Python Prime Number Generator

Its internal state consists of 2 lists and an integer representing the current candidate. The lists are a list of primes and a corresponding list of prime multiples. For a given candidate, the algorithm compares the candidate to current prime multiples. If the candidate is less than a multiple, the prime multiple is increased additively to its next multiple (p + p + … + p) where p is the prime root. If the multiple is equal to the candidate, the candidate is not prime. If there’s no match, the candidate is prime and added to the list (p**2 added to the list of multiples).

class PrimeGen:
    p = [ ] # primes found
    m = [ ] # current multiple of each prime

    def prime(self, i):
        for j in xrange(0, len(self.p)):
            if (i + i) < self.m[j]: break
            if i > self.m[j]: self.m[j] += self.p[j]            if i == self.m[j]: return 0
        self.p.append(i)
        self.m.append(i ** 2)
        return 1

    def gen(self):
        """A prime generator"""
        i = 2
        while 1:
            if self.prime(i): yield(i)
            i += 1

The drawback is running time. Sieves (ex. Eratosthenes) are faster. This one generates the first million primes (<= 15,485,863) in about 10 minutes on modest hardware.