%I #2 Mar 30 2012 17:30:55
%S 2,3,7,11,13,17,19,23,29,31,41,43,59,61,79,83,89,101,107,139,149,151,
%T 163,167,179,223,227,229,277,281,283,331,347,353,379
%N Irreducible trinomials of prime degree for some k: x^p + x^k + 1 is irreducible over GF(5) for at least one k, p>k>0.
%t Do[ k = 1; While[ ToString[ Factor[ x^Prime[n] + x^k + 1, Modulus > 5]] != ToString[ x^Prime[n] + x^k + 1] && k < (Prime[n] + 1)/2, k++ ]; If[k != (Prime[n] + 1)/2, Print[ Prime[n]]], {n, 1, 75}]
%Y Cf. A057751.
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Sep 01 2003
