There is the prophecy at the book of Revelation (ch. 20), for a millennium of Christ’s reign on earth, before Satan is loosed for a while; after that the world is about to end. There are several prophecies during the Byzantine era, that the fall of Constantinople marks ‘the end of times’. This was being repeated in the 14th and 15th centuries, as is natural, but it appears clearly already in the 10th century (when Byzantium was strong), at the Revelation of Andrew, which says that ‘with the end of this city (Constantinople), the end of the world won’t take long to come’.
How long is ‘won't take long’? Of course it can’t be more than a millennium (the whole of the Byzantine period). Since Andrew writes in the 10th century, and not during the last decades of Byzantium, I would say that the ‘not long’ can not be more than six centuries, which brings us to a time between 2000 and 2200. But in any case, 2500 is a certain limit, according to Byzantine prophecies, if I understand them well. Perhaps someone has bibliographical references, I write from memory, but my general impression is that our times (with the limit of the year 2500) are near the end, according to these prophecies.
Do I believe this? I don’t need to. Because the apocalyptic times that really matter for a person, happen in a person’s life. Whether the world ends in 2200 or in 2500, for me it will end in a few decades, during which all that the Bible says happen to me personally. This is why it is written that “Verily I say unto you, This generation shall not pass away, till all be fulfilled”. ‘This generation’ is each of us, and this is the time that matters, i.e., the Second Coming is in the present, always near, in no case more distant than a few decades.
St. Symeon of Thessaloniki, writing in the 15th c. and answering to such rumours about the end of the world, where some related the 7 days of the Creation with the 7 millennia of the world (according to the Byzantines’ measuring of time), says: “the world is created in 7 days, and man grows by weeks... therefore some think... if on the 7th century [millennium] this world will end and be transformed [the 7th century-millennium ended in 1491]. But the knowledge of the Church is not in these. The Church believes that the universe is in the will of God. And just as the universe was created out of nothing for our good, for our good again it will be transformed to perfection. This will happen then, when there will be left to the world no virtue, the height of which and start and perfection is love. For love God made everything and for love has given us His only begotten Son. Thus Himself reveals the signs of the end, saying that love will be gone. Evil will increase, the love of the many will get cold, and he who will endure until the end, will be saved” (Patrologia Graeca 155.920).