1. John's gospel evidence:

Most scholars (and myself) contend GJohn was written in Ephesus (or another city nearby).
In Ac19:1-3, we read:
"While Apollos was at Corinth [52-53C.E?], Paul took the road through the interior and arrived at Ephesus. There he found some disciples and asked them "did you receive the Holy Spirit when you believed?" They answered, "No, we have not even heard that there is a Holy Spirit." So Paul asked, "Then what baptism did you receive?" "John's baptism" they replied."
The preceding quote, plus the degrading treatment of John the Baptist in:
Jn1:19-27 "... "Why then do you baptize if you are not the Christ, nor Elijah,
[opposite of what is suggested in Mk9:11-12 and told in Mt11:14]
` nor the Prophet?". "I baptize with water," John replied, ..."
Jn3:28a "You yourselves bear me witness, that I [John] said, 'I am not the Christ,' ..."
and Jesus & his disciples beating John at his own game:
Jn2:26 "And they came to John and said to him, "Rabbi, He [Jesus] who was with you beyond the Jordan, to whom you have testified; behold, He is baptizing, and all are coming to Him!""
Jn4:1 "... Jesus was gaining and baptizing more disciples than John,"
and the alleged admission by John of his lesser role:
Jn2:30 "He [Jesus] must increase, but I [John] must decrease."
Jn1:30 "This is the one I [John] meant when I said, `A man [Jesus] who comes after me has surpassed me ..."
and Jesus' alleged claim of predominance:
Jn5:36a "I [Jesus] have testimony weightier than that of John."
and the Baptist's alleged testimony (only appearing in GJohn):
Jn1:34 "And I have seen and testified that this is the Son of God."
prove there was a group of latter followers of John the Baptist in Ephesus, seen as competition. Consequently we can assume that, from them, the author knew (and other local Christians too!) when John started to baptize.

In Jn2:20a, during the first Passover (out of the three) mentioned in the gospel, we read:
"The Jews replied, "It has taken forty six years to build this temple ...""

So, when was the temple reconstruction started?

In Josephus' Ant., XV, XI, 1, we read:
"And now Herod [the Great], in the eighteenth year of his reign , and after the acts already mentioned, undertook a very great work, that is, to build of himself the temple of God, and make it larger in compass, and to raise it to a more magnificent altitude, ..."
Note: "the fifteenth year" in Josephus' Wars, I, XXI, 1, appears to be an error that Josephus corrected in 'Antiquities'. With that later date, John would have appeared two or three years before Pontius Pilate's rule over Judea, conflicting with Lk3:1-3:
"... when Pontius Pilate was governor of Judea [from the fall of 26C.E.] ... John ... went ... preaching a baptism ..."

When did Herod start to reign?
In Ant., XVII, VIII, 1, we read:
"Herod] having reigned, since he had procured Antigonus to be slain, thirty-four years;"
Herod died in March-April of 4B.C.E. Therefore, his reign began in: 4 + 34 = 38B.C.E. (however most encyclopaedias state 37B.C.E.)

That means the reconstruction started in 21B.C.E. (38 - 17) or 20B.C.E. (38 - 18).
Notes:
a) "Eighteenth year" means that between 17 and close to 18 years have elapsed.
b) NIV Study Bible's comment on Jn2:20:
"Forty-six years. The temple was not finally completed until A.D. 64. The meaning is that work had been going on for 46 years. Since it had begun in 20 B.C., the year of the event recorded here is A.D. 26 [when John appeared]."
- The fact there is only one year between B.C. 1 and A.D. 1 was obviously missed. If it had been taken in account, A.D. 26 would become A.D. 27. See next note for more details.

Forty-six years later bring us to: 46 - 21 +1 = 26C.E. or 46 -20 + 1 = 27C.E. The later date is more likely because:
a) According to Lk3:1-3, Pilate (from the fall of 26C.E.) was governing Judea when John was baptizing crowds. The first Passover during his rule was in the spring of 27C.E.
b) The most accepted year for the start of the reign of Herod is 37B.C.E.

Note: the "+1" is to allow for the fact that between 1B.C.E. and 1C.E. there is only one year; because, after 1B.C.E. is elapsed, 1C.E. starts.
As example, between the beginning of 4B.C.E. and the start of 3C.E., there are 6 years, not (4+3=) 7.
Another example, more relevant, between the beginning of 20B.C.E. and the start of 27C.E., there are 46 years, not (20+27=) 47.

But when (before the Passover) did John start to baptize and preach (and supposedly met Jesus)?
By the description of the alleged actions of Jesus since that time, it seems the gospel author (and other Christians in the community he was living in) knew it was not long before Passover:
Jn1:29a The next day John saw Jesus coming toward him, and said, "Behold! The Lamb of God ...""
Jn1:35 "Again, the next day ..."
Jn1:43 "The following day Jesus wanted to go to Galilee, [three to four days' walk] ..."
Jn2:1 "On the third day there was a wedding [duration one day?] in Cana [Galilee] ..."
Jn2:12 "After this [the wedding] he went down to Capernaum, [one day's walk] ... [he] did not stay there many days"
Jn2:13a "Now the Passover of the Jews was at hand ..."

These observations suggests that John the Baptist started to baptize (and be well known) only a few weeks before the Passover of 27C.E. In any case, according to Lk3:1-3 already quoted, John could not have started his public life before the fall of 26.C.E.

2. Luke's gospel evidence:

The "problem" lies in the following passage of GLuke:
"In the fifteenth year of the reign of Tiberius Caesar - when Pontius Pilate was governor of Judea, Herod tetrarch of Galilee, his brother Philip of Iturea and Traconitis, and Lysanias tetrarch of Abilene - during the high priesthood of Annas and Caiaphas, the word of God came to John [the Baptist] son of Zechariah in the desert. He went into all the country around the Jordan, preaching a baptism of repentance for the forgiveness of sin." (Lk3:1-4)

2.1 The "earlier reign of Tiberius" hypothesis:

According to any history book or encyclopaedia, Tiberius started to reign after the death of Augustus, his step-father. Augustus died in August 14C.E. Then 14 + 14 = 28C.E. This means that John would have started in the winter/spring of 29C.E.

