On 2015-11-04, William Unruh <unruh@invalid.ca> wrote:

On 2015-11-04, Rainer Rosenthal <r.rosenthal@web.de> wrote:

For a problem in recreational math I am testing numbers of
magnitude around 10^1400 whether they are prime or not.
It takes about two and half an hour per number when I use
the standard isprime() Funktion.

Are there ways inside Maple (I use V) to get the results faster?

That is fast. Remember that if you were to try testing primality by
division it would take many many many times longer than that age of the universe. There exist probabilistic primality tests-- depends on how
much probablility you are willing to accept that the number is reported
as prime but is really not. (the probabillies are verysmall) There is
also a deterministic polynomial time test. But I think the polynomial is quite large.Wikipedia suggests about l^6.

I do not know what Maple uses in the isprime() function.

Always helps to read the documentation. Doing ? isprime, it tells me it
uses a probabilistic primality tester, but not which one. There is thus
a very small probability that it will say the number is prime when it is
not. The probability of your computer being hit by a meteor is probably larger than that probability. Probablilistic tests are about as fast as they
get. Remember also that large number ( and you are using at least 1500
digit arithmetic) is also very slow.

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For a problem in recreational math I am testing numbers of
magnitude around 10^1400 whether they are prime or not.
It takes about two and half an hour per number when I use
the standard isprime() Funktion.

Are there ways inside Maple (I use V) to get the results faster?

Wolfram Alpha doesn's accept large numbers like that without
fee. Are there any sources in the web accepting large numbers
that are free and reliable?

Cheers,
Rainer

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On 2015-11-04, Rainer Rosenthal <r.rosenthal@web.de> wrote:

For a problem in recreational math I am testing numbers of
magnitude around 10^1400 whether they are prime or not.
It takes about two and half an hour per number when I use
the standard isprime() Funktion.

Are there ways inside Maple (I use V) to get the results faster?

That is fast. Remember that if you were to try testing primality by
division it would take many many many times longer than that age of the universe. There exist probabilistic primality tests-- depends on how
much probablility you are willing to accept that the number is reported
as prime but is really not. (the probabillies are verysmall) There is
also a deterministic polynomial time test. But I think the polynomial is
quite large.Wikipedia suggests about l^6.

I do not know what Maple uses in the isprime() function.

Wolfram Alpha doesn's accept large numbers like that without
fee. Are there any sources in the web accepting large numbers
that are free and reliable?

Cheers,
Rainer

--- SoupGate-Win32 v1.05
* Origin: fsxNet Usenet Gateway (21:1/5)

Am Mittwoch, 4. November 2015 15:20:53 UTC+1 schrieb RR:

For a problem in recreational math I am testing numbers of
magnitude around 10^1400 whether they are prime or not.
It takes about two and half an hour per number when I use
the standard isprime() Funktion.

Are there ways inside Maple (I use V) to get the results faster?

Well, if your computer is as old as Maple V (which is from the
last millennium) you probably have no chance to speed this up.

With an Intel i7-2600 3.4GHz, a nice OS like Linux 64-bit and
free software like Primo this takes about 10 minutes.

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