor = ConsoleColor.Black
        WindowHeight = CInt(Math.Truncate(LargestWindowHeight * 0.98))
        WindowWidth = CInt(Math.Truncate(LargestWindowWidth * 0.98))
        CursorVisible = False
        Title = strTitle
        CursorVisible = False

    End Sub



End Module

'=====================================================================================================================

Imports System.Console

Module mod_Main_Menu

    Public MenuWidth(3) As Integer
    Public Menu(2) As String


    Sub Display_Main_Menu()

Display:

        Dim Horizontal_Menu_Marker As Integer = Define_Main_Menu_Options()
        Dim Vertical_Menu_Marker As Integer = 10
        Dim Title_Horizontal_Marker = Default_Cursor_Left
        Dim Title_Vertical_Marker As Integer = 5
        Dim Main_Menu_Footer As String = "SELECT FROM THE OPTIONS ABOVE OR PRESS [ F10 ] TO EXIT"


        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        Clear()

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        SetCursorPosition(Title_Horizontal_Marker, Title_Vertical_Marker)
        JustifyC(strTitle)                                                      ' mod_General_Use_Functions_And_Subs
        Offset(0, 1)                                                            ' mod_General_Use_Functions_And_Subs
        JustifyC(strSubTitle)                                                   ' mod_General_Use_Functions_And_Subs
        SetCursorPosition(Horizontal_Menu_Marker, Vertical_Menu_Marker)
        For i = 0 To Menu.Length - 1
            Write(Menu(i))
            Offset(0, 3)                                                        ' mod_General_Use_Functions_And_Subs
            SetCursorPosition(Horizontal_Menu_Marker, CursorTop)
        Next

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        Menu_Footer_Main(Main_Menu_Footer)                                       ' mod_General_Use_Functions_And_Subs    

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        Main_Menu_Selection()


        GoTo Display

    End Sub

    Function Define_Main_Menu_Options() As Int32

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
        Menu(0) = "[ 1 ] Function That Returns All Proper Divisors Of An Input Integer"
        Menu(1) = "[ 2 ] Function That Returns True/False If An Input Integer Is A Perfect Number"
        Menu(2) = "[ 3 ] Method That Returns All Perfect Numbers Within A Given Range"
        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        For i = 1 To Menu.Length
            MenuWidth(i) = Len(Menu(i - 1))
        Next
        For i = 1 To Menu.Length - 1
            MenuWidth(0) = Math.Max(MenuWidth(0), MenuWidth(i))
        Next

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        Return WindowWidth \ 2 - MenuWidth(0) \ 2

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

    End Function

    Sub Main_Menu_Selection()

        Dim ckiMainMenu As ConsoleKeyInfo

Get_Key_Press:

        ckiMainMenu = ReadKey(True)

        If ckiMainMenu.Key = ConsoleKey.F10 Then
            End
        ElseIf ckiMainMenu.Key = ConsoleKey.NumPad1 Then
            Program_One(1)                                   '      mod_One
        ElseIf ckiMainMenu.Key = ConsoleKey.NumPad2 Then
            Program_Two(2)                                      '   mod_Two
        ElseIf ckiMainMenu.Key = ConsoleKey.NumPad3 Then
            Program_Three(3)                                    '   mod_Three
        Else
            Offset(-1, 0)
            GoTo Get_Key_Press
        End If

    End Sub

End Module

'=====================================================================================================================

Imports System.Console


Module mod_General_Use_Functions_And_Subs

    Sub JustifyC(ByVal StringtoCenter As String)               'For Strings with Len < WindowWidth

        Dim L As Integer = Enumerable.Count(StringtoCenter)

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        If L < WindowWidth Then
            SetCursorPosition(CInt(Math.Truncate(WindowWidth / 2 - L / 2)), CursorTop)
        Else
            SetCursorPosition(0, CursorTop)
        End If

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        Write(StringtoCenter)

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

    End Sub

    Sub Offset(Optional ByVal XOffset As Int32 = 0, Optional ByVal YOffset As Int32 = 0)

        Try
            SetCursorPosition(CursorLeft + XOffset, CursorTop + YOffset)
        Catch ex As Exception
        End Try

    End Sub

    Sub Menu_Footer_Main(ByVal FooterString As String)

        Get_Spot()
        SetCursorPosition(Default_Cursor_Left, Footer_Spot)
        JustifyC(FooterString)
        Go_Spot()

