I recently applied to gSchool. The code I submitted was my answer to Problem 7 at Project Euler:

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?

This was a fun problem to work on. Initially the method I wrote to test if a number (x) is prime involved testing each number that made up x. It resembled something like this:

def prime? number
  return false if number == 0 || number == 1
  integers = *(2..number)
  integers.each do |i|
    return false if number % i == 0
  end
  true
end

Although this approach worked. It took far too long to compute. So I did some research on Wikipedia and came across an integer factorization called Trial division. Incorporating this into the final solution below drastically reduced the time to compute the answer.

def prime? number
  return false if number == 0 || number == 1
  integers = *(2..Math.sqrt(number).round)
  integers.each do |i|
    return false if number % i == 0
  end
  true
end

def findPrime order
  count = 0
  number = 0
  while count != order
      number += 1
      count += 1 if prime? number
  end
  number
end