The Collatz Conjecture
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Profile sosiris
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Message 18326 - Posted: 5 Feb 2014, 16:08:22 UTC

After some investigations into the pre-calculation tables, I had some ideas of getting the calculations faster.

let n = 1048576 k + b, 0<= b < 1048576
1.Discard even b's (that is, 'n' is a even number) : 524288 b's remained

2.Discard those b's sharing the same 'path', leave only one 'b' : 249612 b's remained
e.g. '1048576k + 267605' and '1048576k + 269425' share the same path. Both will become '27k+7' after collatz claculations (one can just calculate this by hand...and a calculator), thus we can just evaluate '1048576k + 267605'

3.Discard those odd b's having the same path with even b's: 116606 b's remained
e.g. '1048576k + 267604' and '1048576k + 267605' share the same path, so 267605 is the same as 267604 (even number). According to idea 1, just discard it!

So we only need to evaluate:
116606/1048576 = 11.12% , about 1/9 of all numbers

And those b's can be presented as static array = {1,27,31,37,41,47,...} and test data can be filled quickly using n = 1048576*i + array[j] without affecting parallel computing(maybe).

-Sosiris-

SuperSluether
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Message 19688 - Posted: 3 Jul 2014, 1:34:16 UTC

How do you know when the project is done, and what happens when it's finished?

Profile sosiris
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Message 19689 - Posted: 3 Jul 2014, 2:36:32 UTC - in response to Message 19688.

Slicker knows the best. However as far as I know, the project is done when we find a counterexample of Collatz conjecture. i.e. it will grow into infinity or maintain a loop not involving 4-2-1 cycle. It will be a remarkable event in the field of mathematics.

Nevertheless, it's proven that going to infinity is not possible, and the minimum length of a loop not involving 4-2-1 cycle is so LONG & the minimum numbers in the loop will be so HUGE that we have many, many years to crunch, if my memory serves me right.
____________
Sosiris, team BOINC@Taiwan

Jozef J
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Message 23933 - Posted: 28 Mar 2017, 16:23:47 UTC

Collatz Conjecture in Color - Numberphile


https://www.youtube.com/watch?v=LqKpkdRRLZw

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