    End Sub

    Sub Menu_Footer_Sub()

        Get_Spot()
        SetCursorPosition(Default_Cursor_Left, Footer_Spot)
        JustifyC(SubMenuFooterString)
        Go_Spot()

    End Sub

    Sub Get_Spot()

        SpotX = CursorLeft
        SpotY = CursorTop

    End Sub

    Sub Go_Spot()

        SetCursorPosition(SpotX, SpotY)

    End Sub

    Sub Go_Home()

        SetCursorPosition(Default_Cursor_Left, Default_Cursor_Top)

    End Sub

    Sub Display_Program_Screen(ByVal Program_Number As Int32)

        Clear()
        Go_Home()
        JustifyC(strTitle)
        Offset(0, 2)
        JustifyC(Right(Menu(Program_Number - 1), MenuWidth(Program_Number) - 6))
        Menu_Footer_Sub()

    End Sub

    Sub Screen_One(ByVal Program_Number As Int32, Optional ByVal PromptString As String = "ENTER A POSITIVE INTEGER: ")

        Display_Program_Screen(Program_Number)

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
        Try
            SetCursorPosition(WindowWidth \ 2 - (Len(PromptString) + Len(Format(Max_Int_Value, "#,###")) \ 2), 10)
        Catch ex As Exception
            SetCursorPosition(0, 10)
        End Try
        JustifyC(PromptString)
        Get_Spot()
        Offset(0, 2)
        JustifyC("(Up To A Maximum Value Of " & Format(Max_Int_Value, "#,###"))
        Go_Spot()

    End Sub

    Function Acquire_Entered_Integer() As Int32

        Dim Entered_String As String
        Dim Entered_Integer As Int32

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

Accept_Input:

        Entered_String = ReadLine()

        Try
            Entered_Integer = CInt(Entered_String)
        Catch ex As Exception
            Go_Spot()
            Write(Strings.StrDup(14, " "))
            Go_Spot()
            Entered_String = ""
            GoTo Accept_Input
        End Try

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

Return_Function_Output:

        Return Entered_Integer

    End Function

    Function Get_Number_From_User() As Int32

        Dim cki As ConsoleKeyInfo
        Dim InputString As String
        Dim N As Int32
        Dim MarkX As Int32

Keep_Going:

        MarkX = CursorLeft
        cki = ReadKey(True)
        If cki.Key = ConsoleKey.F10 Then
            N = -1
            Return N

        ElseIf cki.Key = ConsoleKey.Enter Then
            CursorVisible = False
            GoTo Done
        ElseIf cki.GetHashCode > 47 And cki.GetHashCode < 58 Then
            InputString = InputString & cki.GetHashCode - 48
            Write(cki.GetHashCode - 48)
            GoTo Keep_Going
        ElseIf cki.Key = ConsoleKey.Backspace Then
            SetCursorPosition(MarkX - 1, CursorTop)
            Write(" ")
            SetCursorPosition(MarkX - 1, CursorTop)
            If Len(InputString) > 1 Then
                InputString = Left(InputString, Len(InputString) - 1)
            ElseIf Len(InputString) = 1 Then
                InputString = ""
            End If
            GoTo Keep_Going
        Else
            GoTo Keep_Going
        End If

Done:

        Try
            N = CInt(InputString)
        Catch ex As Exception
            N = 0
        End Try

        Return N

    End Function

    Sub ColumnTitles(ByVal Title As String, ByVal NumberofColumns As Int32, ByVal Margin As Int32, ByVal ColumnWidth As Int32)


        Dim RightMarker As Int32 = Margin + NumberofColumns * ColumnWidth
        Dim StringBuffer As Int32 = (ColumnWidth - Len(Title)) \ 2 - 1

        For a = 0 To NumberofColumns - 1

            SetCursorPosition(Margin + a * ColumnWidth + StringBuffer, CursorTop)
            Write(Title)

        Next

    End Sub

End Module

'=====================================================================================================================

Imports System.Console


Module mod_One

    Sub Program_One(ByVal Program_Number As Integer)

        Dim Proper_Divisor_List As New List(Of Int32)
        Dim Timer As New Stopwatch

Start:

        Screen_One(Program_Number)

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        Dim Input_Number As Int32 = Get_Number_From_User()

        If Input_Number < 0 Then
            Exit Sub
        ElseIf Input_Number = 0 Then
            GoTo Start
        Else
            Go_Spot()
            Write(Strings.StrDup(15, " "))
            WriteLine(Format(Input_Number, "#,###"))
        End If

