" tommy quaternion "

[tommy1729]

also for fans of number theory :

A debunked conjecture is this :

Let the prime p be a mersenne exponent : 2^p - 1 is prime.

Call the set of those p : E.

Then the smallest primitive root g_p (mod p) is always of the form

g_p = 2^A * P

where A is an integer and P is in the set E.



example 

min primitive root ( 2^132049 - 1 ) = 26 = 2 * 13 = 2^1 * (mersenne exponent =13)



However a counterexample is

min primitive root ( 2^42643801 - 1 ) = 11.

11 is a prime and not an element of E !!


regards

tommy1729