Tausent fünffhundert achtzig acht /Now the interesting wrinkle is that the origins of the quatrain are obscure. Robin Barnes states that it was "rarely seen in print before 1570" (Prophecy and Gnosis 163). So I thought it was interesting that it showed up attached to an edition of "Wilhelm Friess" printed in 1558 as an appendix to the prognostication of Nicolaus Caesareus. There Caesareus attributes the quatrain to Cyprian Leowitz.
Das ist das Jar das ich betracht.
Geht in dem die Welt nicht vnder /
So gschicht doch sunst groß mercklich wunder.
Just today the Bayerische Staatsbibliothek released a digital edition of Leowitz's De conjunctionibus of 1564 (VD16 L 1257), so I looked through it quickly and discovered (fol. n3v) that Leowitz provides two Latin versions of the quatrain in his 1564 work, in eight and four lines of verse respectively, and he writes there that he had inserted a German version into his ephemerides seven years earlier.
Leowitz's Eclipsium omnium...descriptio of 1556 (VD16 L 1261) doesn't make any particular mention of 1588. His Ephemeridum novum of 1557 (VD16 L 1263) has been digitized by the SLUB Dresden - although it's over 1000 pages long - but if you check carefully, you'll find on fol. ee10v that the quatrain does indeed appear, which may well be its earliest appearance in print, if one assumes that Leowitz is responsible for giving the quatrain its poetic form. Caesareus at least appears to know the quatrain by way of Leowitz rather than from an oral source, and Leowitz was both a poet and an astronomer.
In the Ephemeridum novum, however, Leowitz only indirectly takes credit for the quatrain. He describes there a metahporical prophecy for the year 1588 "de honesta matrona et mercatore celebri," which Leowitz interprets as the Church and and the impious world. This in turn reminds Leowitz of a prophecy of Johannes Regiomontanus that he remembers once hearing from Johannes Schoener. (When you run into a second-hand, half-remembered prophecy attributed to Regiomontanus, you know you're deep within the province of the apocryphal.) "Estque tale," Leowitz writes, and then he gives the quatrain as cited above. Following it, he remarks that he knows of many learned men in his time who expect something remarkable around that time.
This may be the earliest attestation of the quatrain in print (until we find an earlier one), but it still leaves several things unknown. Did Leowitz actually compose the verse based on prophecies for 1588, or did he merely repeat it from another oral or written source? What other expectations for 1588, or at least for the 1580s, existed already in 1557? (Barnes has something to say on that, if I remember correctly.) And what is this prophecy of a "virtuous woman and a renowned merchant" for the year 1588? That one I'm not familiar with.