Posts by Dave
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1) Message boards : Science : Possible proof (Message 13818)
Posted 2102 days ago by Profile Dave
The Polya conjecture was true until 906,150,257, Mertens conjecture still has no known counter proof value, but it is known that there is some massive number that does disproove it, Skewes number is not proven but lies between 1.53x10^1,165 and 1.65×10^1,165.

Big numbers like that may disprove Collatz eventually, but it will take time.
2) Message boards : News : Server Back Online (Message 13752)
Posted 2111 days ago by Profile Dave
I wondered where you had got to, so did several others on other projects.

This is the first time I have noticed anything happening to CC since I joined.

Hope you had a good Easter.
3) Message boards : Science : The Collatz Conjecture (Message 12828)
Posted 2291 days ago by Profile Dave
To answer my own question with an explanation from another thread, no we probably cannot speed it up.

With parallel processing it is faster to test everything than to sort out the rubbish.

Consider a 50 processor GPU taking 1 second to test a set of 50 numbers, that is 200 numbers in 4 seconds, the 200 numbers could be sorted to yeild only 50 that need testing for 1 second but a GPU is not very good at that type of thing and would take, say, 5 seconds to do it. So without sorting it would take 4 seconds per 200 numbers, with sorting it would take 6 seconds. All timing is simplified for sake of the example.
4) Message boards : Science : Largest number checked? (Message 12827)
Posted 2291 days ago by Profile Dave
OK, and thanks. I get the idea, I think.

With parallel processors (GPU) it is probably faster to test everything than to sort out the unwanted numbers.

Before someone else points it out there could have been a point 4 in that any even number that fails to meet the CC must be an even number multiple of an odd number that also fails so there is no need to test ANY even number, as such any even non CC number must have a smaller nonCC compliant odd precursor. This assumes that a complete sequence of odd numbers has been tested.

To sumarise even numbers do not need testing at all, nor do odd numbers where (3n+1)/2 is even. But sorting them out to save work may take longer than testing them!



5) Message boards : Science : Largest number checked? (Message 12821)
Posted 2296 days ago by Profile Dave
Somewhere above in this thread the question was asked if we check each number, it was answered "yes".

BUT...

IF all numbers up to n have been proved to conform to the conjecture then :-

a) all even numbers up to 2n can be ignored as they will immediatly divide to yeild a tested number. No list of tested numbers is needed here.

b) Alternate odd numbers (x) when processed as (3x+1)/2 will yeild a tested number and so do not need to be tested further for x < 3n/2, again no list is needed.

c) Alternate even numbers between 2n and 4n will yeild numbers proven by a) above.

Therefore IF a complete sequence of proven numbers is known we can speed up the testing by better than 4 times as over 3/4 numbers do not need to be tested.

Has a complete sequence up to the starting point of CC been confirmed? If so then why do we still waste time testing numbers that cannot fail?

If no such complete list exists then would it be worth the time to test those numbers less than the CC start point to establish such a sequence or would this take too long to be worth while in terms of time saving?

Please do not take this as a complaint about the CC method, it is a real question. I simply want to know what the reasons are for testing each number when it seems unneeded.
6) Message boards : Cafe : Last one to post here wins (v5) (Message 12648)
Posted 2362 days ago by Profile Dave
trying again
7) Message boards : Cafe : Last one to post here wins (v5) (Message 12647)
Posted 2362 days ago by Profile Dave
oops missed the picture set up.

Still didnt work
8) Message boards : Cafe : Last one to post here wins (v5) (Message 12646)
Posted 2362 days ago by Profile Dave
oops missed the picture set up.
9) Message boards : Cafe : Last one to post here wins (v5) (Message 12645)
Posted 2362 days ago by Profile Dave
Would someone tell a newbie what I have one (in the v6 thread preferably).
10) Message boards : Science : The Collatz Conjecture (Message 12502)
Posted 2402 days ago by Profile Dave
Can we speed up the process?

I have noticed that iff the numbers 1..n are proven to be within the conjecture then so are the even numbers up to 2n, and alternate odd numbers up to n+n/3 (by the use of (3x+1)/2).

Do we have a value of n for which all previous numbers have been tested?

Is something like this already used? probably as it seems very obvious to me.




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