Prime number generator

[xerox3333]

Hi,

My problem is that i need to generate the first 25 prime numbers and output them, i have seen various bits of code using the "mod" operator but im not sure how this works
no input should be required for this program it just needs to identify a prime number and display the first 25

although this is my first time posting here any help would be appreciated.

Thanks,

Craig

[stanav]

You need to know:
1. What's the definition of a prime number?
2. What does the "mod" operator do?
Once you have the answer, you can very much come up with an algorithm to determine if a number is prime or not. Once you have this algorithm, to get the 1st 25 prime numbers, you start out with a value and run a loop. For each loop iteration, you test if the value is a prime number (and if it is, add it to your list) then increment it by 1. You keep looping until your prime list has 25 numbers in it.

[coolcurrent4u]

what have you tried?

[xerox3333]

I have been trying to workout how to identify a prime number in vb so that i can store them in an array and later output them

[techgnome]

Mod is short for modulo ... the result is the remainder value of the division operation .... 4 mod 2 is 0 because 4 divided by 2 is 2, no remainder. 5 mod 2 is 1 (5/2 = 2R1).... 7 mod 2 is 1.

As for primes....
First, it can never be an even number... so if the number mod 2 is 0 then it's not a prime (that's why I used 2 in the examples above). 1 is a given, so is 3. So that's where I'd start at...1.... then add 2 each time. After adding 2 to the current number, see if it is divisible by any of the previous primes evenly .. if the mod of any of the primes is 0, then that number is divisible evenly by that number and therefore not a prime.

Now, simply create an array with an upper bound of 25... use one counter to keep track of the index in the array... and loop until you reach 25 on the index.

-tg

[Niya]

Here is an implementation of the Sieve of Eratosthenes I did years ago in VB6. I adapted it to VB.Net:-

Public Class PrimeGenerator
 
    Private Class DeselectableNumber
        Public Value As Integer
        Public bStruckOut As Boolean
    End Class
 
    Public Shared Function GetPrimes(ByVal max As Integer) As Integer()
        Return FindPrimes(CreateNumberList(max))
    End Function
 
    Private Shared Function CreateNumberList(ByVal MaxNumber As Integer) As DeselectableNumber()
        'Create an array of type DeselectableNumber. One entry for
        'every number between 0 to MaxNumber
        Return Enumerable.Range(0, MaxNumber + 1).Select(Of DeselectableNumber)(Function(n) New DeselectableNumber With {.Value = n, .bStruckOut = False}).ToArray
    End Function
 
    Private Shared Function FindPrimes(ByVal NumList As IList(Of DeselectableNumber)) As Integer()
 
        Dim lLastPrime As Integer
        Dim i As Integer
        Dim lStruckCount As Integer
        Dim bRemainArePrime As Boolean 'Reached a point where all remaining numbers are prime
 
        Dim lstPrimes As New List(Of Integer)
 
        lLastPrime = 2
 
        Do Until (lStruckCount >= NumList.Count - 1 Or bRemainArePrime = True)
 
            For i = lLastPrime To NumList.Count - 1
                With NumList.Item(i)
 
                    If .Value Mod lLastPrime = 0 And .bStruckOut = False Then
 
                        .bStruckOut = True
                        lStruckCount = lStruckCount + 1
 
                        If .Value = lLastPrime Then
                            lstPrimes.Add(lLastPrime)
                        End If
                    End If
 
                End With
 
            Next
 
            For i = lLastPrime To NumList.Count - 1
                If NumList.Item(i).bStruckOut = False Then lLastPrime = NumList.Item(i).Value : Exit For
            Next
 
            'If the next multiple of the next prime number is greater than
            'our upper limit then all the remaining numbers that were
            'not struck our are prime numbers
            If lLastPrime * 2 > NumList.Count - 1 Then
                bRemainArePrime = True
            End If
 
        Loop
 
        'All remaining unstruck numbers are prime
        If bRemainArePrime Then
            For i = 2 To NumList.Count - 1
                With NumList(i)
                    If .bStruckOut = False Then lstPrimes.Add(.Value)
                End With
            Next
 
        End If
 
        FindPrimes = lstPrimes.ToArray
 
    End Function
 
 
End Class

Open a new Windows Forms project and place a ListBox on Form1 and place this code in Form1_Load:-

'
        Dim primes = PrimeGenerator.GetPrimes(100)
        ListBox1.DataSource = primes

Execute the program and the ListBox would contain a list of primes between 0 and 100.

