🚀 go-pugleaf

I have two questions about primitive polynomials (mod 2):

1)  I was under the impression that if the feedback sequence of a LFSR is
a primitive polynomial (mod 2), then the period of the LFSR is 2^n - 1, where
n is the degree of the polynomial.  I recently got a copy of Zierler and
Brillhart's paper:  "On Primitive Trinomials (mod 2)," Information and 
Control, 13 (1968), 541-554.  The article implies that this is not the case:
"Those n where 2^n - 1 is completely factored, but for which the periods of
the irreducable T_n,k(x) have not as yet been determined...."

2)  Near as I can tell, if x^p + x^q + 1 is a primitive trinomial (mod 2), then
so is x^p + x^(p-q) + 1.  Does this property extend to polynomials with more
coefficients?  Assuming that x^p + x^q + x^r + 1 is primitive, what other
polynomial is necessarily primitive?  Assuming that x^p + x^q + x^r + x^s + 1
is primitive, what other polynomial is necessarily primitive?

Bruce