This compendious entry begins with 'the' (Athenian) Prytaneion, a public building, but shifts into the lower-case sense of the word as already covered by pi 2997 and pi 2998.
[1] From glosses on Herodotus 1.146.2, where mention is made of early Ionians originating 'from the Athenians' prytaneion'; and cf. the scholia to Plato, Protagoras 337D. The comment shows apparent confusion between three different buildings: the Prytaneion, the Thesmotheteion and the Tholos. This confusion may have arisen because all three buildings were venues for dining at public expense. The Tholos also housed the prytaneis (for whom see pi 2995, pi 3000), which may also be a source of confusion. (Wycherley [1957] 171; Pausanias 1.5.1; 1.18.3 [See web address 1 and web address 2 below]).
[2] From the scholia to Aristophanes, Knights 167, where the Prytaneion is mentioned.
[3] There is some evidence that a perpetual fire was housed in the Prytaneion (scholion to Thucydides 2.15.2; Wycherley [1957] 171), so the author seems to be simply reporting another way of referring to the same building.
[4] Aristophanes, Clouds 1135-6 (web address 3), with scholion.
[5] cf. sigma 966.