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

Say I want to build an ECC of composite field 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 :

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

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

Thank you very much!