# Shobute🍻

## Project-Euler / 7

What is the 10 001st prime number?

Here’s my solution in Java:

import static java.lang.Math.sqrt;

public class Problem7 {
public static void main(String[] args) {
int count = 0;
int div = 1;
int result = 1;
while (count < 10_001) {
result++;
for (div=(int)sqrt(result); div>0; div--)
if (result % div == 0) break;
if (div == 1) count++;
}
System.out.println(result);
}
}

The only thing to note is I’m dividing from $$\lfloor\sqrt n\rfloor$$ (and down to 1) to check if $$n$$ is prime. The reason I don’t need to check more than that is if $$d$$ is a divisor of $$n$$ then $$\tfrac{n}{d}$$ is also a divisor of $$n$$. This substantially speeds up the program.

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