[Evil_Giraffe]

I would be tempted to point you at the first three articles from the Craftsman series, where a "naive" Sieve of Eratosthenes implementation is refactored into something clearer:
http://objectmentor.com/resources/ar...craftsman1.pdf
http://objectmentor.com/resources/ar...craftsman2.pdf
http://objectmentor.com/resources/ar...craftsman3.pdf

(In fact, I'd be tempted to point everyone to the entire series, but there's no URL pointing directly to the series by itself, you need to go to http://objectmentor.com/resources/pu...dArticles.html and then click the Craftsman link under "By Topic" which loads the articles in the same page.)

However, the classic Sieve algorithm gets you "the primes in the first n numbers" rather than "the first n primes". I can imagine a slight tweak to the algorithm that would give you that but I'm not sure it's 100% correct. Essentially, I would imagine that you could keep a list of primes plus a multiple of that prime. As you increment the candidate prime, check whether any of the multiples of the prime are equal to the current candidate. If they are, the number is not a prime. Also check whether any of the multiples are less than the prime, if so you add the prime to the multiple again to get the next multiple. This should always be greater than the current candidate.

This approach should be quicker than checking the modulo of the candidate prime because it avoids any division operations, and also only bothers to check for prime factors of the candidate. It looks correct to my brief analysis, but you'd probably want to run a few tests to check.

[.paul.]

As for primes....
First, it can never be an even number...

2 is a prime number...

here's my Prime Number Finder:

Public Class Form1
 
    Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
        Dim seed As Integer, count As Integer
        If Integer.TryParse(TextBox1.Text, seed) AndAlso seed > 0 AndAlso Integer.TryParse(TextBox2.Text, count) Then
            ListBox1.Items.Clear()
            Dim startAt As Integer = seed - 1
            For n As Integer = 1 To count
                startAt = getNextPrime(startAt)
                ListBox1.Items.Add(startAt)
            Next
        End If
    End Sub
 
    ''' <summary>
    ''' isPrime
    ''' </summary>
    ''' <param name="x"></param>
    ''' <returns></returns>
    ''' <remarks>a Prime Number is a number greater than 1 which is divisible only by itself and 1</remarks>
    Private Function isPrime(ByVal x As Integer) As Boolean
        If x < 2 Then Return False
        Return Enumerable.Range(2, x - 2).All(Function(n) x Mod n <> 0)
    End Function
 
    Private Function getNextPrime(ByVal x As Integer) As Integer
        Dim startAt As Integer = x + 1
 
        Do
            If isPrime(startAt) Then
                Return startAt
            Else
                startAt += 1
            End If
        Loop
    End Function
 
    Private Sub Form1_Paint(ByVal sender As Object, ByVal e As System.Windows.Forms.PaintEventArgs) Handles Me.Paint
        For c As Integer = 0 To Me.Width Step 25
            e.Graphics.DrawLine(Pens.LightGray, c, 0, c, Me.Height)
        Next
        For r As Integer = 0 To Me.Height Step 25
            e.Graphics.DrawLine(Pens.LightGray, 0, r, Me.Width, r)
        Next
    End Sub
 
End Class

[Niya]

Essentially, I would imagine that you could keep a list of primes plus a multiple of that prime. As you increment the candidate prime, check whether any of the multiples of the prime are equal to the current candidate. If they are, the number is not a prime. Also check whether any of the multiples are less than the prime, if so you add the prime to the multiple again to get the next multiple. This should always be greater than the current candidate.