According to Suetonius (Roman historian 69-140C.E.), volume 1, the Lives of the Caesars, Book III "Tiberius" XX, (translated by J. C. Rolfe, Loeb Classical Library), we read:
"Since the consuls caused a law to be passed soon after this that he [Tiberius] should govern the provinces jointly with Augustus and hold the census with him, ..."
When did that happen?
According to Chap. XVIII of the same book:
"The next year [following the return to Rome from Illyricum of the victorious Tiberius, right after Varus' defeat & death in Germany in 9C.E.] he [Tiberius] returned to Germania [in 10C.E., likely in the spring] ..."
and Chap. XX:
"After two years he [Tiberius, victorious again] returned to the city from Germania and celebrated the triumph which he had postponed, accompanied also by his generals, for whom he had obtained the triumphal regalia."
the aforementioned law seems to have been passed in 12C.E., following the return (thereafter, Tiberius stayed in Rome).
Now, if "Luke" thought Tiberius began his reign then, and assuming that was in late_spring/summer/fall, the "fifteenth year" therefore would include the first part of 27C.E.

Also in Suetonius, volume 1, the Lives of the Caesars, Book II "The Deified Augustus" CI, we read:
"He [Augustus] appointed as his chief heirs Tiberius, to receive two thirds of the estate, and Livia [his mother and Augustus' wife], one third: this he also bade [ordered to] assume his name [Augustus]."
That was on April 3/13C.E. (but Tiberius did not assume the title until after Augustus' death).
According to this website:
"AD 13, April 3: Augustus writes his will; soon after, Tiberius is given imperium maius which makes him virtual co-emperor with Augustus."
(assuming the later happened in April of the same month, and seen by "Luke" as the start of Tiberius' rule, then the "fifteenth year" would begin in early spring of 27C.E.)

In the last two years of his reign, Augustus (who died at seventy-six years old) was a weak and senile man, and Tiberius was called upon to be a co-ruler.
It is possible that the gospel author took in account an earlier start for Tiberius' reign.

Note: the duration of an emperor's reign was not clear-cut in antiquity and subject to differences and errors.
Now, let's consider:
1) "Afterwards those who are called emperors began in this order: first, Caius Julius, who reigned 3 years 4 months 6 days; then Augustus, 56 years 4 months 1 day; Tiberius, 22 years;" (Theophilus of Antioch (180-185), 'To Autolycus, Book III', XXVII)
2) "... periods of the Roman emperors ... Augustus, forty-three years; Tiberius, twenty-two years;" (Clement of Alexandria (180-200), Stromata, Book I, XXI)
3) "Some set down the dates of the Roman emperors thus: Caius Julius Caesar, three years, four months, five days; after him Augustus reigned forty-six years, four months, one day. Then Tiberius, twenty-six years, six months, nineteen days." (Clement of Alexandria (180-200), Stromata, Book I, XXI)
Then, let's remark about Augustus' dating of his reign:
- In 1), the reign of Augustus starts in early 43B.C.E. That is somewhat logical enough, because this corresponds to the year when Octavian (later known as Augustus) started to be ruler of the Roman empire. From the website previously referred to:
"44 BC:
March 15: Assassination of Caesar; Octavian named his principal heir and adopted by Caesar in his will. ...
Early May: In Rome, meets with Antony in Horti Pompei (Pompey's Gardens); Octavian attempts to collect his legacy from Antony (who has seized Caesar's papers and fortune). They eventually come to blows.
43 BC:
April 14: Battle at Forum Gallorum (Antony defeated)
April 14-27: Octavian, invested with propraetorian imperium, leads legions in battle at Mutina, along with consuls Hirtius and Pansa"
April 14-27 43B.C.E. is within "56 years 4 months 1 day" before August 19th 14C.E. (when Augustus died)!
- In 2), the reign of Augustus starts in early 30B.C.E. That makes sense also, considering the following, from the same website:
"31 BC, September 2: Octavian (now consul for the third time) and Agrippa are victorious over Antony and Cleopatra at Actium.
30 BC, August: Octavian and his forces take Alexandria; Antony and Cleopatra commit suicide."
This dating starts Augustus' rule when his main rival (Anthony) is defeated and dead.
- In 3), the reign of Augustus starts in early 33B.C.E. Why? What happened then? Back to the same website:
"34 BC: Antony breaks with Rome and Octavian for good. ... Officially divorces Octavian's sister Octavia. ... Antony divides much of Rome's eastern empire among Cleopatra's children ... declares Octavian a usurper of Caesar's rightful heir, Caesarion, son of Caesar and Cleopatra.
33 BC: Triumvirate runs out again; Octavian campaigning in Illyria
32 BC: The "war of words" between Antony and Octavian"
Now, Augustus' rule begins when Anthony has become enemy of the empire and there is no more sharing of power!

What about Tiberius' dating of his rule? - For 1) and 2), the "22 years" corresponds roughly to the commonly accepted duration of Tiberius' rule (from August 14C.E. to February/March 37C.E.) (but with a half year not accounted for!).
- For 3), the "twenty-six years, six months, nineteen days" brings us to the latter part of 10C.E. What happened then? Back to the website:
"AD 9, Summer: P. Quinctilius Varus and his three legions are massacred by the Germans in the Teutoburger Wald; panic ensues in Italy; Augustus, distraught, begins his final decline"
That could be a justification for Tiberius' promotion the following year, but nothing is said about it in ancient writings. Furthermore, in 10C.E., Tiberius was no more than a general directing a campaign in Germany.
We may be facing a "historical error", certainly not uncommon in these days. See next ...

2.2 The "historical error" hypothesis:

Here is the start of 'dating GLuke' (be patient, that will make more sense later on). The end will be indicated.

"Luke", who tried to be "historical" (Lk21:20a,21b,24), was also, in this domain, prone to make mistakes. Some historical elements in 'Acts' (same author as Luke's gospel) are in error. For example:

"Some time ago Theudas appeared, claiming to be somebody, and about four hundred men rallied to him. He was killed, all his followers were dispersed, and it all came to nothing. After him, Judas the Galilean appeared in the days of the census
[notice "the" census; prior to this point, only one census is mentioned in GLuke and 'Acts': the one of Jesus' birth (Lk2:1-2) taken under Quirinius (Cyrenius); the author is evidently referring to the same census. I'll come back to it later]
` and led a band of people in revolt. He too was killed, and his followers were scattered." (Ac5:36-37)

Actually, according to Josephus, Judas appeared first:
Wars, II, VIII, 1 "And now Archelaus' part of Judea was reduced into a province [6C.E.], and Coponius, one of the equestrian order among the Romans, was sent as a procurator, having the power of [life and] death put into his hands by Caesar. Under his administration it was that a certain Galilean, whose name was Judas, prevailed with his countrymen to revolt, and said they were cowards if they would endure to pay a tax to the Romans and would after God submit to mortal men as their lords."

