isWilsonPrime now works with unknown Wilson primes

dist/primality.js

@@ -1,5 +1,5 @@
 /*!
- * primality v1.5.5
+ * primality v1.5.6
  * (c) 2012–2013 Kenan Yildirim
  *
  * Includes functions from Lo-Dash
@@ -93,6 +93,24 @@
     var primality;
     var WILSON_PRIMES = [ 5, 13, 563 ];
     var _ = require("./lib/util/");
+    function factorial(value) {
+      return value === 0 ? 1 : value * factorial(value - 1);
+    }
+    function mod(x, y) {
+      if (y > 0) {
+        if (x > 0) {
+          return x % y;
+        } else if (x == 0) {
+          return 0;
+        } else {
+          return x - y * Math.floor(x / y);
+        }
+      } else if (y == 0) {
+        return x;
+      } else {
+        throw new Error("Cannot calculate mod for a negative divisor");
+      }
+    }
     function leastFactor(n) {
       if (n === 0) return 0; else if (n % 1 || n * n < 2) return 1; else if (n % 2 === 0) return 2; else if (n % 3 === 0) return 3; else if (n % 5 === 0) return 5;
       var m = Math.sqrt(n);
@@ -138,8 +156,8 @@
       if (!primality([ a, b ])) return false;
       return true;
     }
-    function isWilsonPrime(a) {
-      return _.contains(WILSON_PRIMES, a);
+    function isWilsonPrime(value) {
+      return _.contains(WILSON_PRIMES, value) ? true : 0 === (mod(factorial(value - 1) + 1, value) === 0);
     }
     primality.VERSION = "1.4.0";
     primality.areTwinPrimes = areTwinPrimes;

primality.js

@@ -13,6 +13,45 @@ var WILSON_PRIMES = [5, 13, 563];
 
 var _ = require('./lib/util/');
 
+/**
+ * Returns the factorial of `value`
+ *
+ * @private
+ * @param {Number} value
+ * @returns {Number} The factorial of `value`.
+ */
+function factorial(value) {
+  return value === 0 ? 1 : value * factorial(value - 1);
+}
+
+/**
+ * Returns the modulus of two numbers.
+ *
+ * @param {Number} x
+ * @param {Number} y
+ * @returns {number} res
+ * @private
+ */
+function mod(x, y) {
+  if (y > 0) {
+    if (x > 0) {
+      return x % y;
+    }
+    else if (x == 0) {
+      return 0;
+    }
+    else {
+      return x - y * Math.floor(x / y);
+    }
+  }
+  else if (y == 0) {
+    return x;
+  }
+  else {
+    throw new Error('Cannot calculate mod for a negative divisor');
+  }
+}
+
 /**
  * Finds the smallest factor of `n`
  *
@@ -153,21 +192,23 @@ function areSexyPrimes(a, b) {
 }
 
 /**
- * Checks if `a` is a Wilson prime.
+ * Checks if `value` is a Wilson prime.
  *
  * <https://en.wikipedia.org/wiki/Wilson_prime>
  *
  * @static
  * @memberOf primality
- * @param {Number} a
- * @returns {Boolean} Returns `true` if `a` is a Wilson prime.
+ * @param {Number} value
+ * @returns {Boolean} Returns `true` if `value` is a Wilson prime.
  * @example
  *
  * primality.isWilsonPrime(5);
  * // => true
  */
-function isWilsonPrime(a) {
-  return _.contains(WILSON_PRIMES, a);
+function isWilsonPrime(value) {
+  return _.contains(WILSON_PRIMES, value)
+         ? true
+         : 0 === (mod(factorial(value - 1) + 1, value) === 0);
 }
 
 /**

test/spec/suite.js

@@ -54,7 +54,7 @@ define(['../../dist/primality'], function(primality) {
         primality.isWilsonPrime(5).should.equal(true);
         primality.isWilsonPrime(13).should.equal(true);
         primality.isWilsonPrime(563).should.equal(true);
-        primality.isWilsonPrime(564).should.equal(false);
+        primality.isWilsonPrime(1000).should.equal(false);
       });
     });
   });