import math

def sieve_of_atkin(limit):
    sieve = [False] * (limit + 1)
    sieve[2], sieve[3] = True, True
    
    for x in range(1, int(math.sqrt(limit)) + 1):
        for y in range(1, int(math.sqrt(limit)) + 1):
            n = 4 * x**2 + y**2
            if n <= limit and (n % 12 == 1 or n % 12 == 5):
                sieve[n] = not sieve[n]
            
            n = 3 * x**2 + y**2
            if n <= limit and n % 12 == 7:
                sieve[n] = not sieve[n]
            
            n = 3 * x**2 - y**2
            if x > y and n <= limit and n % 12 == 11:
                sieve[n] = not sieve[n]

    for x in range(5, int(math.sqrt(limit)) + 1):
        if sieve[x]:
            for y in range(x**2, limit + 1, x**2):
                sieve[y] = False
    
    return sieve

def count_primes(sieve):
    return [i for i in range(2, len(sieve)) if sieve[i]]

def nth_prime_fast(n):
    if n < 1:
        return None
    if n == 1:
        return 2
    
    limit = max(10, n * int(math.log(n) + math.log(math.log(n))))
    while True:
        sieve = sieve_of_atkin(limit)
        primes = count_primes(sieve)
        if len(primes) >= n:
            return primes[n - 1]
        limit *= 2


print(nth_prime_fast(10001))