This task has been clarified. Its programming examples are in need of review to ensure that they still fit the requirements of the task.


The Sieve of Eratosthenes is a simple algorithm that finds the prime numbers up to a given integer.



Task

Implement the   Sieve of Eratosthenes   algorithm, with the only allowed optimization that the outer loop can stop at the square root of the limit, and the inner loop may start at the square of the prime just found.

That means especially that you shouldn't optimize by using pre-computed wheels, i.e. don't assume you need only to cross out odd numbers (wheel based on 2), numbers equal to 1 or 5 modulo 6 (wheel based on 2 and 3), or similar wheels based on low primes.

If there's an easy way to add such a wheel based optimization, implement it as an alternative version.



Note

 It is important that the sieve algorithm be the actual algorithm used to find prime numbers for the task.


Related tasks

   Emirp primes
   count in factors
   prime decomposition
   factors of an integer
   extensible prime generator
   primality by trial division
   factors of a Mersenne number
   trial factoring of a Mersenne number
   partition an integer X into N primes
   sequence of primes by Trial Division


 
    Dim sieve()
	If WScript.Arguments.Count>=1 Then
	    n = WScript.Arguments(0)
	Else 
	    n = 99
	End If
    ReDim sieve(n)
    For i = 1 To n
        sieve(i) = True
    Next
    For i = 2 To n
        If sieve(i) Then
            For j = i * 2 To n Step i
                sieve(j) = False
            Next
        End If
    Next
    For i = 2 To n
        If sieve(i) Then WScript.Echo i
    Next
 