Solution to Project Euler Problem 7: 10001st prime - By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13. What is the 10 001st prime number?

• Java Code

package sikademy;
/**
 *
 * @author Archangel Macsika
 * Copyright (c) Sikademy. All rights reserved
 */

public class SikademyEulerSolution {
	
        public static int sqrt(int x) {
		if (x < 0)
			throw new IllegalArgumentException("Square root of negative number");
		int y = 0;
		for (int i = 1 << 15; i != 0; i >>>= 1) {
			y |= i;
			if (y > 46340 || y * y > x)
				y ^= i;
		}
		return y;
	}


        public static boolean isPrime(int x) {
		if (x < 0)
			throw new IllegalArgumentException("Negative number");
		if (x == 0 || x == 1)
			return false;
		else if (x == 2)
			return true;
		else {
			if (x % 2 == 0)
				return false;
			for (int i = 3, end = sqrt(x); i <= end; i += 2) {
				if (x % i == 0)
					return false;
			}
			return true;
		}
	}

	public String run() {
		for (int i = 2, count = 0; ; i++) {
			if (isPrime(i)) {
				count++;
				if (count == 10001)
					return Integer.toString(i);
			}
		}
	}

	public static void main(String[] args) {
                SikademyEulerSolution solution = new SikademyEulerSolution();
		System.out.println(solution.run());
	}	
}

• Python Code

# 
# @author Archangel Macsika
# Copyright (c) Sikademy. All rights reserved.
# 

import itertools


def sqrt(x):
	assert x >= 0
	i = 1
	while i * i <= x:
		i *= 2
	y = 0
	while i > 0:
		if (y + i)**2 <= x:
			y += i
		i //= 2
	return y


# Tests whether the given integer is a prime number.
def is_prime(x):
	if x <= 1:
		return False
	elif x <= 3:
		return True
	elif x % 2 == 0:
		return False
	else:
		for i in range(3, sqrt(x) + 1, 2):
			if x % i == 0:
				return False
		return True

def compute():
	ans = next(itertools.islice(filter(is_prime, itertools.count(2)), 10000, None))
	return str(ans)


if __name__ == "__main__":
	print(compute())