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Topic: Largest primeproduct with 2 as factor?
Replies: 19   Last Post: Aug 16, 2007 1:06 PM

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Pubkeybreaker

Posts: 1,653
Registered: 2/12/07
Re: Largest primeproduct with 2 as factor?
Posted: Aug 16, 2007 11:48 AM
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jonas.thornv...@hotmail.com wrote:


>
> Is the computional effort for primality test for x bigger or less than
> checking that a composit only have two factors x*2?


I do not understand what you are asking. Please clairify.
Modern algorithms check for primaility by first:

(1) Checking for small prime factors
(2) Performing a probable prime test of some kind
(3) Then proceeds to a full primality proof.

The AKS prime proving algorithms runs in time no worse than a
constant multiple of (log N)^6 where N is the number you are
testing.
The multiple is machine and implementation dependent.

There is a random version that runs in time O( (log N)^4)

The cyclotomy primality test runs in time O( (log N)^ logloglog N)

May I suggest that you read a book on this subject? I can recommend a
number
of good ones.

You might start with:

H. Riesel Prime Numbers and Computer Methods for Factorization

The math in this book is well within the understanding of a good high
school
student.




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