Then Theudas:
Ant., XX, V, 1 "Now it came to pass, while Fadus was procurator of Judea [44-46C.E.], that a certain magician, whose name was Theudas, ...
[as already quoted in "HJ-3a", Section 20. Theudas got killed and his followers dispersed]"
Note: no other Theudas is reported in Josephus' works.

And if we go back to "Judas of Galilee and the census", it is clear that the census was taken under Cyrenius:

Wars, II, XVII, 8:
"In the meantime one Manahem, the son of Judas, that was called the Galilean (who was a very cunning sophister, and had formerly reproached the Jews under Cyrenius, that after God they were subject to the Romans)"
Wars, VII, VIII, 1:
"... Eleazar, a potent man, and the commander of these Sicarii, that had seized upon it. He was a descendant from that Judas who had persuaded abundance of the Jews, as we have formerly related, not to submit to the taxation when Cyrenius was sent into Judea to make one; ..."
Ant., XVIII, I, 1:
"Now Cyrenius, a Roman senator, and one who had gone through other magistracies, and had passed through them till he had been consul, and one who, on other accounts, was of great dignity, came at this time into Syria, with a few others, being sent by Caesar to he a judge of that nation, and to take an account of their substance [the census]. Coponius also, a man of the equestrian order, was sent together with him, to have the supreme power over the Jews.
Moreover, Cyrenius came himself into Judea, which was now added to the province of Syria, to take an account of their substance, and to dispose of Archelaus' money; but the Jews, although at the beginning they took the report of a taxation heinously, yet did they leave off any further opposition to it, by the persuasion of Joazar, who was the son of Beethus, and high priest; so they, being over-persuaded by Joazar's words, gave an account of their estates, without any dispute about it.
Yet was there one Judas, a Gaulonite, of a city whose name was Gamala, who, taking with him Sadduc, a Pharisee, became zealous to draw them to a revolt, who both said that this taxation was no better than an introduction to slavery, and exhorted the nation to assert their liberty;"

Note: when the Romans were taking control of a new province, they set up immediately a census (to find where, how many and by how much people could be taxed), then taxation would follow:
Ant., XVIII, II, 1: "When Cyrenius had now disposed of Archelaus' money, and when the taxing were come to a conclusion, which were made in the thirty-seventh year of Ceasar's victory over Antony at Actium ...
[that means that the taxation occurred between September 6C.E. and August 7C.E.]"

However in Lk2:1-2:
"In those days Caesar Augustus issued a decree that a census should be taken of the entire Roman world. (this was the first census that took place while Quirinius was governor of Syria.)"

Here, it is obvious this Quirinius ('kurhnios') is Cyrenius ('kurinios') as written by Josephus and that Judas was the trouble maker of the census. But then, if Jesus was born (Lk2:1-7) in 6 or 7C.E, during the census, he could not have been about thirty in 27, 28, 29 or even 33C.E:
Lk3:23 "Now Jesus himself was about thirty years old when he began his ministry."
And Mary could not have been about eight to nine years pregnant with Jesus! (see next notes).

Notes:
a) According to the following, Mary is already pregnant when visiting Elizabeth & Zacharias:
Lk1:42 "Then she [Elizabeth] spoke out with a loud voice and said, "Blessed are you [Mary] among women, and blessed is the fruit of your womb! But why is this granted to me, that the mother of my Lord should come to me?" This is confirmed later, when some four months afterwards, Zacharias prophecies:
Lk1:68-69 "Blessed is the Lord God of Israel, for He has visited and redeemed His people, and has raised up a horn of salvation for us in the house of His servant David,"
b) Because allegedly Elizabeth got pregnant during "the time of Herod [the Great] king of Judea" (Lk1:5) and for Mary five to six months later (Lk1:26 "In the sixth month ..."), according to "Luke", Jesus could not have been born more than fifteen months after Herod's death, which occurred in early spring of 4B.C.E., between the 13th of March and at least one week before Passover.

Also, there was only one high priest in Jesus' time: Caiaphas. The other high priest mentioned in Lk3:2 "... Annas ..." seems to be Ananus (another different spelling!) who was deprived of the high priesthood about two years before Caiaphas assumed his. Ananus lived for a long time and there are indications he was the kingpin of the Sadducees. But from Josephus' Antiquities, it is certain only one high priest was appointed at any given time.

In conclusion, we would state that the historical reliability of the gospel (and 'Acts') is questionable, and the author could have made one more mistake about the "fifteenth year of the reign of Tiberius". Let's also say that the author (even the Luke of tradition) was not an eyewitness of Jesus and admitted to compose the gospel from second hand sources:
Lk1:1-3a: "Many have undertaken to draw up an account of the things that have been fulfilled among us, just as they were handed down to us by those who from the first were eyewitnesses and servants of the word. Therefore, since I myself have carefully investigated everything from the beginning, it seemed good also to me to write an orderly account for you, ..."

And there is more ...

2.3 The "Archelaus' reign was missed" hypothesis:

Here, we are going to examine how the aforementioned historical errors in GLuke could have been made.

