Euler problem 12

The sequence of triangle numbers is generated by adding the natural numbers. So the 7^th triangle number would be 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28. The first ten terms would be:

1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ...

Let us list the factors of the first seven triangle numbers:

 1: 1
 3: 1,3
 6: 1,2,3,6
10: 1,2,5,10
15: 1,3,5,15
21: 1,3,7,21
28: 1,2,4,7,14,28

We can see that 28 is the first triangle number to have over five divisors.

What is the value of the first triangle number to have over five hundred divisors?

Below we see a brute force methode to solve this problem.

Performance improvement:

On http://en.wikipedia.org/wiki/Divisor_function an algorithm is described to
determine the divisors of a number by making use of prime numbers. This algorithm dramatical improves performance from 2434335 ms to 57 ms.

Problem12 =    76576500 elapsed time:   57 ms. Test Passed.