## Question perfect cuboid

Alles zum Projekt yoyo@home
Nachricht
Autor
lloyd
Idle-Sammler
Beiträge: 3
Registriert: 20.01.2018 13:31

### Question perfect cuboid

Hi,

We noticed that in the second phase of the calculation of "Perfect Cuboid" (2 ^ 50-2 ^ 51), you decided not to look for Edge, Perfect Complex or Imaginary anymore? Is there a reason ? Was this research less interesting than the research you kept?

Moreover, if nothing is found at the end of this second campaign, do you think that you will further extend the research further? Because this second campaign will end soon enough!

Naz

x3mEn
XBOX360-Installer
Beiträge: 99
Registriert: 20.03.2011 22:23

### Re: Question perfect cuboid

Hi Lloyd,

You are right, from the 2nd batch we've decided to focus on Perfect cuboid search only. There're several reasons for this step:
1) Refusal of checking all cases and focusing on searching exclusively a Perfect cuboid accelerates the program almost at 4 times (unfortunately the first estimate of 7 times advantage was wrong);
2) After the 1st batch we've surpassed the amount of found Edge and Face cuboids more than 6 times. We had discovered: 194'652 Edge, 350'778 Face cuboids (with the space diagonal under 1'125'899'906'842'624), while the best known result is 30'081 Edge and 53'046 Face cuboids (with the smallest integer edge under 157'000'000'000). I hope the search results are exhaustive and can be shared for anyone who is interested in.

Before the very 2nd batch launch we've found a way to add also some special cases of Face cuboids and, consequently, derivative Twilight cuboids, without impact to program speed. But, I emphasize, the search of Face cuboids for ranges over 2^50 is not exhaustive. As it usually happens, after the start of the 2nd batch we found a way to add also derivative Imaginary and, possibly, Perfect Complex cuboids. So fthe 3rd batch we'll start with a new app version, the only difference in comparison with 3.04 will be adding these new types of cuboids and 3 times more found cuboids (each found Face cuboid will entail 11 derivative different cuboids: 2 Imaginary (or maybe Perfect Complex) and 9 Twilight).

lloyd
Idle-Sammler
Beiträge: 3
Registriert: 20.01.2018 13:31

Hi x3mEn,