Quote:
Originally Posted by alpertron
Now the calculation of sum of squares uses GCD of Gaussian integers (for two squares) and GCD of quaternions (for four squares).
The GCD takes about 1 second for numbers of 10000 digits (I tested that with the smallest gigantic prime, which is 10^{9999} + 33603). Most of the time is used for a modular power.
With the previous version, computing the sum of four squares would have taken about one hour.
I will continue doing more tests, and if everything works OK, I will move the new Web application to the "standard" URL.

Now when the code detects that the number can be divided by a very small factor (less than 100000), it will quickly determine the maximum exponent of this small factor that can divide the number, so the factorization proceeds a lot faster.
For example, in the previous version the application needed 15 minutes to factor 2678!. In this version it needs only 10 seconds in the same computer.
Now I will need to change the program to quickly compute big factorials (say bigger than 5000!).