This approach should be quicker than checking the modulo of the candidate prime because it avoids any division operations, and also only bothers to check for prime factors of the candidate. It looks correct to my brief analysis, but you'd probably want to run a few tests to check.

Interesting, off the top of your head, just how much of an improved performance would you expect ?

[Evil_Giraffe]

Interesting, off the top of your head, just how much of an improved performance would you expect ?

For finding the first 25? Microseconds.

For the more general case, I'd guess at orders of magnitude, but that is a complete guess. Even if you restrict the modulo algorithm just to trying the primes you've found already, that's still one module operation (expensive) and a comparison with zero for each prime smaller than your candidate. For the algorithm I posited (and remember that I've not done anything particularly rigorous to prove it works) then you have an equality comparison, a less than comparison and potentially (1 in every p iterations for prime p) an addition operation (very cheap) for each prime smaller than the candidate.

The proof of the pudding is always in the actual performance, however. The best way to get a sense of how much improved performance you'll get is to code both approaches and time them.

[MattP]

My initial thought went to a loop and returning a prime number whenever it was found. In C# I would use the yield keyword which vb.net doesn't have in all but the newest frameworks. To get around this you can create a class that inherits from IEnumerable(Of T) and IEnumerator(Of T).

Public MustInherit Class Yielder(Of T)
    Implements IEnumerable(Of T)
    Implements IEnumerator(Of T)
 
    Private _current As T
 
    Public Sub New()
    End Sub
 
    Protected MustOverride Function [Yield]() As T
 
    Public Function GetEnumerator() As System.Collections.Generic.IEnumerator(Of T) Implements System.Collections.Generic.IEnumerable(Of T).GetEnumerator
        Return Me
    End Function
 
    Public Function GetEnumerator1() As System.Collections.IEnumerator Implements System.Collections.IEnumerable.GetEnumerator
        Return Me
    End Function
 
    Public ReadOnly Property Current As T Implements System.Collections.Generic.IEnumerator(Of T).Current
        Get
            Return _current
        End Get
    End Property
 
    Public ReadOnly Property Current1 As Object Implements System.Collections.IEnumerator.Current
        Get
            Return _current
        End Get
    End Property
 
    Public Function MoveNext() As Boolean Implements System.Collections.IEnumerator.MoveNext
        _current = [Yield]()
        Return True
    End Function
 
    Public Sub Reset() Implements System.Collections.IEnumerator.Reset
        Throw New NotImplementedException()
    End Sub
 
#Region "IDisposable Support"
    Private disposedValue As Boolean = False
 
    Protected Overridable Sub Dispose(disposing As Boolean)
        If Not Me.disposedValue Then
            If disposing Then
                ' TODO: dispose managed state (managed objects).
            End If
 
            ' TODO: free unmanaged resources (unmanaged objects) and override Finalize() below.
            ' TODO: set large fields to null.
        End If
        Me.disposedValue = True
    End Sub
 
    Public Sub Dispose() Implements IDisposable.Dispose
        Dispose(True)
        GC.SuppressFinalize(Me)
    End Sub
#End Region
 
End Class

Next I needed a class that will start calculating prime numbers and spit them out as they're found.

Public Class Primes
    Inherits Yielder(Of Long)
 
    Dim primes As New List(Of Long)
    Dim candidate = 1
 
    Protected Overrides Function [Yield]() As Long
        Do While candidate <= Long.MaxValue
            candidate += 1
            If candidate = 2 Then
                primes.Add(candidate)
                Return candidate
            End If
            Dim IsPrime = Function(n) primes.TakeWhile(Function(p) p <= Math.Sqrt(n)).FirstOrDefault(Function(p) n Mod p = 0) = 0
            If IsPrime(candidate) Then
                primes.Add(candidate)
                Return candidate
            End If
        Loop
        Return Nothing
    End Function
End Class

Here are a couple of examples using the Primes class.

