Nicholas Horsfall, "Virgil's Roman chronography: A reconsideration," Fifty Years at the Sibyl's Heels: Selected Papers on Virgil and Rome
(Oxford: Oxford University Press, 2020), pp. 34-39 (at 34):
Jupiter, in his prophetic speech to Venus (Aen. 1.257ff.) foretells that Aeneas will
rule for three years in Italy, that Ascanius will complete the thirty years of rule at
Lavinium, and that he will then found Alba, under whose kings' rule 300 years will
elapse until the birth of Romulus. The sequence 3–30–300 is unmistakable: tertia
(265) and ternaque (266) . . . triginta (269) . . . ter centum (272); no effort is
required to see that the total of these numbers is 333 and the total is clearly
more significant than the antiquarian associations of the individual numbers
(cf. R.E.A. Palmer, Archaic Community of the Romans (Cambridge 1970) 54).
In the context of ancient attitudes to number, 333 is remarkable in two ways: 3 is
'the magic number par excellence' (Gow on Theocr. 2.17–63) and both powers
(3²: cf. Buc. 8.77; H. Diels, Sibyllinische Blätter (Berlin 1890) 41; 3³: cf. Soph. OC
483; Diels, 42ff.) and repetitions of 3 (Liv. 22.10.7: 333,333 1/3; Theocr. 17.82ff.:
33,333) retained the same character; 333 is of course a threefold repetition!
Secondly, 333, as half of 666, may well have enjoyed a little of that number's
glory;2 to the Pythagoreans 666 will have been remarkable as a doubly 'triangular'
number: the sum of the numbers from 1 to 36, 36 being in turn the sum of the
numbers from 1 to 8, the sacred ogdoad3 Such lore was not the exclusive preserve
of mathematicians and philosophers: it is enough to refer to Donatus' Vita of
Virgil (15) maxime mathematicae operam dedit, and to the fact that Euphorion
actually composed a Mopsopia in which 'perfect numbers' (e.g. 6 as being the sum
of its parts: 1 + 2 + 3) were discussed (L. G. Westerink, Mnemosyne 13.4 (1960)
2 Apoc. 13.18 has no place in this discussion: it is explicable within the tradition of gematria,
the assigning of numerical values to the letters of the alphabet, cf. F. Dornseiff, Das Alphabet in Mystik
u. Magie (Leipzig 1925) 106ff. P. Maury claims (Lettres d'Humanité 3 (1944) 144) that in our passage
333 conceals ΚΑΙΣΑΡΑ: in terms of gematria this is quite correct; F. Boll, Aus der Offenbarung
Johannis (repr. Amsterdam 1967) 26ff., and Dornseiff have demonstrated the wide diffusion of this lore
in antiquity, but its application here is clearly inappropriate.
3 Cf. Plut. Mor. 382 A; Theon of Smyrna 19; G. A. van den Bergh, Zeitschrift für neutestamentliche Wissenschaft 13 (1912) 295ff.