Holy Hebrew Arithmetic: What Age was Jesus when he became Teacher-Priest?

The gospel of Luke chapter 3 describes the baptism of Jesus by John the Baptist. John, six months older than Jesus, was then imprisoned and executed by Herod. John was an Aaronic priest through his mother Elizabeth. His father, Zacharias, was also a priest but not of such a highly esteemed family.
Luke then puts the spotlight on Jesus. He was a son of Mariam who like her cousin Elizabeth, Lk 1:5, was also of 'the daughters of Aaron'. They could trace their family back to Elisheba, wife of Aaron, and Miriam sister of Aaron and Moses. Luke then gives the priestly lineage of Jesus from Joseph to Adam.
The Bible says that a priest had to be 30 years old before he took up the mature, senior office of priest, Num 4:3. "From thirty years old and above, even to fifty years old..." (Some other junior posts could start when men reached twenty.)
"Jesus himself began to be about thirty years of age," says Luke in 3:21.
But if Jesus was born in the autumn of 3 BCE and died at Passover 30 CE after 3 1/2 years mission, how could he be 30 when he started the mission? That would mean he started his mission in the autumn of 26 CE. Are there 30 years between 3BCE and 26CE?
That depends how you count them and Luke is very clear. The King James Version (KJV) says he began to be 'about' 30. The Greek however does not use the normal word 'peri' for 'about'. It uses another word for 'about' which invokes a comparison, oosei.
Why? Clearly it is drawing a distinction between the Greek or Roman calculation or arithmetic and the Hebrew.
Luke is after all writing to the Most Excellent Theophilus, chapter 1:3. This son of high priest Annas of the gospels, Theophilus, was put in office as the high priest in 37 CE by Vitellius who replaced Pontius Pilate. He was thus ethnarch or political leader of the nation. As such he was addressed with the respectful title of Most Excellent or Most Noble, kratiste.
He  was educated. He knew how to count in Greek and also in the Hebrew Torah!
Following the death of Emperor Tiberius who gave 7 years of peace to Nazarenes and Jews, Gaius Caligula threatened the entire Jewish people. He commanded that his statue should be placed and worshipped in all synagogues. Massacres of Jews took place in Alexandria, Egypt under Roman governor Flaccus and elsewhere. Then Caligula announced that he would place a huge golden idol of himself as Jupiter in the Temple itself. He would move the center of the Roman empire to the Temple and install himself there after having his divine status confirmed in Egypt by its pagan priests.

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The cause of Caligula's wrath against the Jews? The Resurrection of Jesus the Christ -- which Tiberius had acknowledged as a fact but which threatened the fragile myths of the Roman gods, the invention of men.
Theophilus was high priest during the whole reign of Caligula. He needed to be stalwart in character to resist wisely with the minimum of bloodshed. That depended on his knowledge and education. How was he educated? By a teaching priest. Luke says:
"Seeing that many did take in hand to set in order a narration of the matters that have been fully assured among us, as they did deliver to us who from the beginning became eye-witnesses and officers of the Word, it seemed good also to me, having followed from the first after all things exactly, to write to you in order, Most Noble Theophilus, that you may know the certainty of the things wherein you were catechised." Lk 1 Literal translation  
Yes, a teacher catechised a potential high priest and one new in office to understand and fulfill all the complex rites and rituals. He was also informed about all recent political events that would effect the Jewish nation. He was the nominal head of government under the Romans. Theophilus had a very delicate task to perform.
In 37 James (Jacob) the brother of Jesus was recognised as the Superintendent (sagan or LXX episkopos, bishop) of the Temple on matters pertaining to the ordering of priests (see Acts 15 and 21:17).  Luke and the other gospels record that the resurrection of Jesus had been witnessed by all at Jerusalem. The priests in the Temple had a full view of the Ascension of Jesus forty days later from the nearby Mount of Olives.
What is a Teacher-Priest? To understand the basics we must rid ourselves of centuries of misinformation and gentile, antisemitic propaganda. Jesus is called throughout the Gospels, 'Teacher'. An unknown person, who according to the common "Christian" belief was a carpenter and who suddenly decided to become a roaming preacher, would not in first century Israel be called a Teacher. He would be called a carpenter. The Temple authorities would dismiss him as a vagabond. 
On the contrary, Jesus taught priests and lawyers in the Temple, many times. Obviously he had better education about the Temple and the Law than they had. He commanded their attention by his authoritative presentations and cutting reprimands, Matt 23. He called them hypocrites and blind guides.
A Temple Teacher must not only have deep learning but also an authentic pedigree to even enter the Holy Place. Genealogies were checked at the outer gates. He could not enter to teach priests if he had not fulfilled the requirements of priest himself. He must have been legally at least 30 years old in 26/27 CE.
So let us go to the Bible rather than traditions of a sect. Teacher in Hebrew is Moreh. It is a title. We find the term Teacher-Priest or Teaching Priest in the early days of the Temple. In Hebrew it is Cohen-Moreh. In 2 Chronicles 15:3 we learn that King Asa of Judah was greatly helped when the post of Teacher-Priest was re-established.
"For many days Israel was without a true God, and without a teaching priest (cohen moreh), and without law (Torah, teaching)."
Asa was the son of Abijah, the son of Rehoboam, the son of Solomon, the son of king David.
He carried out a reform and purified the land of idolatry. This might seem costly in one sense as it required righteousness and energy. But the whole land was in turmoil, city against city and nations were against nations in the area. He destroyed idols. Asa's reforms were a disruption only to those who were not believers in the true God. That included some of his own family.