Let's start by these three observations:
a) In GLuke, the Sea of Galilee is called "lake of Gennesaret" (5:1). In all the other gospels, it is "Sea of Galilee" (also "lake of Tiberias" in GJohn 6:1). In Josephus' Wars (published 78-79C.E.), the same lake is only referred as "lake of Gennesaret" (III, X, 1, 7 & 8).
b) In Lk19:43-44a, we read:
"The days will come upon you [Jerusalem] when your enemies will build an embankment against you and encircle you and hem you in on everyside. They will dash you to the ground, you and the children within your wall."
This is similar to details of the siege of Jerusalem (70C.E.) described in Josephus' Wars, V, VI, 2 & VIII, 5.
No other gospel has these details.
c) In Lk19:33,14-15a, we read:
"He said: "a man of noble birth went to a distant country to be appointed king and then to return ... but his subject hated him and sent a delegation after him to say , 'we don't want this man to be our king.' He was made king, however, and returned home. ...""
This appears to be very much inspired by Josephus' Wars, II, VI, Archelaus' trip to Rome (spring of 4B.C.E.).
d) "Luke" used peculiar words and expressions appearing in Josephus' Wars:
- 'Sicarii' (Ac21:38), meaning terrorists. But the (Greek) word itself is a Latin loanword.
- 'haireseis' meaning Jewish sects (Ac5:17;15:5;26:5) and "Nazarenes" (Ac24:5,14) and Christianity (Ac28:22). The word would later mean "heresy" for Christians. Josephus is the only known author (outside "Luke") to have used this word in this context.
- "Luke" called the Pharisees the 'most precise school' (Ac26:5). Only Josephus is known to use this expression (Wars, I, V, 2 & II, VIII, 14).

So, did "Luke" know about Josephus' Wars?
Why not?
At the time, it was the best & most complete book on Palestine & the Jews (still is) and most helpful for someone interested in history (I know!). Later on, bishop Eusebius (260?-339) made great use of Josephus' works in 'The History of the Church'. And according to Josephus himself:
Life, 65 "... the emperor Titus was so desirous that the knowledge of these affairs should be taken from these books ['Wars of the Jews'] alone, that he subscribed his own hand to them, and ordered that they should be published ..."

Was "Luke" a contemporary and companion of Paul?
Hardly so, considering "Luke" (and obviously his/her community!) was not aware of a thriving Christian community in Rome (according to Paul's Romans letter) well before Paul went there:
Ac28:17-31 "... Therefore I [Paul] want you [the leaders of the Jews of Rome] to know that God's salvation has been sent to the Gentiles, and they will listen! ..."
Furthermore, Luke's theology is not according to Paul's one; for example, for Paul and the author of "Hebrews" (Heb10:30-31,12:23 "God, the judge of all men"), God (and not Jesus) is the Judge of Judgment day:
Ro2:3,
Ro2:5-6 "But in accordance with your hardness and your impenitent heart you are treasuring up for yourself wrath in the day of wrath and revelation of the righteous judgment of God, who "will render to each one according to his deeds""
Ro5:16,
Ro14:10b,12 "For we will all stand before God's judgment seat ... So then, each of us will give an account of himself to God."
However in Luke's Acts:
Ac10:42 "And He commanded us to preach to the people, and to testify that it is He who was ordained by God to be Judge of the living and the dead."
That's very consistent with other late 1st century Christian writings, such as:
Mt25:31-46 "When the Son of Man comes in his glory, and all the angels with him, he will sit on his throne in heavenly glory. All the nations will be gathered before him, and he will separate the people one from another as a shepherd separates the sheep from the goats. ..."
Jn5:22 "For the Father judges no one, but has committed all judgment to the Son"
Jn5:25-30 "I tell you the truth, a time is coming and has now come when the dead will hear the voice of the Son of God and those who hear will live. For as the Father has life in himself, so he has granted the Son to have life in himself. And he has given him authority to judge because he is the Son of Man ..."

But if "Luke" browsed into Josephus' Wars, before or when writing the gospel, how can the aforementioned historical errors be explained?

a) Ananus:
The name of the high priest (Caiaphas and only him) during Pilate's rule is NOT mentioned in 'Wars'. "Luke" must have found Annas and Caiaphas from another (inaccurate) source.

b) The 8 to 9 years pregnancy of Mary:
This could be explained as follows: "Luke" relied on Josephus' Wars to learn about the period following Herod the Great's death (March 4B.C.E.).
In 'Wars', there are seven chapters (Book II, Chapters I to VII) describing the period (between 9 and 10 years) from Herod's death to Judea becoming a Roman province (Book II, Chapter VIII). From Chapter I to the middle of Chapter VII, only the events of the first months after the king's death are narrated:
They include troubles & interventions by the Romans in Judea, chaos & destructions & killings, strong opposition to Archelaus (a son of Herod and the main pretender to his throne) in Judea & also in Rome after he went there (a Jewish delegation of fifty ambassadors from Judea opposed his nomination), deliberations & turmoil in Tiberius' court, a spurious pretender and the splitting by Tiberius of Herod's kingdom between his descendants (end of Chapter VI: Archelaus is one of the recipient and his share is mentioned last).
Finally, in the middle of Chapter VII, we learn that:
"And now Archelaus took possession of his ethnarchy, and used not the Jews only, but the Samaritans also, barbarously; and out of this resentment of their old quarrels with him. Whereupon they both of them sent ambassadors to Caesar; and in the ninth year of his government he was banished to Vienna, a city of Gaul, and his effects were put into Ceasar's treasury."
That's all for the nine years reign of Archelaus. Also, the very short description of his rule gives the impression he was banished soon after his return from Rome.
INTHESEDAYSGREEKTEXTSWEREWRITTENINSAMESIZEDLETTER
SWITHNOPUNCTUATIONANDNOSPACEBETWEENWORDS
INTHISDELUGEOFLETTERSANDBYBROWSINGONLYTHEINTHE
NINTHYEAROFHISGOVERNMENTWASEASYTOMISS
(In these days, Greek texts were written in same-sized letters, with no punctuation and no space between words. In this deluge of letters, and by browsing only, the "in the ninth year of his government" was easy to miss!)
Of course, by missing Archelaus' eight to nine years reign (and assuming it lasted only a few months), there was an opportunity to have Jesus born in Bethlehem during the census of Quirinius/Cyrenius, satisfying prophecies!

Note: a census being the cause of a trip to Bethlehem is totally absurd and against known Roman rules used for administrating the provinces & their people: tax payers were registered where they lived and worked. And then, Nazareth & Galilee were under Herod Antipas' rule and not the Romans.

