Well, there does exist a polynomial f(x_1, x_2, ..., x_N) with integer coefficients such that the [I]positive[/I] values of f, for x_1, ..., x_N integers, are exactly the Mersenne primes.

However, it is completely useless to find Mersenne primes.

what spical form
 

my dear/
we means by spical form that Fermats number: (2^2^x)+1 not for all x but for special values of x (we determined it ) gives Mersenne primes as we say.thanks for all members . :coffee:

[QUOTE=ewmayer]sghodeif is simply trying very hard to get this thread moved to the "miscellaneous math threads forum"[/QUOTE]...Successfully, I might add.

[QUOTE=sghodeif]my dear/
we means by spical form that Fermats number: (2^2^x)+1 not for all x but for special values of x (we determined it ) gives Mersenne primes as we say.thanks for all members . :coffee:[/QUOTE]

Aha. That removed my doubts.

Alex

I guess he needs more :coffee: