Who is the most famous Greek who was named Alexander in the previous 15 centuries (one for each century)?

Imma skip 19th and 20th centuries, which my Greek peers have already amply answered.

EDIT: Filled in with the help of Uri Granta, for which my humble thanks.

• V century: Alexander of Apamea [Uri]
• VI: Alexander of Tralles, medical author
• VII: Alexander, bishop of Cotrada, participated in the 6th Ecumenical Council, 680–81 (Prosopographie der mittelbyzantinischen Zeit: Alexandros 178); Alexander, bishop of Nacolia, ditto (Alexandros 179)
• VIII: Alexander, participated in the Ecumenical Council of Nicaea, 787 (Prosopographie der mittelbyzantinischen Zeit: Alexandros 185)
• IX: Alexander, iconoclast monk in Studium Monastery and possibly bishop, mentioned in Theodore Studites’ Small Catechesis (Prosopographie der mittelbyzantinischen Zeit: Alexandros 187)
• X: Alexander (Byzantine emperor) (912–913)
• XI: Patriarch Alexander II of Alexandria [Uri]
• XII: ?
• XIII: ?
• XIV: Alexander Euripiotes, nobleman around Thessalonica, owner of property in Pungion, 1321 (Prosopographisches Lexikon der Paläologenzeit 6324)
• XV: Antipope Alexander V (1409–10), born Peter Philargos in Crete
• XVI: ?
• XVII: Alexander Mavrocordatos [Uri]
• XVIII: Alexander Helladius [Uri]

You can see I’m really straining to find people; it simply was not a common name, the way Alexius was. Those Prosopography German things? They’re the index of anyone Byzantine named in any written source, for 600–1000 and 1200–1500. I’m sure someone can come up with people for the missing decades (and certainly for the 16th–18th centuries); but that’ll do for now.