The ultimate primes

import random
def primesbelow(n):#Sieve method

    #""" Input n>=6, Returns a list of primes, 2 <= p < n """
    correction = n % 6 > 1
    n = {0:n, 1:n-1, 2:n+4, 3:n+3, 4:n+2, 5:n+1}[n%6]
    sieve = [True] * (n // 3)
    sieve[0] = False
    for i in range(int(n ** .5) // 3 + 1):
        if sieve[i]:
            k = (3 * i + 1) | 1
            sieve[k*k // 3::2*k] = [False] * ((n//6 - (k*k)//6 - 1)//k + 1)
            sieve[(k*k + 4*k - 2*k*(i%2)) // 3::2*k] = [False] * ((n // 6 - (k*k + 4*k - 2*k*(i%2))//6 - 1) // k + 1)
    return [2, 3] + [(3 * i + 1) | 1 for i in range(1, n//3 - correction) if sieve[i]]

smallprimeset = set(primesbelow(100000))
_smallprimeset = 100000

def isprime(n, precision=7):#Miller-Rabin

    if n == 1 or n % 2 == 0:
        return False
    elif n < 1:
        raise ValueError("Out of bounds, first argument must be > 0")
    elif n < _smallprimeset:
        return n in smallprimeset


    d = n - 1
    s = 0
    while d % 2 == 0:
        d //= 2
        s += 1

    for repeat in range(precision):
        a = random.randrange(2, n - 2)
        x = pow(a, d, n)

        if x == 1 or x == n - 1: continue

        for r in range(s - 1):
            x = pow(x, 2, n)
            if x == 1: return False
            if x == n - 1: break
        else: return False

    return True

print( [i for i in range(2,1000) if isprime((2**i)-3)])

import java.util.*;
import java.math.*;

public class Main
{
    public static void main(String[] args)
    {
        int n=2;
        int count=0;
        BigInteger num = new BigInteger("0");
        BigInteger TWO = new BigInteger("2");
        BigInteger THREE = new BigInteger("3");
        for(;;)
        {
            num= ((TWO).pow(n)).subtract(THREE);
            if(num.isProbablePrime(64000))
            {count++;
            }

            if(count==27)
            {break;}
            n++;

        }

        System.out.println("N="+n);
        }

} 

from gmpy2 import is_prime

n=1
count=0
while True:
    if is_prime(2**n-3):
        count+=1
        if count==27:
            print n
            break
    n+=1