How can I improve this code for Project Euler 7?

Question

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?

My solution:

Answer 1

I would comment, but I just joined.

You don't have to check every number between 1 and a numbers square root for potential divisors, you just have to check all previous primes (assuming you start at 1 and iterate up), as any other divisor that is not prime will itself be divisible by a prime of a lower value. the higher the number of primes, the more checks against non prime numbers this saves. the example is in C# but that's more to demonstrate the concept.

    //store found primes here, for checking subsequent primes
    private static List Primes;
    private static bool IsPrime(long number)
    {
        //no number will have a larger divisor withou some smaller divisor
        var maxPrime = Math.Sqrt(number);

        // takes the list of primes less than the square root and 
        //     checks to see if all of that list is not evenly 
        //     divisible into {number}
        var isPrime = Primes
            .TakeWhile(prime => !(prime > maxPrime))
            .All(prime => number % prime != 0);
        if (isPrime)
            Primes.Add(number);
        return isPrime;
    }

    private static long GetNthPrime(int n)
    {
        //reset primes list to prevent persistence
        Primes = new List { 2, 3, 5, 7 };

        //prime in starting set
        if (Primes.Count >= n)
        {
            return Primes[n - 1];
        }

        //iterate by 6 to avoid all divisiors of 2 and 3 
        //  (also have to check i + 2 for this to work)
        //  similar to incrementing by 2 but skips every third increment 
        //  starting with the second, as that is divisible by 3
        for (long i = 11; i < long.MaxValue; i += 6)
        {
            // only check count if is prime
            if ((IsPrime(i) && Primes.Count >= n) || (IsPrime(i + 2) && Primes.Count >= n))
            {
                break;
            };
        }
        //return end of list
        return Primes[n - 1];
    }