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Too long for a comment :

  • The week has a seven-day cycle.

  • The moon has a 19-year Metonic cycle.

  • The sun has a four year Julian cycle, known to the ancients.

  • The sun and the week together have a 4 x 7 = 28-year Solar cycle.

  • The sun and the moon together have a 4 x 19 = 76-year Callippic cycle.

Forming a great cycle of 532 years.

Yielding a total period of LCM(49, 532) = 3,724 years.

Hint : What major event in Jewish history is said to have happened 3,724 years after Creation, and/or the molad tohu of the first year of the Hebrew calendar ?

I've noticed you put a great deal of importance on accuracy and exactness, but have you ever taken into consideration the beauty and depth-of-meaning inherent in numerical symbolism, which was at least as, if not more, important to the ancients ? Or does the latter simply elude your interest ?

Adding some more perspective :

Something similar happens in Christian chronology, which roughly follows the Greek text of the Septuagint, which puts an even 5,000 years between Creation and the dawn of the Ptolemaic era, to which it owes its very existence.

  • Thus, the Alexandrian era counts back 76 Callippic cycles of 76 years each before the beginning of Diocletian's Era of Martyrs in the autumn of 284 CE, only to arrive at the autumn of 5,493 BCE, accommodating the aforementioned longer chronology.

  • Likewise, the Byzantine era of Constantinople, based on 15-year Indiction cycles, starting in the autumn of 312 CE, counts back 388 such cycles before that time, finally arriving at the autumn of 5,509 BCE, for rather similar reasons.

  • The very start of the current Common Era is ultimately based on counting back 15 x 19 = 285 years, representing the least common multiple of the Indiction and Metonic cycles, before the first Passover moon of Diocletian's Era of Martyrs.

In short, though all these various Biblical eras, both Jewish and Christian, do indeed provide a rather decent approximation for the events they aim to signify, accuracy itself is not their ultimate goal, but rather symbolism and convenience.