  We report extensive computational evidence that Gauss period equations are
minimal discriminant polynomials for primitive elements representing Abelian
(cyclic) polynomials of prime degrees $p$. By computing 200 period equations up
to $p=97$, we significantly extend tables in the compendious number fields
database of Kl\"uners and Malle. Up to $p=7$, period equations reproduce known
results proved to have minimum discriminant. For $11\leq p\leq 23$, period
equations coincide with 53 known but unproved cases of minimum discriminant in
the database, and fill a gap of 19 missing cases. For $29\leq p\leq 97$, we
report 128 not previously known cases, 16 of them conjectured to be minimum
discriminant polynomials of Galois group $pT1$. The significant advantage of
period equations is that they all may be obtained analytically using a
procedure that works for fields of arbitrary degrees, and which are extremely
hard to detect by systematic numerical search.
