mellorjc/problem12.html

## problem12.html
<!DOCTYPE HTML>
<html>
<body>
  <p>Problem 12</p>
  <script>
     function is_prime(n) {
         /*
          * Try to divide n by all the numbers from 2 to the square root
          * of n. If any divide exactly then we know that n is not prime
          * and return false, otherwise if after testing all the mentioned
          * numbers then we know that n is prime as so return true.
          */
         for (var i = 2; i <= Math.sqrt(n); i++) {
             if (n % i == 0) {
                 return false;
             }
         }
         return true;
     }
     function next_prime(n) {
         /*
          * Starting from n, as given by the function argument,
          * find the next prime by increasing n until n is prime.
          * We test if n is prime using the is_prime function.
          */
         while (true) {
             n = n + 1;
             if (is_prime(n)) {
                 return n;
             }
         }
     }
     function prime_factors(n) {
         /*
          * Starting from 2 (the 1st prime number) as the current prime p, repeatedly
          * divide n by p up until there is a remainer, at which point alter the current
          * prime p to the next largest prime (using the function next_prime) and repeat
          * this procedure until n is 1. Each time p will divide into n, increase the number
          * of times p is a prime factor that is recorded in the dictionary pfacs.
          */
         var p = 2;
         var pfacs = {};
         while (n > 1) {
             while (n % p == 0) {
                 n = n / p;
                 if (!(p in pfacs)) {
                     pfacs[p] = 0;
                 }
                 pfacs[p] = pfacs[p] + 1;
             }
             p = next_prime(p);
         }
         return pfacs;
     }
     function num_factors(pfacs) {
         /*
          * Given a dictionary, where the keys are the unique prime factors
          * and the values are the number of times the unique prime factor
          * occurs, we use the form (v_1 + 1)(v_2 + 1)(v_3 + 1)...
          * to calculate the number of factors (including non-prime)
          *
          * Here v_1 is value associated with the 1st key in the dictionary,
          * and so number of times that the unique prime factor appears as a
          * prime factor.
          */
         var r = 1;
         for (p in pfacs) {
             r = r*(pfacs[p] + 1);
         }
         return r;
     }
     /* This is the main loop for solving the problem.
      * The program starts at the 1st triangle number.
      * It calculates the number of factors this number has.
      * It checks if the number of factors is 500 or above.
      * If it does, it stops and displays the current triangle number.
      * If it doesn't, it goes to the next triangle number and repeats the process.
      * It does this until it finds the corrent answer.
      */
     var i = 1;
     while (true) {
         var x = i*(i+1)/2;  /* x not contains the ith triangle number */
         var num_f = num_factors(prime_factors(x)); /* calculate the number of factors for the ith triangle number */
         if (num_f >= 500) { /* if it contains 500 factors of over then stop searching a display the answer */
             alert(x);
             break;
         }
         i = i + 1;
     }
  </script>
</body>
</html>
	<!DOCTYPE HTML>
	<html>
	<body>
	<p>Problem 12</p>
	<script>
	function is_prime(n) {
	/*
	* Try to divide n by all the numbers from 2 to the square root
	* of n. If any divide exactly then we know that n is not prime
	* and return false, otherwise if after testing all the mentioned
	* numbers then we know that n is prime as so return true.
	*/
	for (var i = 2; i <= Math.sqrt(n); i++) {
	if (n % i == 0) {
	return false;
	}
	}
	return true;
	}
	function next_prime(n) {
	/*
	* Starting from n, as given by the function argument,
	* find the next prime by increasing n until n is prime.
	* We test if n is prime using the is_prime function.
	*/
	while (true) {
	n = n + 1;
	if (is_prime(n)) {
	return n;
	}
	}
	}
	function prime_factors(n) {
	/*
	* Starting from 2 (the 1st prime number) as the current prime p, repeatedly
	* divide n by p up until there is a remainer, at which point alter the current
	* prime p to the next largest prime (using the function next_prime) and repeat
	* this procedure until n is 1. Each time p will divide into n, increase the number
	* of times p is a prime factor that is recorded in the dictionary pfacs.
	*/
	var p = 2;
	var pfacs = {};
	while (n > 1) {
	while (n % p == 0) {
	n = n / p;
	if (!(p in pfacs)) {
	pfacs[p] = 0;
	}
	pfacs[p] = pfacs[p] + 1;
	}
	p = next_prime(p);
	}
	return pfacs;
	}
	function num_factors(pfacs) {
	/*
	* Given a dictionary, where the keys are the unique prime factors
	* and the values are the number of times the unique prime factor
	* occurs, we use the form (v_1 + 1)(v_2 + 1)(v_3 + 1)...
	* to calculate the number of factors (including non-prime)
	*
	* Here v_1 is value associated with the 1st key in the dictionary,
	* and so number of times that the unique prime factor appears as a
	* prime factor.
	*/
	var r = 1;
	for (p in pfacs) {
	r = r*(pfacs[p] + 1);
	}
	return r;
	}
	/* This is the main loop for solving the problem.
	* The program starts at the 1st triangle number.
	* It calculates the number of factors this number has.
	* It checks if the number of factors is 500 or above.
	* If it does, it stops and displays the current triangle number.
	* If it doesn't, it goes to the next triangle number and repeats the process.
	* It does this until it finds the corrent answer.
	*/
	var i = 1;
	while (true) {
	var x = i(i+1)/2; / x not contains the ith triangle number */
	var num_f = num_factors(prime_factors(x)); /* calculate the number of factors for the ith triangle number */
	if (num_f >= 500) { /* if it contains 500 factors of over then stop searching a display the answer */
	alert(x);
	break;
	}
	i = i + 1;
	}
	</script>
	</body>
	</html>