diff --git a/SieveOfEratosthenes.lua b/SieveOfEratosthenes.lua
new file mode 100644
index 0000000..3c72285
--- /dev/null
+++ b/SieveOfEratosthenes.lua
@@ -0,0 +1,77 @@
+--luaClasses/SieveOfEratosthenes.lua
+--Matthew Ellison
+-- Created: 06-30-21
+--Modified: 06-30-21
+--This creates a class that uses the Sieve of Eratosthenes to generate an infinite number of primes
+--[[
+	Copyright (C) 2021  Matthew Ellison
+
+	This program is free software: you can redistribute it and/or modify
+	it under the terms of the GNU Lesser General Public License as published by
+	the Free Software Foundation, either version 3 of the License, or
+	(at your option) any later version.
+
+	This program is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+	GNU Lesser General Public License for more details.
+
+	You should have received a copy of the GNU Lesser General Public License
+	along with this program.  If not, see <https://www.gnu.org/licenses/>.
+]]
+
+
+--Create the table
+SieveOfEratosthenes = {};
+SieveOfEratosthenes.__index = SieveOfEratosthenes;
+
+--This is needed to create a Sieve and link the variables and functions
+--It should be called before anything when creating a Sieve
+function SieveOfEratosthenes:create()
+	local sieve = {
+		possiblePrime = 2;
+		compositeMap = {};
+	};
+	setmetatable(sieve, SieveOfEratosthenes);	--This links the new variable with the functions from the SieveOfEratosthenes
+	return sieve;
+end
+
+--This function returns the next prime number
+function SieveOfEratosthenes:next()
+	local prime = 0;
+	if(self.possiblePrime > 2) then
+		--Loop until you find a prime number
+		while(self.compositeMap[self.possiblePrime] ~= nil) do
+			--Create the next entry for all entries in the map
+			for cnt = 1, #self.compositeMap[self.possiblePrime] do
+				local num = self.compositeMap[self.possiblePrime][cnt];
+				if(self.compositeMap[self.possiblePrime + num + num] == nil) then
+					local tempArray = {num};
+					self.compositeMap[self.possiblePrime + num + num] = tempArray;
+				else
+					table.insert(self.compositeMap[self.possiblePrime + num + num], num);
+				end
+			end
+			--Delete the current entry
+			self.compositeMap[self.possiblePrime] = nil;
+			--table.remove(self.compositeMap, self.possiblePrime);
+			self.possiblePrime = self.possiblePrime + 2;
+		end
+		--Save that the number is prime
+		prime = self.possiblePrime;
+		--Add the next entry to the prime
+		if(self.compositeMap[prime * 3] == nil) then
+			local tempArray = {prime};
+			self.compositeMap[prime * 3] = tempArray;
+		else
+			table.insert(self.compositeMap[prime * 3], prime);
+		end
+		--Move on to the next possible prime
+		self.possiblePrime = self.possiblePrime + 2;
+	else
+		--Return 2 and move to 3
+		prime = self.possiblePrime;
+		self.possiblePrime = self.possiblePrime + 1;
+	end
+	return prime;
+end
diff --git a/testSieveOfEratosthenes.lua b/testSieveOfEratosthenes.lua
new file mode 100644
index 0000000..f8780a0
--- /dev/null
+++ b/testSieveOfEratosthenes.lua
@@ -0,0 +1,49 @@
+--luaClasses/testSieveOfEratosthenes.lua
+--Matthew Ellison
+-- Created: 06-30-21
+--Modified: 06-30-21
+--This tests the SieveOfEratosthenes class
+--[[
+	Copyright (C) 2021  Matthew Ellison
+
+	This program is free software: you can redistribute it and/or modify
+	it under the terms of the GNU Lesser General Public License as published by
+	the Free Software Foundation, either version 3 of the License, or
+	(at your option) any later version.
+
+	This program is distributed in the hope that it will be useful,
+	but WITHOUT ANY WARRANTY; without even the implied warranty of
+	MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+	GNU Lesser General Public License for more details.
+
+	You should have received a copy of the GNU Lesser General Public License
+	along with this program.  If not, see <https://www.gnu.org/licenses/>.
+]]
+
+require "SieveOfEratosthenes"
+require "Algorithms"
+
+
+local function testSieveOfEratosthenes()
+	local failed = false;	--Signals whether a test was failed
+
+	--Test 1
+	local sieve = SieveOfEratosthenes:create();
+	local correctAnswer = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97};
+	local answer = {};
+	for _ = 0, 25 do
+		table.insert(answer, sieve:next());
+	end
+	if(table.unpack(correctAnswer) ~= table.unpack(answer)) then
+		io.write("SieveOfEratosthenes failed the test\n");
+		failed = true;
+	end
+
+	--Print a message if all of the tests passed
+	if(not failed) then
+		io.write("SieveOfEratosthenes passed all tests\n");
+	end
+end
+
+--Test SieveOfEratosthenes
+testSieveOfEratosthenes();
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