        '= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 

        Timer.Restart()
        Proper_Divisor_List = Proper_Divisors(Input_Number)
        Timer.Stop()

        '= = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = 

        SetCursorPosition(CursorLeft, 15)
        JustifyC("CALCULATIONS COMPLETE. " & Format(Proper_Divisor_List.Count, "#,###") & " FOUND.")
        WriteLine()
        JustifyC("FUNCTION PROCESSING TIME:  " & Timer.Elapsed.ToString)
        Offset(0, 2)
        JustifyC("PRESS ANY KEY TO DISPLAY THE PROPER DIVISORS OF " & Format(Input_Number, "#,###") & "...")
        ReadKey(True)

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

        Create_Columns(Program_Number, Proper_Divisor_List)
        SetCursorPosition(0, 8)
        JustifyC("PROPER DIVISORS OF " & Format(Input_Number, "#,###"))

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

        WriteLine()
        JustifyC("PRESS ANY KEY ...")
        ReadKey(True)
        GoTo Start

    End Sub

    Function Proper_Divisors(Num As Int32) As List(Of Int32)

        Dim Proper_Divisor_List As New List(Of Int32)
        Dim Loop_Max As Int32 = Num
        Dim Divisor As Int32 = 2

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

        Do While Divisor < Loop_Max And Divisor < Num
            If Num Mod Divisor = 0 Then
                Proper_Divisor_List.Add(Divisor)
                Proper_Divisor_List.Add(Num \ Divisor)
                Loop_Max = Num \ Divisor
            End If
            Divisor = Divisor + 1
        Loop

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

        Proper_Divisor_List = Proper_Divisor_List.Distinct.ToList
        Proper_Divisor_List.Add(1)
        Proper_Divisor_List.Sort()
        Return Proper_Divisor_List

    End Function

    Sub Create_Columns(ByVal Program_Number As Int32, ByVal PD_List As List(Of Int32))

        Dim PNCount As Int32 = PD_List.Count
        Dim ColumnWidth As Int32 = Len(Format(Int32.MaxValue, "#,###")) + 4
        Dim M As Int32 = 5
        Dim NumofColumns As Int32 = (WindowWidth - 2 * M) \ ColumnWidth
        Dim TopRow As Int32 = 12
        Dim ColBuffer As Int32 = 4
        Dim S As String
        Dim CTitleA As String = "PROPER"
        Dim CTitleB As String = " DIVISOR"
        Dim CTitleC As String = Strings.StrDup(ColumnWidth - ColBuffer, "-")
        Dim TotalMargin As Int32 = WindowWidth - NumofColumns * ColumnWidth
        Dim LeftMargin As Int32 = TotalMargin \ 2
        Dim MaxRows As Int32 = Footer_Spot - TopRow - 2
        Dim PNPerPage As Int32 = MaxRows * NumofColumns
        Dim NumofPages As Int32 = 1
        If PNCount > PNPerPage Then
            NumofPages = NumofPages + PNCount \ PNPerPage
        End If

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

        Display_Program_Screen(Program_Number)

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

        
        SetCursorPosition(0, 10)
        ColumnTitles(CTitleA, NumofColumns, M, ColumnWidth)
        Offset(0, 1)
        ColumnTitles(CTitleB, NumofColumns, M, ColumnWidth)
        Offset(0, 1)
        ColumnTitles(CTitleC, NumofColumns, M, ColumnWidth)
        WriteLine()

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

        Dim C As Int32 = 1
        Dim R As Int32 = 1
        Dim P As Int32 = 1
        Dim PN_Table(NumofPages, MaxRows, NumofColumns) As String


        For i = 0 To PNCount - 1
            S = CStr(Format(PD_List(i), "#,###"))
            PN_Table(P - 1, R - 1, C - 1) = S
            SetCursorPosition(M + ColumnWidth * C - ColBuffer - Len(S) + 1, TopRow + R)
            Write(S)
            If C = NumofColumns Then
                C = 1
                R = R + 1
                If R = MaxRows Then
                    R = 1
                    P = P + 1
                    Clear_Screen(TopRow, MaxRows)
                End If
            Else
                C = C + 1
            End If
        Next

        WriteLine()

    End Sub

    Sub Clear_Screen(ByVal FirstRow As Int32, ByVal MaxRows As Int32)