Let's go back to the parable of the ten minas:
Lk19:12,14-15a "He said: "a man of noble birth went to a distant country to be appointed king and then to return ... but his subject hated him and sent a delegation after him to say, 'we don't want this man to be our king.' He was made king, however, and returned home.""
I mentioned already it was very much drawn from Josephus' Wars, II, VI, Archelaus' trip to Rome (spring of 4B.C.E.).
1 "But now came another accusation from the Jews against Archelaus at Rome, which he was to answer to. It was made by those ambassadors who, before the revolt, had come, by Varus's permission, to plead for the liberty of their country; those that came were fifty in number, but there were more than eight thousand of the Jews at Rome who supported them. And when Caesar [Tiberius] had assembled a council of the principal Romans in Apollo's temple, that was in the palace, (...) the multitude of the Jews stood with the ambassadors, and on the other side stood Archelaus, with his friends; ..."
2 "And now, upon the permission that was given the accusers to speak, they, in the first place, went over Herod's breaches of their law, and said that he was not a king, but the most barbarous of all tyrants, and that they had found him to be such by the sufferings they underwent from him;
[the accusers tried to link Archelaus to his father's (Herod the Great) abuse of power. But by reading quickly, one might think these accusations are about Archelaus himself]
` that when a very great number had been slain by him, those that were left had endured such miseries, ..."
At the end of the parable of the ten minas, we have:
Lk19:27 "[After the return as king] But those enemies of mine who did not want me to be king over them--bring them here and kill them in front of me."
There is nothing of that sort reported in Josephus' Wars (or any other work). Actually, Archelaus was rather forgiving on that issue:
Ant., XVII, XIII, 1 "When Archelaus was entered on his ethnarchy, and was come into Judea, he accused Joazar the son of Boethus, of assisting the seditious, and took away the high priesthood from him, and put Eleazar his brother in his place."
So, how did "Luke" think of that?
With "Luke" assuming a very short reign for Archelaus, by missing the "nine years", the answer may very well be (or confirmed) in:
Josephus' Wars, II, VII, 3 "And now Archelaus took possession of his ethnarchy, and used not the Jews only, but the Samaritans also, barbarously;
[but that was nine years later, not right after he came back from Rome as the ethnarch!]
` and out of this resentment of their old quarrels with him. Whereupon they both of them sent ambassadors to Caesar; ... he was banished ..."

Let's go in Luke's mindset now: the author must have thought that, after Herod's death, several months went by because of the chaos which followed, Archelaus' aborted reign and Judas' revolt when the census took place, under Roman rule over Judea. That would place Jesus' birth in summer/early fall of 4B.C.E.

Note: it is unlikely "Luke" was thinking about the cool & wet winter for the time of Jesus' birth:
Lk2:8 "And there were shepherds living out in the fields [only in the dry season!] nearby, keeping watch over their flocks at night."
Remark: Jesus' birth was set on the 25th of December not earlier than the 4th century!

Going back to Lk3:23, "Now Jesus himself was about thirty years old when he began his ministry.", that would bring us to (legend: years/Jesus' age):
3B.C.E./1, 2B.C.E./2, 1B.C.E./3, 1C.E./4
(Note: between 1B.C.E. and 1C.E. there is only one year)
2C.E./5, 3C.E./6, 4C.E./7 (you get the idea now)
then we have:
26C.E./29, 27C.E./30

So, it looks that my first hypothesis ("earlier reign of Tiberius") might be right (either that or an error on "the fifteenth year of the reign of Tiberius").

In the next Section, I will show that Jesus, very likely, started his "ministry" in Capernaum in late spring or early summer.

PS: Did "Luke" know about Josephus' Antiquities (published 93C.E.)?
Likely NOT: if "Luke" had 'Antiquities' when writing the gospel, most of the historical mistakes (and different spellings) would have been avoided, including:

A) In 'Antiquities' Caiaphas is clearly identified as the only high priest during most of Pilate's rule as prefect (up to the Passover of 36C.E; Caiaphas was replaced then).
Ant., XVIII, II, 2 "This man [Gratus the prefect] deprived Ananus of the high priesthood, and appointed Ismael, the son of Phabi, to be high priest. He also deprived him in a little time, and ordained Eleazar, the son of Ananus, who had been high priest before, to be high priest; which office, when he had held for a year, Gratus deprived him of it, and gave the high priesthood to Simon, the son of Camithus; and when he had possessed that dignity no longer than a year, Joseph Caiaphas was made his successor. When Gratus had done those things, he went back to Rome, after he had tarried in Judea eleven years, when Pontius Pilate came as his successor."
Ant., XVIII, IV, 3 "But Vitellius came into Judea, and went up to Jerusalem; it was at the time of that festival which is called the Passover ... Besides which, he [Vitellius] also deprived Joseph, who was also called Caiaphas, of the high priesthood, and appointed Jonathan the son of Ananus, the former high priest, to succeed him. After which, he took his journey back to Antioch."
In conclusion, no error could had been made if "Luke" had 'Antiquities': here one high priest (not two) is assigned!

Notes:
1) From where "Luke" might have got the idea of dual high priests? Likely from Josephus' Wars:
"both Jonathan and Ananias, the high priests" (II, XII, 6)
In 'Wars', Josephus invoked often the "high priests" as the high priest of the time, plus one, some or all of the (living) ex-ones:
II, XX, 4 "Jesus, the son of Sapphias, one of the high priests; and Eleazar, the son of Ananias, the high priest ..."
II, XXI, 9 "The best esteemed also of the high priests, Jesus the son of Gamalas, and Ananus the son of Ananus ..."
VI, II, 2"Some also there were who, watching a proper opportunity when they might quietly get away, fled to the Romans, of whom were the high priests Joseph and Jesus ..."

But in 'Antiquities', Josephus was very meticulous about the high priesthood and clearly recorded the succession of high priests, one by one, as we saw already.

B) In 'Acts' (23:3,24:1), the high priest during Paul's last visit to Jerusalem is "Ananias". At this time, the governor of Judea is Felix, two years before he was replaced (Ac24:27). But according to Josephus' Ant., XX, VIII, 5 & 8, it is very clear that during Felix' years as governor (52-60), there were only two successive high priests, "Jonathan", then "Ismael". "Ananias" is also recorded in 'Antiquities', but his tenure ended during the rule of Cumanus, the predecessor of Felix (Ant., XX, VI, 2). Once again, if "Luke" had 'Antiquities', this mistake would not occur.

