Since somebody asked me more, I'll post another message on this list.
The theorical background is not yet demonstrated (I suppose there is a sort of conjecture below) but we can verify the usefulness of my test with a simple bigger (?) test.
My test can actually tell (with any odd number): - the number is not prime (mathematical security); - else cannot tell if the number is prime or not (undeceivability, ALL prime numbers are undeceivable for my test, but not the inverse of this proposition)
Let's suppose to have a very big supercomputer that checks randomly generated numbers for their primality via a standard algorithm (Fermat, Rabin-Miller, Solovay-Strassen, Lucas-Lehmer, Ellipitc Cuver Method or a combination of these), and let's suppose to put in parallel my test on the same numbers: if my test always tells an "undeceivable" result, my test is useless, if my test else in at least one case shows to negate the "traditional" result, well...in future, to have more secure keys, we should always perform my test and luckily it is very short in CPU time.
I have not yet done this big test, but I am preparing a source code (in
C language) release that will be soon available and perhaps somebody else can do it; I will also inform other people interested in prime numbers research in these days. In the mean time, you can test any
number via my server-side application at
http://www.nexogen.it/gm/primality/
Please note that other links in that page are broken, everything will be alright in a few days (when I'll finish the translation, I'll post another message in this list)
I have just implemented the Rabin Miller; I have the source code (in different languages) of every other test mentioned above, but I haven't yet translated them to PHP...
Please contact me if interested, you can also post on my new forums:
Mathematical subjects: http://www.nexogen.it/forums/viewforum.php?f=1
Programming related: http://www.nexogen.it/forums/viewforum.php?f=2
----------------------------- Think different. (A.Einstein)
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