prime.py

from math import sqrt, floor

__all__ = ['is_prime', 'Prime']

class Prime(object):
    def __init__(self):
        self._primes = [2, 3, 5]

    def is_prime(self, n):
        if n < 2:
            return False

        if n in self._primes:
            return True

        for p in self._primes:
            if n % p == 0:
                return False
            if p * p > n:
                break

        limit = int(floor(sqrt(n))) + 1

        for i in xrange(self._primes[-1] + 2, limit):
            if not self.is_prime(i):
                continue
            if n % i == 0:
                return False

        for i in xrange(limit, n):
            if 0 in (n % 2, n % 3, n % 5):
                continue
            self.is_prime(i)

        self._primes.append(n)

        return True

_prime = Prime()

def is_prime(n):
    return _prime.is_prime(n)

test_prime.py

import unittest
import random

from prime import Prime

class PrimeTestCase(unittest.TestCase):
    def assertPrime(self, n):
        self.assertTrue(Prime().is_prime(n))

    def assertNotPrime(self, n):
        self.assertFalse(Prime().is_prime(n))

    def test_boundary_minus(self):
        self.assertNotPrime(-1)

    def test_boundary_zero(self):
        self.assertNotPrime(0)

    def test_boundary_one(self):
        self.assertNotPrime(1)

    def test_boundary_two(self):
        self.assertPrime(2)

    def test_square(self):
        self.assertNotPrime(49)

    def test_gap(self):
        self.assertPrime(97)
        self.assertNotPrime(77)
        self.assertPrime(7)
        self.assertPrime(23)

    def test_big_prime(self):
        self.assertPrime(997)

    def test_big_non_prime(self):
        self.assertNotPrime(10000)

    def test_all_small_primes(self):
        p = Prime()
        r = range(100)
        random.shuffle(r)
        q = [i for i in r if p.is_prime(i)]
        # print r, '=>', q
        expected = [2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41,
                    43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97]
        self.assertEquals(sorted(q), expected)

if __name__ == '__main__':
    unittest.main()