python version of the answer

def prime_s(num):

primes = [True]*(num+1)

primes[0] = False
primes[1] = False

for i in range(2, int(num**0.5)+1):
    if primes[i]:
        for j in range(i*i, num+1, i):
            primes[j] = False
primes = [i for i in range(num+1) if primes[i]]
return primes

def nth_prime(n, precomputed_primes): import math if n <= len(precomputed_primes): return precomputed_primes[n-1] else: limit = int(n*math.log(n)*1.5) if n > 5 else 15

    primes = prime_s(limit)

    while len(primes) < n:
        limit *= 2
        primes = prime_s(limit)
    return primes[n-1]

precomputed_primes = prime_s(10**6) t = int(input().strip()) for a0 in range(t): n = int(input().strip())

if n==1:
    print(2)
    continue

result = nth_prime(n, precomputed_primes)
print(result)