Cryptographic Random Number Generator function implementation
This will be a better random number generator than the other options
you mentioned, yes.
The code is nicely indented, but some whitespace between variable declarations and logic would be nice. 

Public Sub Randomgenerator()
    Dim byte_count As Byte() = New Byte(6) {}
    Dim random_number As New RNGCryptoServiceProvider()

    random_number.GetBytes(byte_count)
    Dim Output As Integer = BitConverter.ToInt32(byte_count, 0)

    MsgBox(Output)
End Sub

Method names should be PascalCased, so Randomgenerator should be RandomGenerator. Don't use underscore in variable/parameter names. They should be camelCased. Please see the official MSDN capitalization recommendations for more information.
This is begging to be a function that returns a Integer. There should be a main routine that calls and displays the generated number.

Public Function RandomGenerator() As Integer
    Dim byteCount As Byte() = New Byte(6) {}
    Dim randomNumber As New RNGCryptoServiceProvider()

    randomNumber.GetBytes(byteCount)
    Return BitConverter.ToInt32(byteCount, 0)
End Function


Sub Main()
    MsgBox(RandomGenerator())
End Sub

MsgBox is depreciated and left only for backwards compatibility with vb6. Replace it with a MessageBox.
RNGCryptoServiceProvider implements IDisposable. This means that you need to properly dispose randomNumber. From the documentation link you provided: 


  This type implements the IDisposable interface. When you have finished using the type, you should dispose of it either directly or indirectly. To dispose of the type directly, call its Dispose method in a try/catch block. To dispose of it indirectly, use a language construct such as using (in C#) or Using (in Visual Basic). For more information, see the “Using an Object that Implements IDisposable” section in the IDisposable interface topic.