Re: Proving primality of an integer

From: D. Touie (dtouie@tscnet.com)
Date: 02/09/03 

From: D. Touie <dtouie@tscnet.com>
Date: Sun, 09 Feb 2003 21:42:22 GMT

On 8 Feb 2003 18:12:21 -0800, gasparuga@yahoo.ca (Aldo) wrote:
>
>To test the program let try some nice integers, for example:
> 2^127-1, 2^2281-1, 2^2279-1, (10^317-1)\9, (10^1031-1)\9, ...
>.... Check that !(37)+1 is a prime number.
>Try n = !(556)+1 (a consequence of Wilson's theorem).
>Dare to try n = !(557)+1 ;-)
>
2^127-1 is Mersenne prime #12. 0.00 CPU secs.

2^2281-1 is Mersenne prime #17. 0.14 secs.

2^2279-1 is a composite number divisible by 3.

(10^317-1)\9 is prime. 0.06 secs. This number is 317 sequential ones.

(10^1031-1)\9 is prime. 1.31 secs. This number is 1031 sequential
ones.

!(37)+1 is a prime number. Agreed. 0.00 secs. 44 digits.

Try n = !(556)+1 (a consequence of Wilson's theorem). This is a 1287
digit composite number divisible by 3.

Try n = !(557)+1. This is a 1290 digit composite number divisible by
3.
--------------------------------------------------------------------

I use my own home-grown formula in Magma, an excellent interactive
math program from the University of Sydney, Australia. I have a 2.4
ghz P4 running Windows XP (SP1) and its latest security upgrades. My
formula runs out of poop (from my impatient point of view) at about
40,000 decimal digits.

dtouie@tscnet.com

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