### How to implement a program for Sieve of Eratosthenes in Smalltalk

###### widgets Article
Sieve of Eratosthenes
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.

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.

## Smalltalk

A simple implementation that you can run in a workspace. It finds all the prime numbers up to and including limit—for the sake of example, up to and including 100.

| potentialPrimes limit |limit := 100.potentialPrimes := Array new: limit.potentialPrimes atAllPut: true.2 to: limit sqrt do: [:testNumber |    (potentialPrimes at: testNumber) ifTrue: [        (testNumber * 2) to: limit by: testNumber do: [:nonPrime |            potentialPrimes at: nonPrime put: false        ]    ]].2 to: limit do: [:testNumber |    (potentialPrimes at: testNumber) ifTrue: [        Transcript show: testNumber asString; cr    ]]