From e6a6bd34f6e4ff70d8a93f11703092859dc7a5bb Mon Sep 17 00:00:00 2001
From: Colin McMillen <colin@semicolin.games>
Date: Tue, 17 Nov 2020 14:25:33 -0500
Subject: [PATCH] solution for problem #3

---
 Program.cs | 49 +++++++++++++++++++++++++++++++++++++++++--------
 1 file changed, 41 insertions(+), 8 deletions(-)

diff --git a/Program.cs b/Program.cs
index b6fc517..4ab91d3 100644
--- a/Program.cs
+++ b/Program.cs
@@ -5,9 +5,9 @@ namespace Euler {
 
   class Program {
 
-  	static int Problem1() {
-  		int sum = 0;
-  		for (int i = 1; i < 1000; i++) {
+  	static long Problem1() {
+  		long sum = 0;
+  		for (long i = 1; i < 1000; i++) {
   			if (i % 3 == 0 || i % 5 == 0) {
   				sum += i;
   			}
@@ -16,18 +16,18 @@ namespace Euler {
   	}
 
   	static long Problem2() {
-  		int max = 4_000_000;
+  		long max = 4_000_000;
 
-  		var fibs = new List<int>();
+  		var fibs = new List<long>();
   		fibs.Add(1);
   		fibs.Add(2);
 
   		while (fibs[fibs.Count - 1] < max) {
-  			int num = fibs[fibs.Count - 1] + fibs[fibs.Count - 2];
+  			long num = fibs[fibs.Count - 1] + fibs[fibs.Count - 2];
  			  fibs.Add(num);
   		}
 
-      int sum = 0;
+      long sum = 0;
   		foreach (int i in fibs) {
   			if (i % 2 == 0 && i <= max) {
   				sum += i;
@@ -37,8 +37,41 @@ namespace Euler {
   		return sum;
   	}
 
+  	static bool IsPrime(long num, List<long> primes) {
+  		foreach (long i in primes) {
+  			if (num % i == 0) {
+  				return false;
+  			}
+  		}
+  		return true;
+  	}
+
+  	static List<long> PrimesUpThrough(long num) {
+  		var primes = new List<long>();
+  		primes.Add(2);
+  		for (int i = 3; i <= num; i += 2) {
+  			if (IsPrime(i, primes)) {
+  				primes.Add(i);
+  			}
+  		}
+  		return primes;
+  	}
+
+  	static long Problem3() {
+  		long target = 600_851_475_143;
+  		long targetSqrt = (long) Math.Sqrt(target);
+  		List<long> primes = PrimesUpThrough(targetSqrt);
+  		long highestPrimeFactor = 0;
+  		foreach (long i in primes) {
+  			if (target % i == 0) {
+  				highestPrimeFactor = i;
+  			}
+  		}
+  		return highestPrimeFactor;
+  	}
+
     static void Main(string[] args) {
-      Console.WriteLine(Problem2());
+      Console.WriteLine(Problem3());
     }
   }
 }
\ No newline at end of file