--- In

primenumbers@yahoogroups.com, Norman Luhn <nluhn@...> wrote:

>

> Hello , I have found a relation for Mersenne primes.

> Perhaps is it know(n) ?! (probably not!)

>

if R=(2*Mp-2)/3=((T^2) mod Mp), then...

>

(it's a plausible idea), but if it works?? it's better than LL

I can determine the exact T(sub k) to use in this test.

e.g. #1

Suppose that Mp= 7, and p= 3;

R = (2*7 -2)/3 =4 == ((2^2) mod 7) == 4; M3 is prime!

T was chosen by taking R/2 = 4/2 = 2 = T(1);

..2.....4....6...8... and so on...

T(1)...(2)..(3).(4)...

where k= floor[(p+1)/2 -1] = floor[(3+1)/2 -1] = 1; p= 3 from M(3).

e.g #2

Suppose that Mp= 31, and p= 5;

R = (2*31 -2)/3 =20 == ((2^12) mod 31) == 20; M5 is prime!

T was chosen by taking R/2 = 20/2 = 10 = T(1); but k equals 2(below)

.10...12....14... and so on...

T(1)..(2)...(3) ...

where k= floor[(p+1)/2] -1 = floor[(5+1)/2] -1 = 2; p= 5 from M5.

Try another Norm... and see if I'm right. Imagine... a single test

to determine the primality of Mp's! We can call it the Luhn-Bouris

test for Mersennes. It can always be confirmed using the LL-test.

Bill Bouris

>

> Example:

>

> M(13)=8191

> R=5460

> we found T=5929

>

> The idea is a consequence of the Lucas Lehmer Test.

>

>

> regards

>

> Norman

>

>

>

> Lesen Sie Ihre E-Mails jetzt einfach von unterwegs.

> www.yahoo.de/go

>