Note: but how did "Luke" get "Ananias"?
From Josephus' Wars, as follows:
As previously quoted, we have: "both Jonathan and Ananias, the high priests" (Wars, II, XII, 6). This is during the rule of Cumanus. Here it would seem to "Luke" there were two high priests then. But later in the book, we learn that, after Felix became governor (II, XIII, 2), "the first man who was slain by them [sicarii] was Jonathan the high priest"(II, XIII, 3).
Nobody is mentioned in 'Wars' as the replacement for Jonathan. Then who is left as a high priest? Ananias, of course!
By the way, this is, in my opinion, a strong piece of evidence advocating "Luke" knew about 'Wars' (and did not read 'Antiquities').

C) In 'Antiquities' Cyrenius is mentioned (and also again Ananus) in his chronological "niche" and a direct reference is indicated for the dating of his census/taxation:
Ant., XVIII, II, 1 "When Cyrenius had now disposed of Archelaus's money, and when the taxings were come to a conclusion [6-7C.E.], which were made in the thirty-seventh year of Caesar's victory over Antony at Actium,
[September 2, 31B.C.E. In the corresponding section of 'Wars' (II, IX, 1), no dating is given]
` he deprived Joazar of the high priesthood, which dignity had been conferred on him by the multitude, and he appointed Ananus, the son of Seth, to be high priest; while Herod and Philip had each of them received their own tetrarchy, and settled the affairs thereof."
Again, with 'Antiquities', it would have been impossible for "Luke" to set Jesus' birth during the census (with, as discussed before, Jesus about thirty around 30C.E., and Mary pregnant before, or soon after, Herod the Great's death (4B.C.E.)).

D) Archelaus' nine years rule over Judea is described in no less than a whole section in 'Antiquities' (XVII, XIII, 1), and not in a few words as in 'Wars'. A whole section would be hard to skip!

E) Theudas and Judas reversed in 'Acts':
Richard Carrier wrote: "When Luke brings up Theudas and Judas in the same speech [Ac5:36-37], he reverses the correct order [agreed], having Theudas appear first, even though that does not fit what Josephus reports--indeed, Josephus places Theudas as much as fifteen years after the dramatic time in which Luke even has him mentioned. That Luke should be forced to use a rebel leader before his time is best explained by the fact that he needed someone to mention, and Josephus, his likely source, only details three distinct movements (though he goes into the rebel relatives of Judas, they are all associated with Judas). And when Josephus mentions Theudas, he immediately follows with a description of the fate of the sons of Judas (JA 20.97-102) and uses the occasion to recap the actions of Judas himself (associating him with the census, as Acts does). Thus, that Luke should repeat this very same incorrect sequence, which makes sense in Josephus but not in Acts, is a signature of borrowing. Further evidence is afforded here by similar vocabulary: both use the words aphistêmi "incited" and laos "the people.""
The passage referred by Carrier is Ant., XX, V, 1-2a:
"NOW it came to pass, while Fadus was procurator of Judea, that a certain magician, whose name was Theudas, persuaded a great part of the people to take their effects with them, and follow him to the river Jordan; for he told them he was a prophet, and that he would, by his own command, divide the river, and afford them an easy passage over it; and many were deluded by his words. However, Fadus did not permit them to make any advantage of his wild attempt, but sent a troop of horsemen out against them; who, falling upon them unexpectedly, slew many of them, and took many of them alive. They also took Theudas alive, and cut off his head, and carried it to Jerusalem. This was what befell the Jews in the time of Cuspius Fadus's government. Then came Tiberius Alexander as successor to Fadus; ... [about 90 words here]. And besides this, the sons of Judas of Galilee were now slain; I mean of that Judas who caused the people to revolt, when Cyrenius came to take an account of the estates of the Jews, as we have showed in a foregoing book [Ant., XVIII, I, 1]. The names of those sons were James and Simon, whom Alexander commanded to be crucified."
If "Luke" ever read that, how could this Theudas' incident be NOT noticed as happening during Fadus' rule (44-46C.E.)?
Furthermore, its narration appears within the proper chronological "niche" and two books after the initial description of Judas' revolt & the summary of Pilate's government. And "Luke" knew Judas rebelled during the census (Ac5:37) (likely from Josephus' Wars, II, VIII, 1), which the author placed around the time of Jesus' birth, several decades before Fadus.
And "Luke" would have missed the next paragraph being about Judas' sons, not Judas himself, and the mention of Alexander's tenure (46-48C.E.)! That's a lot of erroneous reading to ask from "Luke"!
Let's also note "Luke" described the Theudas' episode with significant differences as compared with Josephus' account in 'Antiquities':
Ac5:36 Darby "for before these days Theudas rose up, alleging himself to be somebody, to whom a number of men, about four hundred, were joined; who was slain, and all, as many as obeyed him, were dispersed and came to nothing."
Therefore I find Carrier's argument rather preposterous. And mainly considering the very clear location in time of Theudas' story in Josephus' Antiquities (hard to miss!), Luke's knowledge of the Judas' revolt happening much earlier and the dissimilar accounts, it is most likely "Luke" never knew about Ant., XX, V, 1-2a. Actually, if the author had just browsed through it, one more mistake would have been avoided (Judas, then Theudas).
What about 'aphistêmi' "incited" and 'laos' "the people"?
It happens these two words were very much used in Luke's works:
'aphistemi': GMark=20, GMatthew=6, GJohn=8, GLuke=27, 'Acts'=43
'laos': GMark=2, GMatthew=15, GJohn=3, GLuke=36, 'Acts'=47

Note: because Theudas does not appear in 'Wars', so again "Luke" must have got the name from another source. And it is undeniable "Luke" had other (sometimes dubious) historical accounts. For example:
- Iturea, an area in the northern mountains of Lebanon, was not part of Philip's tetrarchy. As I explained earlier, "Luke" probably did not browse over the whole or parts of Chapters VI & VII of Book II in Josephus' Wars where it is written "... but Batanea, and Trachonitis, and Auranitis, ... were made subject to Philip"
- "Lysanias tetrarch of Abilene", during Pilate's rule over Judea.
These do not appear in Josephus' works.

