Algrbra Package

[kmcollins]

As part of my algebra package I just wrote a prime number sieve. I hereby place the following code ito the public domain:

    def primeNumbers(a):
        "return a list of prime numbers <= a using a sieve"
        if a == None or not isinstance(a, int) or a <= 1:
            return []
        sieve = []
        idx = 0
        while idx <= a:
            sieve.append(idx)
            idx += 1
        sieve[1]    = sieve[0]  = None
        prime = sieve[2]
        while prime <= a:
            multiplier = 2
            while prime*multiplier <= a:
                sieve[prime*multiplier] = None
                multiplier += 1
            start = prime+1
            while start <= a and sieve[start] == None:
                start += 1
            prime = start
        #print(str(sieve))
        primes = []
        idx = 2
        while idx < len(sieve):
            if sieve[idx] != None:
                primes.append(idx)
            idx += 1
        return tuple(primes)