(warning, blatant patch marketing)

You think this is a shame:

-----------------------------------------------------------
Magma:

R<x>:=PolynomialRing(GF(2));
P:=x^257+x^31+x^2+x+1;
time IsPrimitive(P);

true
Time: 0.010

-----------------------------------------------------------
Sage:

R.<x>=GF(2)[]
P=x^257+x^31+x^2+x+1
time P.is_primitive()

[still waiting]
-----------------------------------------------------------

then, take a look at trac tickets #7239 and #7340
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