The result was that peace reigned instead of internal turmoil and external wars. In reality righteousness was a very inexpensive policy and it was a sure-fire way of protecting national security.
In 15:2 Asa was told: "The Eternal is with you while you are with him. If you seek him he will be found of you."
Soon after he started the reform, Judah and Israel were faced with a massive invasion from Egypt, then controlled by the Ethiopians and led by Zerah. He expected easy pickings from the what he had heard of turmoil and wars.
All Judah could muster as an army was 280,000 men. That is a considerable army in modern terms. But it was far outclassed by the Ethiopian army. They numbered one million!
In spite of being massively outnumbered the Jews vanquished the invaders.
Thus instituting reform towards the true God of Israel was the best insurance policy that anyone could ever have.
So what was the office of Teacher-Priest? This post is mentioned to Aaron in Leviticus 10:11, so it is very ancient. When the Bible uses the term Teacher it does not mean 'preacher'. That is a Protestant term. It means teacher of Torah. It is associated with the Temple. Who was the Teacher-Priest in the time of Jesus?
The lineage that follows in Luke 3 shows that Joseph, his father, was this teacher before him and Heli or Eli before him. Joseph is called a tekton in the gospels. This word means 'technical expert'. It does not mean carpenter in the Jewish context. It means expert teacher of the Torah. Jesus too was a tekton, a teacher.  From Asa's experience we see that a Hebrew tekton was a master of security for the nation because he could turn Jews and their surrounding gentiles to God.
Josephus, the first century historian, calls Jesus a teacher and also refers to him by another Greek word in the famous passage in Antiquities book 18. That is poietes, a divinely inspired prophet.  (Our English word 'poet' derives from this word.) Jesus, he said, was
"a wise man, if it be lawful to call him a man, for he was a doer (poietes) of wonderful works, a teacher of such men as receive the truth with pleasure. He drew over to him both many of the Jews and many of the Gentiles. He was the Anointed of God (Christ)."
So we have not only a priest and teacher but an anointed one. Anointing was not performed for the  high priests, like Theophilus, Annas or Caiaphas. The Talmud records that an anointed priest is in a higher category of holiness from an unanointed one and the latter must withdraw before him.
So having established that Jesus had this special, divine office of Teaching Priest, how can we show he was of an age that allowed him to take office, namely 30 years?
Understanding how the Hebrews counted reigns of kings and priests will explain why the Bible does not mention that king X reigned 5 years three months and two days. It always gives a whole number of years. Why?
In the Hebrew scriptures, the dates of kings and priests were governed by regnal years. Instead of noting a specific date in the calendar when the last king died and counting the days, the method was to note who was the king on the first day of the beginning of the civil year and then count the number of years that this applied. The civil year began on the first day of the month of Tishri, the Feast of Trumpets.
Counting the number of number of these feast days gives the length of the regnal years for the king. If a king B took over from his father king A in January and stayed on the throne until Trumpets, then he had reigned a year. If he died before Trumpets he would not have reigned that year, but the year would be given to the next king C who was in office on Trumpets. This would be noted as C's first year. The chronologer would not bother to note that he had only reigned a few months of that year.
So how does this apply to Christ?
According to the calculation made by Dr Ernest L Martin in his book, The Star that astonished the World, Jesus was born at the beginning of the first of Tishri at the start of the Feast of Trumpets, 3 BCE.
So we can calculate:
3 BCE to 2BCE is one year.
3 BCE to 1 BCE is two years.
Then we have to remember that there was no year zero. The next year is 1 CE.
3 BCE to 1 CE is 3 years.
3 BCE to 6 CE is 8 years.
3 BCE to 26 CE is 28 years!
So how could Jesus be reckoned to be 30?
Firstly, we should note that Jesus was born at the beginning of Trumpets -- at night. Hebrew days begin at sunset and end at sunset. There were shepherds in the field at night who announced that he had been born in their crib in their tents. (Jesus, James Joseph chapter 15)
So what part of the whole day of the Feast of Trumpets was the critical time that marked the king's reign and distinguished it from the previous king?
The clue is in the name -- Feast of Trumpets. It was the time when the trumpets sounded. If this was midday, then if the king B died before the trumpet he was without the regnal year.  If he took office only just before and died a few seconds after the trumpet he had reigned a whole year!
So we must count the time before the trumpets of 3 BCE as the first year of Jesus's life. The second year started with the Trumpet and continued to the next first of Tishri in 2 BCE.
So the calculation should read as following:
Birth to the time of Trumpets 3 BCE year one
3 BCE to 2 BCE 2 years.
3 BCE to 1 BCE is three years.
3 BCE to 26 CE is 29 years.
But aren't we still a year short of 30?
That's when we need to look at the gospel of Luke again. Luke 3:23 says:
"And Jesus himself began to be about thirty years of age, being according to Torah law (Greek does not mean 'supposed' as Jerome mistranslated it into Latin for doctrinal purposes. The word 'enomizeto' means regulated and according to nomos, Hebrew or Torah Law, literally legalized)  son of Joseph, ... "
Jesus was beginning his thirtieth year. Come the1st of Tishri, this would all be recognized as his year.  Under Hebrew law he was entitled to count this year. As Jesus was alive on this next feast of Trumpets, we can say with Luke Jesus was beginning to be thirty years and fully qualified to be priest.
Jesus, James, Joseph and the past and future Temple is available free on www.academia.edu/25051668 or in bookshops.