Added Sieve of Eratosthenes

Algorithms.ts

@@ -65,6 +65,73 @@ export function sqrtBig(value: bigint): bigint{
 	return x;
 }
 
+//Generate an infinite sequence of prime numbers using the Sieve of Eratosthenes
+export function* sieveOfEratosthenes(){
+	//Return 2 the first time, this lets us skip all even numbers later
+	yield 2;
+
+	//Dictionary to hold the primes we have already found
+	let dict = new Map<number, number[]>();
+
+	//Start checking for primes with the number 3 and skip all even numbers
+	for(let possiblePrime = 3;true;possiblePrime += 2){
+		//If possiblePrime is not in the dictionary it is a new prime number
+		//Return it and mark its next multiple
+		if(!dict.has(possiblePrime)){
+			yield possiblePrime;
+			dict.set(possiblePrime * possiblePrime, [possiblePrime]);
+		}
+		//If possiblePrime is in the dictionary it is a composite number
+		else{
+			//Move each witness to its next multiple
+			for(let num of dict.get(possiblePrime)){
+				let loc: number = possiblePrime + num + num;
+				if(dict.has(loc)){
+					dict.get(loc).push(num);
+				}
+				else{
+					dict.set(loc, [num]);
+				}
+				//We no longer need this, free the memory
+				dict.delete(possiblePrime);
+			}
+		}
+	}
+}
+
+export function* sieveOfEratosthenesBig(){
+	//Return 2 the first time, this lets us skip all even numbers later
+	yield 2n;
+
+	//Dictionary to hold the priems we have already found
+	let dict = new Map<bigint, bigint[]>();
+
+	//Start checking for primes with the number 3 and skip all even numbers
+	for(let possiblePrime = 3n;true;possiblePrime += 2n){
+		//If possiblePrime is not in the dictionary it is a new prime number
+		//Return it and mark its next multiple
+		if(!dict.has(possiblePrime)){
+			yield possiblePrime;
+			dict.set(possiblePrime * possiblePrime, [possiblePrime]);
+		}
+		//If possiblePrime is in the dictionary it is a composite number
+		else{
+			//Move each witness to its next multiple
+			for(let num of dict.get(possiblePrime)){
+				let loc: bigint = possiblePrime + num + num;
+				if(dict.has(loc)){
+					dict.get(loc).push(num);
+				}
+				else{
+					dict.set(loc, [num]);
+				}
+				//We no longer need this, free the memory
+				dict.delete(possiblePrime);
+			}
+		}
+	}
+}
+
 export function getAllFib(goalNumber: number): number[]{
 	//Setup the variables
 	let fibNums: number[] = [];