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JDN=2457502.

      Remainder of division (JDN mod 7) =5, therefore, it is Saturday.

      Finding dates based on the Julian days

      The method of calculation based on the Julian days can be useful, for example, for finding the date for Tisri 1. We don’t know the interval between Nisan 15 and Tisri 1 within one year. But the interval between Tisri 1 of the year to be found and Nisan 15 of the previous year is always 163 days because Nisan, Iyyar, Siwan, Tammuz, Ab, and Elul have an unchanging number of days. If you know the Julian day number for Nisan 15, you can, by adding 163, find the Julian day number for Tisri 1 of the following year.

      For example, based on the Gauss formulas, Nisan 15 of the year 5775 in the Jewish calendar corresponds to March 22, 2015, in the Julian calendar. Now we can calculate JDN for this date (JDN =2457117). Consequently, Tisri 1 of the year 5776 corresponds to JDN=2457280. The remainder of division is 0. Therefore, the day is Monday. We have already determined that Nisan 15 of the year 5776 in the Jewish calendar (2016 NE) falls on Saturday. Using Table 3 (see above), we see that the year 5776 of the Jewish calendar is embolismic, that is, its duration is 385 days (an excessive year).

      The procedure for converting a Julian day number (JDN) into a Julian calendar date is as follows:

      1) c=JDN+32082.

      2) d= [(4c+3) /1461].

      3) e=c- [1461d/4].

      4) m= [(5e+2) /153].

      5) day=e- [(153m+2) /5] +1.

      6) month=m+3—12* [m/10].

      7) year=d-4800+ [m/10].

      Where year is the year of NE; month is the number of the month; day is the day of the month; value in brackets is the integer part.

      For example, let us convert the Julian day number JDN=2457280 (Tisri 1 of the year 5776 in the Jewish calendar) into a Julian calendar date:

      1) c=2489362.

      2) d=6815.

      3) e=184.

      4) m=6.

      5) day=1.

      6) month=9.

      7) year=2015.

      Consequently, Tisri 1 of the year 5776 in the Jewish calendar falls on September 1 2015 of the Julian calendar, or September 14 of the Gregorian calendar.

      The Julian day and the Egyptian calendar

      To convert a Jewish calendar date into a Julian calendar date, we should first find the the Julian day number:

      JDN= (N-1) *365+ (M-1) *30+ (D-1) +1448638,

      where “N” is the year of the Nabonassar era; “M” is the ordinal number of the Egyptian calendar month; “D” is the date of the month.

      The calculation procedure of date is the same as the one described in the previous chapter.

      Для For example, let us calculate the day of the Julian calendar corresponding to Pharmuthi 25 of the year 777 of the Nabonassar era.

      Julian day number:

      JDN= (777—1) *365+ (8—1) *30+ (25—1) +1448638=1732112.

      Julian calendar date:

      1) c=1764194.

      2) d=4830.

      3) e=37.

      4) m=1.

      5) day=7.

      6) month=4.

      7) year=30.

      So, Pharmuthi 25 of the year 777 of the Nabonassar era falls on April 7th 30 NE.

      Calculations simplified

      Chronology calculations became so much easier now that we have computers. The above algorithms can be effectively implemented using popular computational programs or programming language scripts. Also, there are ready-to-use programs and online services designed specifically for calendar calculations; some of them are described in the Addendum.

      Section 2. The Old Testament chronology

      Speaking of the challenges of calculating dates in the era “from the foundation of the world”, or “from Adam” in Section 1, we didn’t mention one important reason for the lack of consensus regarding the biblical chronology. There are several versions of the Old Testament text (Jewish-Masoretic, Samaritan, Septuagint). For the most part, they are identical, but there are discrepancies which may affect chronology. Some passages contain significant chronological inconsistencies, so a natural question arises as to which dating is more accurate.

      Eastern Orthodox Church regards the Septuagint as the canonical text of the Old Testament (The Septuagint comes from Latin “Interpretatio septuaginta seniorum” – “The translation of the seventy scholars”). The Septuagint is the translation of the Jewish Scripture into Greek completed at the initiative of Demetrius of Phalerum (350 – 283 BNE), the founder and head of the Library of Alexandria. Demetrius persuaded the Egyptian king Ptolemy II Philadelphus (308 – 245 BNE) to have the sacred books of the Jewish canon translated into Greek. Torah (the Pentateuch) was translated in the 3rd century BNE. The remaining Old Testament books were translated later – in the second and first centuries BNE. Some details regarding the process of translation for the Pentateuch are provided in the “Letter of Aristeas, the bodyguard of Philadelphus, to brother Philocrates”. This letter is cited, for example, by Philo of Alexandria (The Life of Moses, 2,6—7), by Josephus Flavius (Judean Antiquities, 12,1—2), in the Talmud (Megillah, 9), by Clement of Alexandria (Stromata, 1,22), by Irenaeus of Lyons (Against Heresies, 3,21,2), by Cyril of Jerusalem (Catechetical Lextures and Mystagogic Catecheses, 4.34), by Epiphanius of Cyprus (On the Seventy Interpreters), by Augustine the Blessed (The City of God, 18,42).

      Below are listed some of the arguments in favor of the higher degree of accuracy of the Septuagint:

      1) The translation of the Old Testament (Tanakh) into Greek, known as Septuagint, was completed in 3rd-1st centuries BNE and was based on the authentic Jewish text provided by the Jewish high priest. This is a sufficient warranty of the accuracy of the resulting text. One can argue about the nuances of meaning in the translated text, but it is hardly possible to assume that the dates and numbers could have been mistranslated.

      2) The translators of the Septuagint were highly educated Jewish scribes. Those seventy two men continued to interact with each other as they were working on the Pentateuch (each Semitic tribe was represented by 6 scribes). One and the same passage was translated by different groups of scribes; then, the results were compared against each other. Thanks to this procedure, the probability of mistakes is very low.

      3) The Septuagint was not created just for the Library of Alexandria. The Greek text was distributed far and wide. One copy was always at the disposal of the Jewish high priest:

      “After he had arrived in Jerusalem, he [Egyptian king Ptolemy IV Philopator (c. 242 – 203 BNE)] offered sacrifice to the supreme God and made thank offerings and did what was fitting for the holy place. Then, upon entering the place and being impressed by its excellence and its beauty, he marveled at the good order of the temple, and conceived a desire to enter the sanctuary. When they said that this was not permitted, because not even members of their own nation were allowed to enter, not even all of the priests, but only the high priest who was pre-eminent over all – and he only once a year – the king was by no means persuaded. Even after the law had been read to him, he did not cease to maintain that he ought to enter, saying, ‘Even if those men are deprived of this honor, I ought not to be.’ And he inquired why, when he entered every other temple, no one there had stopped him” (3 Macc 1:9—12).

      4) The Apostles and early Church Fathers quoted predominantly from the Greek text of the Old

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