Timeline for What is so special about Prime?
Current License: CC BY-SA 3.0
10 events
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| May 24, 2013 at 20:45 | comment | added | Stefan | @DanielLichtblau oh! How much I do enjoy reading your answers :) | |
| May 24, 2013 at 15:54 | history | edited | J. M.'s missing motivation♦ | CC BY-SA 3.0 |
added 13 characters in body
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| Mar 29, 2012 at 23:04 | comment | added | Artes |
@DanielLichtblau I believe that there is a helpful comment by Oleksandr R. mathematica.stackexchange.com/questions/3327/…. I suppose, that Prime works having defined in the system a kind of a sparse map of the values of PrimePi, and to evaluate Prime for an argument between any two consecutive values in that map it has to work in the same way as NextPrime. However I may be completely wrong with this.
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| Mar 29, 2012 at 22:49 | comment | added | Artes |
@DanielLichtblau I have to emphasize that the domain of Prime is extensible during a session (I mentioned that in the post). I mean that Prime[7783516108362] returns the same with the fresh kernel. However after some playing around with e.g. NextPrime I can evaluate it getting what I wrote before in my comment.
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| Mar 29, 2012 at 22:39 | comment | added | Artes |
@DanielLichtblau Thank You for the edit. The constant you've mentioned OmegaPrime1 is such that Prime[OmegaPrime1]= 249999999999977 is the largest prime smaller than OmegaPrimePi, so it is also such that PrimePi[2.5*10^14]=OmegaPrime1, however I have OmegaPrime = 7783516045221 in Mathematica ver 7 as well as in ver. 8 (under Windows) so it is still a bit more puzzling why it is different.
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| Mar 29, 2012 at 22:18 | comment | added | Daniel Lichtblau | @Artes See edited response. It's not much, but it's all I have to offer right now. | |
| Mar 29, 2012 at 22:17 | history | edited | Daniel Lichtblau | CC BY-SA 3.0 |
explanatory comments, of sorts
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| Mar 25, 2012 at 6:54 | comment | added | nixeagle | I have run into this too and wondered why Mathematica had this limit. A way to circumvent it would be some sort of mathlink/library link and C++ mixture. | |
| Mar 23, 2012 at 10:35 | comment | added | Artes |
I would love to hear from you more about those internal implementation issues. Have you got any idea why the value of OmegaPrime is 7783516045221 ? There seems to be no strict relation between implementation of Prime and PrimePi. Does Prime use NextPrime (or do they both use primality tests as in PrimeQ) when arguments exceed OmegaPrime?
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| Mar 22, 2012 at 18:38 | history | answered | Daniel Lichtblau | CC BY-SA 3.0 |