More graphs and primes!

tools/math/primes.ts

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+/**
+ * A cache of prime numbers.
+ * 
+ * This cache is unfortunately bounded by the memory constraints JavaScript
+ * imposes on arrays. This means the highest prime number that can be generated
+ * is NOT anywhere close to `Number.MAX_SAFE_INTEGER` (2^53 - 1), but instead
+ * much lower, at around the (2^32 - 2)th prime.
+ * @private
+ */
+const knownPrimesArr: number[] = [2]
+
+/**
+ * Yields prime numbers in ascending order
+ *
+ * @remarks
+ * 
+ * This function has a heavy memory footprint, is unfortunately bounded
+ * by the memory constraints JavaScript imposes on arrays. This means
+ * the highest prime number that can be generated is NOT `Number.MAX_SAFE_INTEGER`, but
+ * instead the (2^32 - 2)th prime.
+ * 
+ * However, since primality only needs to be verified for numbers up to sqrt(n), this
+ * function is sufficient for telling if any number between 2 and `Number.MAX_SAFE_INTEGER` is prime
+ * 
+ * @example
+ * for (const prime of primes()) {
+ *     if (prime > 100) break
+ *     console.log(prime)
+ * }
+ * 
+ * @author MindfulMinun
+ * @since 2022-10-13
+ */
+export function* primes(): Generator<number, never, undefined> {
+    // First we yield all the known primes
+    // yield* knownPrimes.values()
+    yield* knownPrimesArr
+    
+    // Then we generate new primes using the sieve of Eratosthenes
+    while (true) {
+        const length = knownPrimesArr.length
+        let n = knownPrimesArr[length - 1] + 1
+
+        while (!_isPrime(n)) n++
+
+        if (2 ** 32 - 3 < length) throw Error("Too many primes!")
+
+        knownPrimesArr.push(n)
+        yield n
+    }
+}
+
+function _isPrime(n: number) {
+    if (n < 2) return false
+
+    if (Number.MAX_SAFE_INTEGER < n) throw Error("Number is too large to verify X(")
+
+    const sqrt = Math.ceil(Math.sqrt(n))
+
+    for (const prime of knownPrimesArr) {
+        if (n % prime === 0) return false
+        if (sqrt < prime) break
+    }
+    return true
+}
+
+/**
+ * Verify if a given number is prime.
+ */
+export function isPrime(n: number): boolean {
+    // To verify if a number is prime, we only need to check if it is divisible by
+    // any of the primes less than or equal to its square root.
+
+    const sqrt = Math.ceil(Math.sqrt(n))
+
+    for (const prime of primes()) {
+        if (n % prime === 0) return false
+        if (sqrt < prime) break
+    }
+    return true
+}