        SetCursorPosition(0, FirstRow)
        For i = 1 To MaxRows
            Write(Strings.StrDup(WindowWidth, " "))
        Next

    End Sub

End Module

'=====================================================================================================================

Imports System.Console

Module mod_Two

    Sub Program_Two(ByVal Program_Number As Integer)

        Dim Input_Number As Int32
        Dim Is_Perfect As String
        Dim Timer As New Stopwatch

Start:

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 
        Clear()
        Screen_One(Program_Number)
        Input_Number = Get_Number_From_User()

        If Input_Number < 0 Then
            Exit Sub
        ElseIf Input_Number = 0 Then
            GoTo Start
        Else
            Go_Spot()
            Write(Strings.StrDup(15, " "))
            WriteLine(Format(Input_Number, "#,###"))
        End If

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        Timer.Restart()
        Is_Perfect = Perfect_Number_Check(Input_Number)
        Timer.Stop()

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        SetCursorPosition(0, WindowHeight \ 2 - 10)
        JustifyC(Format(Input_Number, "#,###") & " IS A PERFECT NUMBER = " & Is_Perfect)
        Offset(0, 5)
        JustifyC("Execution Time:  " & Timer.Elapsed.ToString)
        Offset(0, 10)
        JustifyC("Press any key  ...")
        ReadKey(True)
        GoTo Start

    End Sub

    Function Perfect_Number_Check(ByVal Num As Int32) As String

        Dim Quotient As Int32
        Dim Divisor As Int32 = 2
        Dim Dividend As Int32 = Num
        Dim Interval As Int32
        Dim Divisor_Sum As Decimal = 1D
        Dim Perfect_Number As Boolean = False

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        If Dividend Mod 2 = 0 Then
            Interval = 1
        Else
            Divisor = 3
            Interval = 2
        End If

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        Do Until Divisor >= Math.Sqrt(Num)
            If Dividend Mod Divisor = 0 Then
                Quotient = Dividend \ Divisor
                Divisor_Sum = Divisor_Sum + Quotient + Divisor
                If Divisor_Sum > Num Then
                    Exit Do
                End If
            End If
            Divisor = Divisor + Interval
        Loop

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        If Divisor_Sum = Num Then
            Perfect_Number = True
            Return Strings.UCase(Perfect_Number.ToString)
        ElseIf Divisor_Sum > Num Then
            Return Strings.UCase(Perfect_Number.ToString) & ".  THE NUMBER IS ABUNDANT."
        ElseIf Divisor_Sum < Num Then
            Return Strings.UCase(Perfect_Number.ToString) & ".  THE NUMBER IS DEFICIENT."
        Else
            Return "Function Failed."
        End If

    End Function

End Module

'=====================================================================================================================

Imports System.Console

Module mod_Three

    Sub Program_Three(ByVal Program_Number As Integer)

        Dim Input_String(1) As String
        Dim Input_Number(1) As Int32
        Dim Timer As New Stopwatch

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        Clear()
        Screen_One(Program_Number, "ENTER A POSITIVE INTEGER TO SET THE LOWER VALUE OF YOUR RANGE OR PRESS [ ENTER ] TO USE THE MINIMUM VALUE:  ")
        CursorVisible = True
        Input_Number(0) = Get_Number_From_User()
        CursorVisible = False
        If Input_Number(0) < 1 Then
            Input_Number(0) = 1
        End If
        Screen_One(Program_Number, "ENTER A POSITIVE INTEGER TO SET THE HIGHER VALUE OF YOUR RANGE OR PRESS [ ENTER ] TO USE THE MAXIMUM VALUE:  ")
        CursorVisible = True
        Input_Number(1) = Get_Number_From_User()
        CursorVisible = False
        If Input_Number(1) < 2 Then Input_Number(1) = Int32.MaxValue
        Display_Program_Screen(Program_Number)
        SetCursorPosition(0, 10)
        JustifyC("SEARCHING FOR PERFECT NUMBERS BETWEEN  " & Format(Input_Number(0), "#,###") & "  AND " & Format(Input_Number(1), "#,###") & "...")
        WriteLine()
        Offset(0, 2)

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        Dim Lp As Decimal = Math.Truncate(Calc_Range_of_p(Input_Number(0)))
        Dim Hp As Decimal = Math.Truncate(Calc_Range_of_p(Input_Number(1))) + 1
        Dim Primes As New List(Of Decimal)
        Dim Mersenne_Primes As New List(Of Decimal)
        Dim Preliminary_Perfects As New List(Of Decimal)
        Dim Perfects As New List(Of Decimal)

