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.
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. 


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. 

