All about Primes - The Prime Suite - _primes.au3 UDF lots of math functions

[jennico]

i updated the zip file according to the ideas in this thread.

update 23.10. _Primes.au3 v1.2 (corrected _Factorial, improved _IsPrime, _PrimeNext and PrimePrevious, corrected loop declarations)

[Ximorro]

Really impressive!!!!

jennico, I've noticed that in AutoIt testing divisivility with IsInt(a/c) is faster than Mod(a,c) = 0.

You also make a division but maybe the fact that the remainder is not needed makes it faster.

For instance in your basic IsPrime function (without resorting to SPRR or Miller-Rabin) I've got this improvements just with that change:

737373737373737 improves from 16.5 secs to 13.3 secs

9007199254740881 from 57.5 secs to 46.5 secs

I've also noticed that integer limit is not 2^64, but 2^53. You can see for instance that (2^53+1) - (2^53) is ZERO, not ONE. (So the biggest direct integer prime is 2^53-111 = 9007199254740881).

Edited July 31, 2009 by Ximorro

[twitchyliquid64]

Love. It.

I think Im going to use this to generate Primes for my Public Cryptography Encryption.

Just wondering...How did you keep the big numbers from rolling into Sci Notation?

[Mat]

Love. It.

I think Im going to use this to generate Primes for my Public Cryptography Encryption.

Just wondering...How did you keep the big numbers from rolling into Sci Notation?

If you want to use big numbers, then the no. 1 thing to use is a library made by Eukalyptus here. Several people have tried to write bigint or bignum UDF's (myself included) but none have got anywhere near that set