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        Timer.Restart()
        Primes = Check_Prime_Factors(Lp, Hp)
        Mersenne_Primes = Select_Mersennes_Primes(Primes)
        Preliminary_Perfects = Perfect_Prelim(Mersenne_Primes)
        Perfects = Verify_Perfect_Numbers(Preliminary_Perfects)
        Timer.Stop()

        '- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 

        JustifyC(Perfects.Count & " PERFECT NUMBERS WERE FOUND IN YOUR RANGE:  ")
        WriteLine()
        WriteLine()

        Dim mark As Int32 = WindowWidth \ 2 + 7
        For Each PN In Perfects
            SetCursorPosition(mark, CursorTop)
            Offset(-Len(Format(PN, "#,###")))
            WriteLine(Format(PN, "#,###"))
        Next
        WriteLine()
        WriteLine()
        JustifyC("EXECUTION TIME OF OPERATION:  " & Timer.Elapsed.ToString)
        WriteLine()
        WriteLine()
        JustifyC("Press Any Key ...")
        ReadKey(True)


    End Sub

    Function Calc_Range_of_p(ByVal N As Int32) As Decimal

        If N < 2D Then
            Return 2D
        Else
            Return CDec((((Math.Log(N) / Math.Log(2D)) + 1D) / 2D))
        End If

    End Function

    Function Check_Prime_Factors(ByVal p1 As Decimal, ByVal p2 As Decimal) As List(Of Decimal)

        Dim Prime_Factor_List As New List(Of Decimal)

        If p1 <= 2D Then
            Prime_Factor_List.Add(p1)
            p1 = 3D
        End If

        For p = p1 To p2 Step 2
            If Check_Primality(p) = True Then
                Prime_Factor_List.Add(p)
            End If
        Next

        Return Prime_Factor_List

    End Function

    Function Check_Primality(ByVal p As Decimal) As Boolean

        Dim Return_Value As Boolean = True

        For i = 2D To p - 1
            If p Mod i = 0 Then
                Return_Value = False
                Exit For
            End If
        Next

        Return Return_Value

    End Function

    Function Select_Mersennes_Primes(ByVal Prime_List As List(Of Decimal)) As List(Of Decimal)

        Dim Mersenne_List As New List(Of Decimal)

        For Each p In Prime_List
            If Check_Primality(CDec(2D ^ p - 1D)) = True Then
                Mersenne_List.Add(p)
            End If
        Next

        Return Mersenne_List

    End Function

    Function Perfect_Prelim(ByVal List_Of_Mersenne_Primes As List(Of Decimal)) As List(Of Decimal)
        Dim Perfect_List_Draft As New List(Of Decimal)

        For Each p In List_Of_Mersenne_Primes
            Perfect_List_Draft.Add(CDec((2D ^ (p - 1D)) * ((2D ^ p) - 1D)))
        Next

        Return Perfect_List_Draft

    End Function

    Function Verify_Perfect_Numbers(ByVal Prelim_List As List(Of Decimal)) As List(Of Decimal)

        Dim Perfect_Numbers As New List(Of Decimal)

        For Each PN In Prelim_List
            If Validate_Perfect_Number(PN) = True Then
                Perfect_Numbers.Add(PN)
            End If
        Next

        Return Perfect_Numbers

    End Function

    Function Validate_Perfect_Number(ByVal PPN As Decimal) As Boolean

        Dim Quotient As Decimal
        Dim Divisor As Decimal = 2D
        Dim Dividend As Decimal = PPN
        Dim Interval As Decimal
        Dim Divisor_Sum As Decimal = 1D
        Dim Perfect_Number As Boolean = False

        If Dividend Mod 2D = 0 Then
            Interval = 1D
        Else
            Divisor = 3D
            Interval = 2D
        End If

        Do Until Divisor >= Math.Sqrt(PPN)
            If Dividend Mod Divisor = 0 Then
                Quotient = Dividend / Divisor
                Divisor_Sum = Divisor_Sum + Quotient + Divisor
                If Divisor_Sum > PPN Then
                    Exit Do
                End If
            End If
            Divisor = Divisor + Interval
        Loop

        If Divisor_Sum = PPN Then
            Perfect_Number = True
        End If

        Return Perfect_Number

    End Function

End Module