N 番目の素数を探す（Find Nth prime）

nthprime.py

import math


def _is_prime_slow(prime_candidate):
    for i in range(2, prime_candidate - 1):
        if prime_candidate % i == 0:
            return False
    return True


def nthprime_slow(nth):
    primes = [2]
    next_prime_candidate = 3
    while len(primes) < nth:
        if _is_prime_slow(next_prime_candidate):
            primes.append(next_prime_candidate)
        next_prime_candidate += 1
    return primes[-1]


def _is_prime(prime_candidate, primes):
    sqrt = int(math.sqrt(prime_candidate))
    for i in primes:
        if sqrt < i:
            break
        if prime_candidate % i == 0:
            return False
    return True


def nthprime(nth):
    primes = [2]
    next_prime = 3
    while len(primes) < nth:
        if _is_prime(next_prime, primes):
            primes.append(next_prime)
        next_prime += 2
    return primes[-1]