Facing some problems here. Hope you guys can help me out,

Say I want to build an ECC of composite field $\displaystyle GF((((2^2)^2)^2)^{37})$ . In order to build this composite field I need 4 irreducible polynomials.

So I would like my first irreducible polynomial in format of :

$\displaystyle P(x) = x^{37} + x^t + 1 $

so what are the possible value for $\displaystyle t$ for $\displaystyle P(x)$ trinomial to be irreducible?

Thank you very much!