![]() Logically, Collatz Product will continuously decrease as higher even functions show up for the loss of lower even functions and the value of Weighted Even Decreasing Function becomes smaller. In general, the Collatz Product for a range should remain lower than n for the dual function to collapse to 1. Probabilistically, the Collatz function reaches smallest even number (followed by 1).įor the range 1 – 200 the Collatz product becomes which is less than the Collatz Product for the range 1 – 100 because Weighted Even Decreasing Function continuously decreases for higher range. The vector of function points in the negative direction. Which means, statistically, the Collatz function as a twice tendency to decrease the function than to increase it. The Collatz Product is less than value of n (for all n >2) for range 1 – 100. ![]() The product is called the Collatz Product for the given range. Hence the Collatz function decreases to the smallest even number 2 followed by 1. As the smaller even numbers are a subset of smaller numbers the Collatz function finds smaller even numbers. Because the even function is statistically strong, the Collatz function eventually moves down finding smaller numbers. The net effect is that the function statistically moves in the decreasing direction. The Collatz function statistically works with Odd 1 increasing function (3n + 1) with the Weighted Even (0.1676n) Decreasing Function. ![]() ![]() This is the central idea of this article. These 50 even numbers are working against the 50 odd numbers which are necessarily Odd 1 only. The weighted sum of the following frequencies is given by, Odd 1 cannot be followed by Odd 2 as 3n + 1 will always give even number. The Table 2 shows the frequency of occurrence of each of these numbers in the range 1 – 100. The range 1 – 100 has up to Even 6 numbers. Even 2 are numbers withing the same range, that can be divided twice before the quotient is an odd number. Less likely, but not impossible, is that the Linux application is much better optimized than the Windows port (I doubt that).Even 1 are even numbers within the range 1 – 100 that can only be divided once before the quotient is an odd number. The latter point means that my observation of much longer estimated runtimes on Windows were probably caused by different types of tasks loaded to the Windows machine.(Or you wait until they finished their work and compare then on a PPD basis.) machine unless you make sure that you loaded them with same tasks. At least on Broadwell-EP + Linux, having Hyperthreading on and using all hardware threads gives better throughput than having HT off.HT off, 100 % load: >30 days estimated time remaining, Collatz Sieve 1.20.HT off, 100 % load: 3d03h average est.Session 3, from there rebooted into session 4 with identical set of tasks, Linux: time remaining, Collatz Sieve, version not noted This runs at 2.8 GHz which is its non-AVX all-core turbo. I made some quick tests with E5-2696v4 (Broadwell-EP). More importantly, practically no CPU usage (0.7%).Ībout the CPU tasks which Collatz Conjecture also offers: I have no idea why anyone would want to run this project.oh, I see, uh, got a couple tasks in already, now I know why they run it. In all, a real pain compared to most projects, and it feels a bit unfriendly in the forums when other's also missed the info on the main page. Just close and restart BOINC if that happens) (Then I got locked out of requesting more tasks for 24 hours, due to the errors. The instructions say it's needed for CPU crunching, but it is needed for GPU crunching as well, as I found out when all my tasks immediately showed computation errors on a GTX1080. What I missed was that you need to download and install both x86 AND 64-bit versions of C++, found here. On the main page, (linked above at the start of this thread) you will need to carefully read the system requirements. ![]() It is spammerssuck and is subject to be changed without notice. I have tried joining the project before, but never received my invitation code. After you join, you might as well go ahead and set your preferences (GPU only for example) before you add the project to your BOINC manager. Additionally, users without credit will be deleted, and so will clients/computers without credit. This private project has a real axe to grind with spammers, and doesn't allow you to simply join from the BOINC client, you have to join from the home page, and you have to have an invitation code. Collazt is one of the possible projects for a future Sprint race in the Formula BOINC race, so I thought I might want to get familiar with it. ![]()
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