The focus of this paper is testing the irreducibility of polynomials over finite fields. In particular there is an emphasis on testing trinomials over the finite field GF(2). We also prove a the probability of a trinomial satisfying Swan's theorem is asymptotically 5/8 as n goes to infinity.
Hayman, Steven, "Testing Irreducibility of Trinomials over GF(2)" (2012). Honors Projects. Paper 14.