Did the creation of the world occur in 3761 BC or 5509 BC?

from the series of short articles about calendars

One of the diachronic needs of the human kind was to determine the exact date of the creation of the universe or better the creation of the heaven and earth, as it is mentioned in the Genesis of the Pentateuch.
Jewish and Christians had included in their sacred texts the famous description of the creation 'Let there be light' (Gen.1:3). But when exactly was this start of the cycle of day-night alterations? Obviously, in the ancient times none of the recent astronomical theories and data were available and there was an inclination to shorter measures of space and time in respect to the real ones. Greek astronomers, mainly Aristarchus of Samos and Archimedes had suggested models of the universe, where the dimension of the world was indeed huge. Based on a model of Aristarchus, Archimedes, in his work Sand Reckoner, tried to estimate the number of grains of sand that fit into the universe. In the frame of this project he introduced a revolutionary concept of large numbers, taking as his base the number of one myriad and extending it, through the operation of arithmetical power, to consecutive orders of numbers and then groups of orders into periods. Archimedes concluded that the diameter of the Universe was no more than 10 to the power of 14 stadia (in modern units, about 2 light years), and that it would require no more than 10 to the power of 63 grains of sand to fill it. As we know the estimate is very poor in comparison to the real dimension of the Universe, but Archimedes' methodology was incredibly smart and scientific.
But what about the age of the Universe? Greek astronomers had not confronted this question, because the most widely accepted theory was that the Universe existed eternally, so there was not a moment when it was created. Things change in the Judeo-Christian philosophy and theology, where it is said explicitly that the Universe was created in a moment, which is characterized as the start of the time. In this context, some scholars tried to define that sacred moment. Nowadays we know that the Universe was created 13.7 billion years before, the Earth 4.5 billion years before and the humanly presence is recorded at least some million years before. Therefore the estimation of the creation year 3761 B.C. by the Jewish rabbis and 5509 B.C. by the Christian fathers appear naive or ridiculous. On the other hand we should not depreciate the fact that the scientific data (such as palaeontological remains) were non existent and the biblical texts, which most of the scholars belived unreservedly, were giving the impression of a paradise occurred not deeply in the past. Besides, we should respect the anxious struggle of the human thinkers to understand the nature of the universe and first of all its origin. I'll present next the two more widespread estimations given by the Jewish rabbis and the Christian Byzantines. Both of them constitute a serious milestone in the history of the calendars. We must not forget the religious Byzantine calendar was used by the Orthodox Church until the 18th century and the Russian authorities until 1700 AD, while the Jewish calendar is the religious currently used calendar, where the chronology used is the the year after the creation of the world, in 3761 BC (Anno Mundi).
The estimation of the creation of the world by Jewish rabbis is based on Genesis and some other Hebrew texts. The start of a Jewish year (1st of month Tishrei) falls on the birth (Molad) of the Moon (New Moon), following the Autumn Equinox. According to tradition, there was a Molad at exactly 14 hours after sunset on the Day-6 (Friday) of Creation (Hebrew years start on 6 pm of the day), the date and time that Adam is supposed to be created. This time corresponds to 8 am of the next day. The creation of Adam signals the start of a new year. This new-year day (Rosh Hashana) occurred on the next Shabbat, since Rosh Hashana cannot fall on a Friday. This is regarded as Rosh Hashana of Year 2, since the six days of creation are considered to belong to year 1. Moving backwards to the past, the previous Molad of Tishrei (start of year 1) was on the Day-1 (Sunday), at exactly 11 hours 204 chalakim after Sunday sunset (chalakim is the plural of 1 chelek=3 and 1/3 sec or 1/18 min. 1 hour=1080 chalakim). This date and time corresponds to Day-2 (Monday) at 5 hours and 204 chalakim am. Writing 2, 5, 200, 4 in Hebrew characters gives us BeHaRaD, so this is known as Molad BeHaRaD. It is also sometimes called Molad Tohu ("without form"), since it occurred while the world was still "without form and void" (Gen.1). This date of Molad-Tohu and Rosh Hashana of Year 1, is according to Jewish rabbis the Monday, October 7 in the proleptic Julian calendar. The following years are 2,3,4 etc from the Creation of the world (Anno Mundi). Since each Hebrew year starts near to the Autumn Equinox, it follows that each Gregorian year belongs to a pair of consecutive Hebrew years. Current year 2018 AD corresponds to years 5778/ 5779 Anno Mundi (AM).
The Byzantine Calendar was officially used by the Eastern Orthodox Church from ca. AD 691 to 1728 in the Ecumenical Patriarchate, by the Byzantine Empire from AD 988 to 1453, and in Russia from ca. AD 988 to 1700. Byzantine years retain the structure of the months and duration of each month of the Julian Calendar, but the start of the year is not in Jan. 1 but on Sept. 1. The date of the creation of the world is supposed to be September 1, 5509 BC. Therefore the year 1 of the Byzantine calendar is the period from Sep. 1, 5509 BC to Aug. 31, 5508 BC. The following years are 2,3,4 etc from the Creation of the world (Annus Mundi).
In the case of the estimation of the Byzantine Era of the world there were a lot of propositions, based on various suggestions. One of the most serious propositions was introduced by the Alexandrine monk Panodorus, who reckoned that 5904 years had passed from Adam until the year AD 412. Therefore he concluded that the year of the creation of the world was 5493 BC. The start of the year in Panodorus' chronology was August 29, corresponding to the 1st of Thoth, the Egyptian new-year day. Annianus of Alexandria however, preferred the March 25, the Annunciation date as the date of the creation of the world, suggesting it also as the New Year's Day. In this way, Alexandrian civil years had as their origin the 29th of August, 5493 BC, while the ecclesiastical years the 25th of March, 5493 BC. Annianus had reckoned as date of the Annunciation of Jesus Christ the 25th of March, 8 AD (Julian Calendar), exactly 5500 integrated years after the creation of the world, resulting to the 25th of December, 8 AD, as the date of the birth of Christ (Christmas Day). This is the reason for defining as year 1 of the Ethiopian Calendar the year starting on 29th of August, 8 AD in the Julian Calendar (see also the Info article 15 about the Ethiopian Calendar). Following this hypothesis, we can see the harmonization of the three main dates of the world's history: the beginning of Creation, the Annunciation and the Resurrection of Christ. All these events happened, according to the Alexandrian chronology, on 25 March; furthermore, the first two events were separated by the period of exactly 5500 years; the first and the third one occurred on Sunday, the sacred day of the beginning of the Creation and its renovation through Christ. The year of creation proposed by Annianus (5493 BC) has also an interesting relation to the starting year of the Coptic Calendar (284 AD, the year of the reign of Diocletian) through the Paschal cycles of 532 years and the Meton cycles of 19 years. Indeed 284 AD is at a distance of exactly 11 Pascal cycles minus 4 Meton cycles from the creation of the world.
But finally the year 5509 BC was prevailed as the true year of the Creation. One of the older official documents, where the finally adopted 5509 BC as the year 1 after creation is met, is the so-called Letter of three Patriarchs to the emperor Theophilos (April, indiction 14, 6344 Annus Mundi = 836 AD).
Since each Byzantine year starts on 1st of September, it follows that each Gregorian year belongs to a pair of consecutive Byzantine years. Current year 2018 AD corresponds to years 7526/ 7527 Annus Mundi (AM).