"""
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Generate the n'th prime
      import Primes
      prime = Primes.prime
      nthprime = primes[n]
      prime.get(n)  retrieve the nth prime

"""
# Primes is a class that computes the list of primes
#  303 primes are pre computed and added as necessary.
#  Usually, our graphs are much smaller than this so
#  the seive of Erasthosthenes is actually not used.
class Primes:
    primes = [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,
        101, 103, 107, 109, 113, 127, 131, 137, 139, 149,
        151, 157, 163, 167, 173, 179, 181, 191, 193, 197,
        199, 211, 223, 227, 229, 233, 239, 241, 251, 257,
        263, 269, 271, 277, 281, 283, 293, 307, 311, 313,
        317, 331, 337, 347, 349, 353, 359, 367, 373, 379,
        383, 389, 397, 401, 409, 419, 421, 431, 433, 439,
        443, 449, 457, 461, 463, 467, 479, 487, 491, 499,
        503, 509, 521, 523, 541, 547, 557, 563, 569, 571,
        577, 587, 593, 599, 601, 607, 613, 617, 619, 631,
        641, 643, 647, 653, 659, 661, 673, 677, 683, 691,
        701, 709, 719, 727, 733, 739, 743, 751, 757, 761,
        769, 773, 787, 797, 809, 811, 821, 823, 827, 829,
        839, 853, 857, 859, 863, 877, 881, 883, 887, 907,
        911, 919, 929, 937, 941, 947, 953, 967, 971, 977,
        983, 991, 997, 1009, 1013, 1019, 1021, 1031, 1033,
        1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091,
        1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151,
        1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213,
        1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277,
        1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307,
        1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399,
        1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451,
        1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493,
        1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559,
        1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609,
        1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667,
        1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733,
        1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789,
        1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871,
        1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931,
        1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997,
        1999, 2003, 2011, 2017, 2027, 2029, 2039, 2053,
        2063, 2069, 2081, 2083, 2087, 2089, 2099, 2111,
        2113, 2129, 2131, 2137, 2141, 2143, 2153, 2161,
        2179, 2203, 2207, 2213, 2221, 2237, 2239, 2243,
        2251, 2267, 2269, 2273, 2281, 2287, 2293, 2297,
        2309, 2311, 2333, 2339, 2341, 2347, 2351, 2357,
        2371, 2377, 2381, 2383, 2389, 2393, 2399, 2411,
        2417, 2423, 2437, 2441, 2447, 2459, 2467, 2473,
        2477, 2503, 2521, 2531, 2539, 2543, 2549, 2551,
        2557, 2579, 2591, 2593, 2609, 2617, 2621, 2633,
        2647, 2657, 2659, 2663, 2671, 2677, 2683, 2687,
        2689, 2693, 2699, 2707, 2711, 2713]
    # good old Sieve of Erasthosthenes
    def _findNextPrime(self, N):
        """Generate the first N primes"""
        primes = self.primes
        nextPrime = primes[-1]+1
        while(len(primes)<N):
            maximum = nextPrime * nextPrime
            prime = 1
            for i in primes:
                if i > maximum:
                    break
                if nextPrime % i == 0:
                    prime = 0
                    break
            if prime:
                primes.append(nextPrime)
            nextPrime+=1

    def __getitem__(self, i):
        assert i>=0, "Index must be greater than 0!"
        if i >= len(self.primes)-1:
            self._findNextPrime(i+1)
        return self.primes[i]

    def get(self, i):
        return self[i]

primes = Primes()

