ed pegg wrote:

> Is the following true?

>

> For any number n with less than 20000 digits, if n+1 or n-1 is

> an easily factorable smooth number, then the primality/non-primality

> of n can be established with certainty.

>

> If so, what is the primality proof method called?

>

> Ed Pegg Jr.

>

>

>

>

> Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

> The Prime Pages : http://www.primepages.org/

>

The Prime Pages contain all sorts of useful knowledge about prime

numbers. For your question, yes, it's true, it can be established with

certainty, and it's not just limited to 20,000 digits. In fact, by

modifying the tests, you don't have to completely factor 'N-1' or 'N+1'

... you just have to factor them 'enough'. See

http://primes.utm.edu/prove/index.html for more information on the 'N-1'

tests and the 'N+1' tests. These pages will also give you references to

find more detailed information.

Jonathan Zylstra

>

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