diff --git a/Algorithms.hpp b/Algorithms.hpp
index 6d37cd4..dca330a 100644
--- a/Algorithms.hpp
+++ b/Algorithms.hpp
@@ -27,6 +27,7 @@
 #include <cinttypes>
 #include <algorithm>
 #include <string>
+#include <cmath>
 //This library is licensed under lgplv3
 //You can find more information at gmplib.org
 //In order to use this functionality you must use the -DNEEDGMP flag in your compiler
@@ -103,7 +104,8 @@ std::vector<T> getPrimes(T goalNumber){
 	//We can now start at 3 and skip all of the even numbers
 	for(T possiblePrime = 3;possiblePrime <= goalNumber;possiblePrime += 2){
 		//Step through every element in the current primes. If you don't find anything that divides it, it must be a prime itself
-		for(uint64_t cnt = 0;(cnt < primes.size()) && ((primes.at(cnt) * primes.at(cnt)) < goalNumber);++cnt){
+		uint64_t topPossibleFactor = ceil(sqrt(possiblePrime));
+		for(uint64_t cnt = 0;(cnt < primes.size()) && (primes.at(cnt) <= topPossibleFactor);++cnt){
 			if((possiblePrime % primes.at(cnt)) == 0){
 				foundFactor = true;
 				break;
@@ -141,7 +143,8 @@ std::vector<T> getNumPrimes(T numberOfPrimes){
 	//Using possiblePrime >= 3 to make sure it doesn't loop back around in an overflow error and create an infinite loop
 	for(T possiblePrime = 3;(primes.size() < numberOfPrimes) && (possiblePrime >= 3);possiblePrime += 2){
 		//Step through every element in the current primes. If you don't find anything that divides it, it must be a prime itself
-		for(uint64_t cnt = 0;(cnt < primes.size()) && ((primes.at(cnt) * primes.at(cnt)) < possiblePrime);++cnt){
+		uint64_t topPossibleFactor = ceil(sqrt(possiblePrime));
+		for(uint64_t cnt = 0;(cnt < primes.size()) && (primes.at(cnt) <= topPossibleFactor);++cnt){
 			if((possiblePrime % primes.at(cnt)) == 0){
 				foundFactor = true;
 				break;