This polynomial is the characteristic polynomial of the Fibonacci and Lucas n-step recursions. Are the n-step recursions different -- in some way -- for the values of n that yield a prime discriminant? No other n < 10000.

REFERENCES

Mohammad K. Azarian, On the Hyperfactorial Function, Hypertriangular Function, and the Discriminants of Certain Polynomials, International Journal of Pure and Applied Mathematics, Vol. 36, No. 2, 2007, pp. 251-257. Mathematical Reviews, MR2312537. Zentralblatt MATH, Zbl 1133.11012.