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%I #6 May 09 2016 15:02:35
%S 13,19,37,43,53,59,61,67,83,101,107,109,131,139,149,157,163,173,179,
%T 181,197,211,227,229,251,269,277,283,293,307,311,317,331,347,349,373,
%U 379,389,397,419,421,443,461,467,491,499,509,523,541,547,557,563,571
%N Prime degrees of absolutely reducible trinomials: primes p such that x^p + x^k + 1 is reducible over GF(2) for all k, p>k>0.
%t Do[ k = 1; While[ ToString[ Factor[ x^Prime[ n ] + x^k + 1, Modulus -> 2 ] ] != ToString[ x^Prime[ n ] + x^k + 1 ] && k < Prime[ n ], k++ ]; If[ k == Prime[ n ], Print[ Prime[ n ] ] ], {n, 1, 144} ]
%o (PARI) lista(nn) = {forprime(p=2, nn, ok = 1; for (k=1, p-1, if (polisirreducible(Mod(1,2)*(x^p + x^k + 1)), ok = 0; break);); if (ok, print1(p, ", ")););}
%K nonn
%O 1,1
%A _Robert G. Wilson v_, Oct 30 2000