A special prime q is a prime
which divides the discriminant of a general period polynomial of degree e associated
with the prime p = ef + 1, but q is neither an e-th power residue of p nor a divisor of
any value of this polynomial.
These primes are very rare. Evans found some for the classical cyclotomic octic.
There are none for lower degree cyclotomic polynomials. This paper finds special
primes for the two quartics arising from the cyclotomy of Kloosterman sums for e = 8
and shows that there are none for e < 8.
