Definitions

   A   safe prime   is a prime   p   and where   (p-1)/2   is also prime.
   The corresponding prime  (p-1)/2   is known as a   Sophie Germain   prime.
   An   unsafe prime   is a prime   p   and where   (p-1)/2   isn't   a prime.
   An   unsafe prime   is a prime that   isn't   a   safe   prime.


Task

   Find and display (on one line) the first   35   safe primes.
   Find and display the   count   of the safe primes below   1,000,000.
   Find and display the   count   of the safe primes below 10,000,000.
   Find and display (on one line) the first   40   unsafe primes.
   Find and display the   count   of the unsafe primes below   1,000,000.
   Find and display the   count   of the unsafe primes below 10,000,000.
   (Optional)   display the   counts   and   "below numbers"   with commas.
Show all output here.



Related Task

   strong and weak primes.


Also see

   The OEIS article:     safe   primes.
   The OEIS article:   unsafe primes.


Imports System.Console
 
Namespace safety
    Module SafePrimes
        Dim pri_HS As HashSet(Of Integer) = Primes(10_000_000).ToHashSet()
 
        Sub Main()
            For Each UnSafe In {False, True} : Dim n As Integer = If(UnSafe, 40, 35)
                WriteLine($"The first {n} {If(UnSafe, "un", "")}safe primes are:")
                WriteLine(String.Join(" ", pri_HS.Where(Function(p) UnSafe Xor
                                                            pri_HS.Contains(p \ 2)).Take(n)))
            Next : Dim limit As Integer = 1_000_000 : Do
                Dim part = pri_HS.TakeWhile(Function(l) l < limit),
                 sc As Integer = part.Count(Function(p) pri_HS.Contains(p \ 2))
                WriteLine($"Of the primes below {limit:n0}: {sc:n0} are safe, and {part.Count() -
                          sc:n0} are unsafe.") : If limit = 1_000_000 Then limit *= 10 Else Exit Do
            Loop
        End Sub
 
        Private Iterator Function Primes(ByVal bound As Integer) As IEnumerable(Of Integer)
            If bound < 2 Then Return
            Yield 2
            Dim composite As BitArray = New BitArray((bound - 1) \ 2)
            Dim limit As Integer = (CInt((Math.Sqrt(bound))) - 1) \ 2
            For i As Integer = 0 To limit - 1 : If composite(i) Then Continue For
                Dim prime As Integer = 2 * i + 3 : Yield prime
                Dim j As Integer = (prime * prime - 2) \ 2
                While j < composite.Count : composite(j) = True : j += prime : End While
            Next
            For i As integer = limit To composite.Count - 1 : If Not composite(i) Then Yield 2 * i + 3
            Next
        End Function
    End Module
End Namespace