E) Miscellaneous notes:

a) Luke's account of the death of Agrippa I (Ac12:19a-23) shows marked differences, even conflicts, with Josephus' only narration of it in Ant., XIX, VIII, 2. "Luke" must have drawn from a different source.

b) Drusilla, the wife of Felix, is not mentioned in 'Wars', only in 'Antiquities' (XX, VII, 2). But she is featured along Felix (governor of Judea, 52-60C.E.) in Ac24:24. So from where "Luke" might have known about her? Possibly from one of the "we". The "we" passages are very detailed in 'Acts' and likely (for most of them) benefited from testimonies of Paul's traveling companions (more explanations later). And the second "we" trip ends in Jerusalem (Ac21:17, around 58C.E.), while the third one starts from Cesarea (Ac27:1), the residence of Felix. Gossips about Drusilla & Felix could have been heard then, including immoral behavior of the twosome, as suggested in Ac24:25-26.
Remark: Bernice (Ac25:23), Agrippa II's sister, is mentioned prominently in Wars, II, XV, 1.

c) The famine under Claudius, mentioned in Ant. XX, II, 5 and Ac11:28 "... a severe famine would spread over the entire Roman world." This famine, caused by a crop failure in Egypt (the bread basket of the Roman empire then), made the price of food too expensive for the poor all over the empire. Consequently, "Luke" did not need 'Antiquities' to know about it. Furthermore, in Josephus' book, the famine is presented as local, that is affecting Jerusalem only.

d) It seems "Luke" was very much confused about the "Egyptian":
Ac21:38 "... the Egyptian who started a revolt and led four thousand terrorists [sicarii] out into the desert ..."
Wars, II, XIII, 5 "But there was an Egyptian false prophet that did the Jews more mischief than the former; for he was a cheat, and pretended to be a prophet also, and got together thirty thousand men that were deluded by him; these he led round about from the wilderness to the mount which was called the Mount of Olives [across Jerusalem] ..."
(there is no mention of journey about the "Egyptian" in Ant., XX, VIII, 6 )
In view of these discrepancies, some questions may be asked:
- Did "Luke" know about the "Egyptian" from another source (as for Theudas)?
- Did "Luke" misread 'Wars' when writing?
- Did "Luke" read parts of 'Wars' and then later wrote GLuke & 'Acts', without the book?
The later is my preferred option, looking back at my previous findings (including 'kurhnios' <=> 'kurinios').
Also, because Theudas did bring his people towards the desert (that is the Jordan valley), "Luke" might have assigned by mistake to the "Egyptian" something which was known about Theudas.

Remarks about the three "we" passages in 'Acts' (16:10-17, 20:6-21:17 & 27:1-28:16):

A) The first two (out of three) "we" passages keep going when the "we" travel by land and even after arriving at destination (Philippi & Jerusalem).

B) In Acts20:1-6, the "we" member(s) are not named (as in the two other "we" passages) but are those who reached Troas with Paul, ahead of the "we":
Ac20:4-6 "And Sopater of Berea accompanied him [Paul] to Asia--also Aristarchus and Secundus of the Thessalonians, and Gaius of Derbe, and Timothy, and Tychicus and Trophimus of Asia. These men, going ahead, waited for us at Troas. But we sailed away from Philippi after the Days of Unleavened Bread, and in five days joined them at Troas, where we stayed seven days."

C) The first "we" "appears" with Paul at/near Troas (which had no Christians then) as a Christian missionary close to him:
Ac16:10 "Now after he [Paul] had seen the vision, immediately we sought to go to Macedonia, concluding that the Lord had called us to preach the gospel to them."
Then "we" goes to Macedonia with Paul. However it "disappears" when staying in Philippi (as a guest, not a resident --Ac16:15), before Paul & Silas get in trouble & go to jail, but after a Christian community has been created among Gentile women (Ac16:13-15).

Notes:
a) Since Paul traveled with Timothy & Silas only (according to Ac16:1-3), with the former, a new addition from "southern" Galatia, the lesser one of the trio then, the "we" is most likely Timothy. At least, that's what "Luke" wanted his/her audience to believe.
b) In the first "we" passage (Ac16:10-17), Timothy is never named but resurfaced later in Berea (Ac17:14-15), when he & Silas stay behind while Paul goes to Athens.
c) According to my research, "Luke" was a Gentile Roman Christian woman from Philippi; see this page for explanation. That would explain "Luke" using Timothy as a witness for the "historic" crossing from Asia to Macedonia (because of the vision & God!) and the way Christianity started in Philippi (among women, one of them named & mentioned prominently!).
d) Timothy was well known to the Philippians, more so because later he visited them (without Paul): Php4:15 + Ac18:5, Ac19:22, & Php2:19-22
Php2:19-22 "But I trust in the Lord Jesus to send Timothy to you shortly, ... For I have no one like-minded, who will sincerely care for your state. For all seek their own, not the things which are of Christ Jesus. But you know his proven character, that as a son with his father he served with me in the gospel."

D) On the second "we" trip (Ac20:6-21:17, from Philippi to/in Jerusalem), Timothy is named among Paul's companions and consequently cannot be one of the "we" (20:4). Because this "we" starts from Philippi, there is a good chance they were from Corinth or/and Philippi: these cities harbored important Christian communities then, but do not have named representatives with Paul (but Berea and Thessalonica have some! Ac20:4, previously quoted).

E) For the third "we" travel (Ac27:1-28:16, from Cesarea to Rome), the "we" starts as apparently being with Paul in Cesarea, according to:
Ac27:1-2 "And when it was decided that we should sail to Italy, they delivered Paul and some other prisoners to one named Julius, a centurion of the Augustan Regiment. So, entering a ship of Adramyttium, we put to sea, meaning to sail along the coasts of Asia. Aristarchus, a Macedonian of Thessalonica, was with us."
But no other Christian is reported to be a prisoner then with Paul, according to 'Acts' itself! However, Ac24:23 suggests Paul's friends were allowed to visit him.
That could be one of those or "Aristarchus", a close associate of Paul (Ac19:29,20:4 (already quoted), Phm1:24), who would follow his boss wherever he was staying or going.
It is possible; but what about "was with us" (better translated as "being with us")?

Notes:
a) Here "us" can mean all people on board, as the preceding "we" and the other "we" & "us" in Ac27:4-7:
Ac27:7 "When we had sailed slowly many days, and arrived with difficulty off Cnidus, the wind not permitting us to proceed, we sailed under the shelter of Crete off Salmone."
b) In ancient literature, it was customary to use first person plural when on board a ship.
c) It seems "them" (in Ac27:2) would have been out of place in the "we" overall context and would wrongly associate Aristarchus with "they", that is the Roman authorities of Cesarea.