Private Sub Form1_Load(sender As System.Object, e As System.EventArgs) Handles MyBase.Load
        Dim first25Primes = New Primes().Take(25).ToList()
        Dim maxValue = 1000
        Dim primesUnder1000 = New Primes().TakeWhile(Function(p) p <= maxValue).ToList()
        Dim maxPrimeUnder1000 = New Primes().TakeWhile(Function(p) p <= maxValue).Max()
    End Sub

[xerox3333]

Thanks for everyone's help but i figured out the simplest way do do this

Public Class frmMain

    Const Required_No_Primes = 25

    Dim primes_Found As Integer = 0
    Dim CurrentNumber As Integer = 0
    Dim is_Prime As Boolean = False

    Private Sub btnRun_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles btnRun.Click

        Do

            CurrentNumber += 1

            If CurrentNumber = 1 Then
                is_Prime = False
            ElseIf CurrentNumber = 2 Or CurrentNumber = 3 Then
                is_Prime = True
            Else
                For counter As Integer = 2 To (CurrentNumber - 1)
                    If CurrentNumber Mod counter = 0 Then
                        is_Prime = False
                        Exit For
                    Else
                        is_Prime = True
                    End If
                Next
            End If

            If is_Prime = True Then
                lstOutput.Items.Add(CurrentNumber)
                primes_Found += 1
            End If

        Loop Until primes_Found = Required_No_Primes

    End Sub

End Class

[Evil_Giraffe]

Thanks for everyone's help but i figured out the simplest way do do this

Actually, given your requirements, no you didn't. Let's recap:

My problem is that i need to generate the first 25 prime numbers and output them
[...]
no input should be required for this program it just needs to identify a prime number and display the first 25

"Identifying a prime number" isn't actually a requirement. It's an implementation detail disguised as a requirement. Thus, a professional programmer would need to clarify whether there was a hidden requirement behind this and if not then they are free to ignore it. Which I will preceed to do (since the only hidden requirement would be to have a variable number of primes priduced which is explicitly ruled out. So that leaves us with the only requirement (bolded) being to display the first 25 primes. Which seems to me your solution is more complicated than this:

Public Class Form1
 
    Private Sub btnRun_Click(sender As System.Object, e As System.EventArgs) Handles btnRun.Click
 
        Dim primes() As Integer = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97}
 
        For Each prime In primes
            lstOutput.Items.Add(prime)
        Next
 
    End Sub
 
End Class

No, I'm not being (totally) facetious. The point being that for the current requirements, do you actually need to identify primes? No, you don't. Hard coding the list is far quicker than writing the prime algorithm, so you get your software to a finished state sooner and can get it into customers' hands generating revenue earlier.

In the future you might find that the number of primes it is required to generate increases. At this stage, it might be simpler to increase the number of hardcoded primes, or it might make sense to implement the algorithm then to allow for fa more primes than you could hard code reliably. That is a decision you can take then. Of course, such real world concerns would be very unlikely to impress a programming course instructor.

[Niya]

There is also a middle of the road solution....you can use prime generating code to generate the code itself. You just need to generate a string enclose in curly braces with each number separated by commas and embed that to initialize your array. A simple look-up will always outperform any algorithm to generate primes.

[SJWhiteley]

No, I'm not being (totally) facetious. The point being that for the current requirements, do you actually need to identify primes? No, you don't. Hard coding the list is far quicker than writing the prime algorithm, so you get your software to a finished state sooner and can get it into customers' hands generating revenue earlier.

In the future you might find that the number of primes it is required to generate increases. At this stage, it might be simpler to increase the number of hardcoded primes, or it might make sense to implement the algorithm then to allow for fa more primes than you could hard code reliably. That is a decision you can take then. Of course, such real world concerns would be very unlikely to impress a programming course instructor.

A very good point, and will be relevant over the next few weeks/months as screwl is back in session.

Also, you demonstrate a flaw with going to the forums for help - your code generates the required primes but would score few points in the non-real world