Add Integer::isPrime.

Author: markrogoyski

src/NumberTheory/Integer.php

@@ -349,6 +349,39 @@ function ($m) use ($√n) {
         return [];
     }
 
+    /**
+     * Primality test (prime number test)
+     * https://en.wikipedia.org/wiki/Primality_test
+     *
+     * Determines whether a number is a prime number.
+     *
+     * @param int $n
+     *
+     * @return bool
+     */
+    public static function isPrime(int $n): bool
+    {
+        if ($n <= 1) {
+            return false;
+        }
+
+        if ($n === 2 || $n === 3) {
+            return true;
+        }
+
+        if ($n % 2 === 0 || $n % 3 === 0) {
+            return false;
+        }
+
+        for ($i = 5; $i <= \sqrt($n); $i += 6) {
+            if ($n % $i === 0 || $n % ($i + 2) === 0) {
+                return false;
+            }
+        }
+
+        return true;
+    }
+
     /**
      * Prime factorization
      * The prime factors of an integer.

tests/NumberTheory/IntegerAxiomsTest.php

@@ -15,6 +15,8 @@
  * Axioms tested:
  *  - Coprime
  *    - lcm(a, b) = ab
+ *  - Prime factorization
+ *    - All primes
  */
 class IntegerAxiomsTest extends \PHPUnit\Framework\TestCase
 {
@@ -109,4 +111,18 @@ public function dataProviderForCoprime(): array
             [29, 30],
         ];
     }
+
+    /**
+     * Axiom: Prime factorization produces only primes
+     * @return void
+     */
+    public function testPrimeFactorizationAllPrimes(): void
+    {
+        for ($i = 2; $i < 10000; $i++) {
+            $primes = Integer::primeFactorization($i);
+            foreach ($primes as $prime) {
+                $this->assertTrue(Integer::isPrime($prime));
+            }
+        }
+    }
 }