[GAP Forum] A permutation group with huge finite orbits

[Stefan Kohl]

Dear Jason,

> The length of the orbit is 47610700792.
>
> Using C with GMP and OpenMP, the result can be found in roughly 3 days on a
> new core i7 machine. It is possible to compute the orbit in both directions
> at the same time on separate cores, stopping when they meet somewhere in
> the orbit. The maximum length of a digit in the orbit is 76,785.
>
> You can find the C code here: http://www.jasonbhill.com/residue-collatz/

I have compared the performance of your C program and GAP -- for the
495448-cycle of 736, your C program took about 0.25s, while GAP (compiled
with GMP) took about 1.25s. Thus your program was about 5 times faster.
For the 245719352-cycle of 25952, I measured 875s (your program) vs.
1200s (GAP), so when numbers get large (in the 1000's of digits),
GAP's overhead apparently becomes less relevant for the performance.

Congratulations for solving my puzzle!!!

    Stefan