

A057751


Irreducible trinomials of prime degree for some k: x^p + x^k + 1 is irreducible over GF(2) for at least one k, p>k>0.


1



2, 3, 5, 7, 11, 17, 23, 29, 31, 41, 47, 71, 73, 79, 89, 97, 103, 113, 127, 137, 151, 167, 191, 193, 199, 223, 233, 239, 241, 257, 263, 271, 281, 313, 337, 353, 359, 367, 383, 401, 409, 431, 433, 439, 449, 457, 463, 479, 487, 503, 521, 569, 577, 593, 599, 601
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OFFSET

0,1


LINKS



EXAMPLE

The prime 79 is included because x^79 + x^9 + 1 is irreducible over GF(2). Only the primes 2 and 3 are irreducible for all ks between 0 and p. So far about onehalf of all trinomials of a prime power are irreducible over GF(2) for at least one k between 0 and p.


MATHEMATICA

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, 100} ]


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



