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

Gauss periods are minimal polynomials for totally real cyclic fields of prime degree