Let $d$ be a prime number. Is the polynomial $x^d+x+1$ a primitive polynomial? In other words I need the minimal polynomial of $\alpha$ in $F\_{2^d}=F\_{2}(\alpha)$. 


Thank you. 



primitive polynomial in $F_2$
See <http://oeis.org/A073639> for the list of n such that x^n+x+1 is primitive modulo 2.
The sequence begins [2,3,4,6,7,15,22,60,63,127,153,471,532,865,900,1366]
You will also find some pertinent references there.


I found this using Maple's function "Primitive(f(x)) mod p" which returns true if f(x) is primitive mod p, and false otherwise. 


