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Project Euler
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**7**

Problem 7 asks:

What is the 10 001

^{st}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.