F) It is clear there is no general rule about the "we". In the first case, it is implied the "we" is from the perspective of (allegedly!) Timothy; in the second one, from the one of unnamed companion(s) of Paul from Corinth or/and Philippi (but NOT Timothy or Aristarchus; see Ac20:4-6). And finally in the last case, the "we" is probably some (free) companion(s) of Paul in Cesarea, or even only Aristarchus.
The "we" word is therefore loosely used and does not indicate a same "we" person (such as the author) participated in the three journeys, but rather different ones. And it appears "Luke" used "we" to suggest a certain passage is quoted directly from eyewitness(es) when the rest would be collected/compiled from various second/third hand sources.

Note: these eyewitnesses might have died before 'Acts' was written, allowing the author to embellish their story (more so on the journey to Rome!).

3. Dating of John the Baptist's arrest:

The main clue about the length of John the Baptist's "ministry" is Jesus' forty days in the desert (Mk1:12, Mt4:2, Lk4:2). This is probably symbolic and reminiscent of
Ex24:18 "Then Moses entered a cloud as he went up the mountain. And he stayed on the mountain forty days and forty nights"
However, it is a clear indication of the shortness of John's "ministry".
Let's consider:
a) "And so John came baptizing in the desert ..." (Mk1:4)

b) Then, "At that time, Jesus came from Nazareth in Galilee
[probably just before Passover. Note: John was baptizing along a route used by the Galileans going to Jerusalem]
` and was baptized by John in the Jordan ..." (Mk1:9a)

c) Then, "At once, the Spirit sent him in the desert, and he was in the desert forty days,being tempted by Satan. He was with the wild animals, and angels attended him." (Mk1:12-13)
Note: "At once": "Mark" seems anxious not to have Jesus staying around John as just one of his followers.

d) Then, "After John was put in prison, Jesus went to Galilee, [out of the desert] ..." (Mk1:14a)

This sequence of events advocates for the shortness of John the Baptist's public life. Its briefness would also explain why the works of Philo of Alexandria (and others in those days such as Josephus' Wars) did not mention him.

Note: later, in 'Antiquities', Josephus introduced John's story only because:
Ant., XVIII, V, 2, "Now [36C.E.], some of the Jews thought that the destruction of Herod's army came from God, and was very justly, as a punishment of what he did against John [the Baptist]; ... ; For Herod slew him ..."
However, in 'Wars', the war/quarrel between Herod Antipas & Aretas and the ensuing defeat of Herod's army are not mentioned at all.

In GLuke (3:1-3,7a), a particular year is specified for John's appearance and activities:
"In the fifteenth year of the reign of Tiberius Caesar - when Pontius Pilate was governor of Judea, ... the word of God came to John [the Baptist] son of Zechariah in the desert. He went into all the country around the Jordan, preaching a baptism ... John said to the crowds coming out to be baptized by him, ..."
But no other year is mentioned for his arrest:
Lk3:19a-20 "But when John rebuked Herod the tetrarch because of Herodias, his brother's wife, ... Herod added this to them all: He locked John up in prison."
Next in the gospel is Jesus' appearance:
Lk3:21a " When all the people were being baptized, Jesus was baptized too."
After the forty days in the desert (and after John's arrest, according to GMark 1:14):
Lk4:14a "Jesus returned to Galilee ..."
And none of the gospels (and any other ancient writings) suggests that John was active for years.

In GJohn, the Baptist's activities are reported to occur a few weeks before (the first mentioned) Passover (Jn1:15-36), and right after the same feast (Jn3:22-30), when, as we are reminded, "This was before John was put in prison." Then, the next mention of John the Baptist is in the past tense:
Jn5:35 "John was a lamp that burned and gave light, and you chose for a time to enjoy his light."
The context of this alleged declaration is sometime before the second mentioned Passover (Jn6:4), during a prior and unspecified "feast of the Jews" in Jerusalem (Jn5:1). However, "John" was thinking summer because, at this time, some people are described to be bathing at an outdoor pool (Jn5:1-6). In other words, according to "John", the Baptist's ministry lasted only a few months.

Certainly the gospel writers' perception was John the Baptist's public life had been short, in months and not in years. In conclusion, and trusting the "forty days" as a valid clue, we can propose that by the latter part of the spring of 27C.E, John the Baptist's public life was all over.

Notes:
a) Mark's account of John's death might be embellished and drawn from latter John's followers, but provide some information about when the Baptist was executed:
Mk6:19-28 "So Herodias
[Herod's new wife, presented as ambitious and scheming by Josephus]
` nursed a grudge against John and wanted to kill him. ... On his birthday Herod [Antipas] gave a banquet for his high officials and military commanders and the leading men of Galilee. When the daughter of Herodias
[young Salome (whose father was Herodias' previous husband), later married to Philip, the king (tetrarch) of Cesarea Philippi (Ant., XVIII, V, 4), who died in 33-34C.E (Ant., XVIII, IV, 6). Why later? Simply, Salome could not have performed a lascivious dance in front of a court of men as a married woman (to a king!) or as a royal widow. That would have been most improper, even scandalous]
` came in and danced, she pleased Herod and his dinner guests. The king said to the girl,
[a married woman or widow could not be called a "girl"]
` At once the girl hurried in to the king ... He presented it to the girl, and she gave it to her mother."
b) Let's consider John's arrest being caused by his opposition to Herod Antipas & Herodias impending wedding. If for any reason, the remarriage had to be delayed (let's say, to have Herod address the situation caused by the planned repudiation and afterwards, the flight of Aretas' daughter, his wife then) and with the ensuing winter preventing Herodias to journey by ship from Rome to Galilee (travelling by ship was much more comfortable and faster than going overland; however, this kind of travel was highly dangerous from October to April, due to the winter storms), then the most logical time for the wedding ceremonies in Galilee would have been around Pentecost (late May to early June).

=> Next: Appendix B: 28 C.E.
In this page, I'll show Jesus' public life lasted one year. Then, independently of those aforementioned findings and following a new line of argumentation (with full evidence backup), I'll demonstrate the year of Jesus' crucifixion was 28C.E.