20190804, 12:58  #1 
"David Barina"
Jul 2016
Brno
2^{3}·5 Posts 
Checking of Collatz problem / conjecture
While playing with the Collatz problem, I have realized that the trajectory (of any number) can be efficiently computed using the ctz operation (count trailing zeros) and a small lookup table mapping n to 3^n. The idea is described here.
Would anyone be able to further optimize this approach? Any feedback is welcome. 
20190806, 15:52  #2 
"David Barina"
Jul 2016
Brno
2^{3}·5 Posts 
How far has Collatz conjecture been computationally verified?
Does anyone provide reference for how far has Collatz conjecture been computationally verified? This page from 2017 by Eric Roosendaal claims that the yoyo@home project checked for convergence all numbers up to approx. 2^{66}. Is this record still valid today?

20190806, 19:44  #3 
6809 > 6502
"""""""""""""""""""
Aug 2003
101×103 Posts
2^{2}×2,339 Posts 
Have you tried looking around the internet for the answer yet?

20190807, 08:13  #4 
Dec 2012
The Netherlands
652_{16} Posts 
Maybe this will help:
https://www.mdpi.com/23065729/4/2/89 
20190807, 20:49  #6 
"Dylan"
Mar 2017
2·281 Posts 
From one of my recently completed work units from the Collatz conjecture BOINC project (https://boinc.thesonntags.com/collat...ultid=40842156), it appears numbers near 6.16*10^21 are being tested, which is between 2^72 and 2^73. Although with the large number of pending tasks, the actual search limit might be lower than this.

20190808, 18:35  #7 
"David Barina"
Jul 2016
Brno
50_{8} Posts 
Currently, I am able to verify the convergence of all numbers below 2^{32} in less than one second (singlethreaded program running at Intel Xeon E52680 @ 2.40GHz).

20190808, 18:58  #8  
"Robert Gerbicz"
Oct 2005
Hungary
2·7·103 Posts 
Quote:
https://onlinejudge.org/index.php?op...lem&problem=36 and look at the statistics page (for this problem) on rank=15. Note that the judge in those times was way slower than the current judge or your computer. Beat this. 

20190809, 12:16  #9  
"David Barina"
Jul 2016
Brno
2^{3}×5 Posts 
Quote:
How can I find out the number of unfinished (pending) tasks? I cannot find any overall progress page. Thanks. 

20190809, 13:29  #10  
"David Barina"
Jul 2016
Brno
2^{3}·5 Posts 
Quote:
I have 2^32 integers, whereas computations can be handled in either in 64bit or, in the worst case, in arbitrarily precision arithmetic. 

20190809, 18:30  #11  
"Dylan"
Mar 2017
2×281 Posts 
Quote:
To your second question: This page says how many tasks are out in the wild and how many are queued up to be processed. Unfortunately, it does not say where the leading or trailing edge of the search is. That would be a good thing to have on that page. 

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