How can I test for primality?

Question

I am writing a little library with some prime number related methods. As I\'ve done the groundwork (aka working methods) and now I\'m looking for some optimization. Ofcours

Answer 1

This works very fast for testing primes (vb.net)

Dim rnd As New Random()
Const one = 1UL

    Function IsPrime(ByVal n As ULong) As Boolean
        If n Mod 3 = 0 OrElse n Mod 5 = 0 OrElse n Mod 7 = 0 OrElse n Mod 11 = 0 OrElse n Mod 13 = 0 OrElse n Mod 17 = 0 OrElse n Mod 19 = 0 OrElse n Mod 23 = 0 Then
           return false
        End If

        Dim s = n - one

        While s Mod 2 = 0
            s >>= one
        End While

        For i = 0 To 10 - 1
            Dim a = CULng(rnd.NextDouble * n + 1)
            Dim temp = s
            Dim m = Numerics.BigInteger.ModPow(a, s, n)

            While temp <> n - one AndAlso m <> one AndAlso m <> n - one
                m = (m * m) Mod n
                temp = temp * 2UL
            End While

            If m <> n - one AndAlso temp Mod 2 = 0 Then
                Return False
            End If
        Next i

        Return True
    End Function