Talk:Primorial numbers: Difference between revisions
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== a faster-than-exponential growth rate in CPU time stated by dinosaur ==
===Story===
school - multiplication ist quadratic in runtime O(count of digits) ~ (count of digits)^2
<pre>Prime(100000) = 1299709, Primorial(100000) ~ 0.1909604E+563921 121.547 seconds.
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:These were for data only up to n = 800,000 because there was a change in slope subsequently, probably because I stopped using the computer for other minor activity and thus didn't disrupt its various buffers. The Mersenne prime calculations continued. The points wobble above and below the fitted line across the span, and there is a bend visible at the start where the overall line is too low. That is, at the start the calculation is going a little faster and presumably, one could talk about not yet overflowing some on-chip memory buffer as another reason for non-linearity. Similarly, at the high end the points start to rise above the fitted line, and one could talk about a growth factor such as log(n) rather than a constant. This is obscured by the greater speed later on when I had walked away from the toiling computer. Nevertheless, one can see that a slight curve is being approximated by a straight line over a limited span, which means that using the start to attempt to identify the effect of a cpu buffer size will be tricky. Even so, a log(n) vs. log(t) plot shows a change of slope at the start - except that is for only the first few points. Alas, with "only" a few thousand digits to the big number, the resolution of the CPU timing function is insufficient to show finer details, and repeating the calculation a hundred times (say) will require auxiliary storage to enable the repetition and this will change the workings of the presumed buffering processes away from what was intended to be investigated. A frustrating business.
:Unfortunately, there is no provision for posting images, and anyway I've had a lot of trouble with Octave producing damaged plot files (.svg, .png, etc.) having to resort to screen image captures, so instead, here are the data:
:: You should be able to post images now. Look for an "Upload File" link at the bottom of the page. Also, you might want to look at where the time is going in your implementation - I am going to guess that it's in your code to generate the prime numbers. --[[User:Rdm|Rdm]] ([[User talk:Rdm|talk]]) 03:00, 10 April 2016 (UTC)
:::Pox! I have just created file Primorial.cpuTime.svg, but, "Error creating thumbnail: /bin/bash: rsvg-convert: command not found" results. Inkscape however draws the plot without difficulty, though at 657KB the file is a bit large for just a thousand points, a line, and some annotation. And now that it is uploaded, I can't see how to delete it. I shall attempt to replace it by a screen capture. As for Octave, it won't "Print" the plot as either a .png nor a .jpg due to some complaint of its own "'C:\Program' is not recognized as an internal or external command, operable program or batch file." so a tar pit there.
:::The calculation of the primes is not a problem, because all million are prepared in array PRIME before any Primorial attempts are made, and the time for this is somewhere in the blink of starting the run and the first Primorial results appearing even as the screen window manifests. [[User:Dinosaur|Dinosaur]] ([[User talk:Dinosaur|talk]]) 06:30, 10 April 2016 (UTC)
===Grist===
<pre>
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