One of the most positive proofs for the most likely correct form of the Hebrew text in the first century is Josephus: for although people often assume that he is simply using the LXX-Septuagint in his Antiquities, especially when it comes to the genealogies of the antediluvian patriarchs and the flood narrative, that is not what he himself claims. He plainly states in several different places that he is translating the Hebrew scriptures of his day into the Greek tongue or language.
That is a huge difference from what is generally, mistakenly, assumed: for if indeed this is true then it means that his Hebrew text must have contained the same numbers for the genealogies of the antediluvian patriarchs and the flood narrative which are still found in the Septuagint, the only exception being the begetting ages of Methuselah and Lamek, which are corrupted in the majority text of the OG LXX but still found in other lesser extant LXX texts, (the correct readings are not in the OG LXX because it also is a composite or morph text like our modern N/T Greek texts). Josephus also confirms that the Hebrew scriptures contained a history of five thousand years in his day.
“But let no one blame me for writing down everything of this nature,
as I find it in our ancient books; for as to that matter, I have plainly assured those that think me defective in any such point, or complain of my management, and have told them, in the beginning of this history,
that I intended to do no more than translate the Hebrew books into the Greek language, and promised them to explain those facts, without adding anything to them of my own, or taking anything away from them.” (Josephus, Antiquities 10:218)
“I suppose that, by my books of the Antiquities of the Jews, most excellent Epaphroditus, I have made it evident to those who peruse them, that our Jewish nation is of very great antiquity, and had a distinct subsistence of its own originally; as also I have therein declared how we came to inhabit this country wherein we now live.
Those Antiquities contain the history of five thousand years,
and are taken out of our sacred books;
but are translated by me into the Greek tongue.” (Josephus, Against Apion 1.1)
Josephus, Antiquities, Book 1, Chapter 3:3-4
3.
This calamity happened in the six hundredth year of Noah's government, in the second month, called by the Macedonians Dius, but by the Hebrews Marchesuan: for so did they order their year in Egypt. But Moses appointed that Nisan, which is the same with Xanthicus, should be the first month for their festivals, because he brought them out of Egypt in that month: so that this month began the year as to all the solemnities they observed to the honor of God, although he preserved the original order of the months as to selling and buying, and other ordinary affairs. Now he says that this flood began
on the twenty-seventh day of the forementioned month; and this was
two thousand six [
two]
hundred and fifty-six years from Adam, the first man;
and the time is written down in our sacred books, those who then lived having noted down, with great accuracy, both the births and deaths of illustrious men.
4.
For indeed Seth was born when Adam was in his two hundred and thirtieth year, who lived nine hundred and thirty years.
Seth begat Enos in his two hundred and fifth year; who, when he had lived nine hundred and twelve years, delivered the government to Cainan his son,
whom he had in his hundred and ninetieth year. He lived nine hundred and five years. Cainan, when he had lived nine hundred and ten years, had his son Malaleel,
who was born in his hundred and seventieth year. This Malaleel, having lived eight hundred and ninety-five years, died, leaving his son Jared,
whom he begat when he was in his hundred and sixty-fifth year. He lived nine hundred and sixty-two years; and then his son Enoch succeeded him,
who was born when his father was one hundred and sixty-two years old. Now he, when he had lived three hundred and sixty-five years, departed and went to God; whence it is that they have not written down his death. Now Mathusela, the son of Enoch,
who was born to him when he was one hundred and sixty-five years old,
had Lamech for his son when he was one hundred and eighty-seven years of age; to whom he delivered the government, when he had retained it nine hundred and sixty-nine years. Now Lamech,
when he had governed seven hundred and seventy-seven years, appointed Noah, his son, to be ruler of the people,
who was born to Lamech when he was one hundred and eighty-two years old, and retained the government nine hundred and fifty years.
These years collected together make up the sum before set down. But let no one inquire into the deaths of these men; for they extended their lives along together with their children and grandchildren; but let him have regard to their births only.
The statement
two thousand six hundred and fifty six years from Adam in the above cannot be correct, and is the only thing necessary to be corrected in the text, (which I have done here), because it cannot be true when the rest of the numbers in the passage are added together. The correct number is two thousand two hundred and fifty six years from Adam, which, when the numbers having been changed in the Masoretic Hebrew text are added back in, is the correct number: for six hundred years were removed from the genealogy of the antediluvian patriarchs in the Hebrew text of Genesis 5, which now amounts to one thousand six hundred and fifty six years from Adam to the flood, (1656+600=2256).
The overall point here is that Josephus states that he himself was translating the Hebrew text of his day and the numbers he says were in the text agree with the LXX-Septuagint all the way through up to the begetting ages of Methuselah and Lamek. That's the important part because that is the portion where six hundred years appear to be missing from the modern Hebrew text.
@HARK!
As for the OP, when Kainan the son of Arphaxad is included in the text of the Genesis 11 genealogy, the chronology from the birth of Henok to 70AD is 4,900 years, that is, seventy generations, or one hundred Yoblim, or the ten great weeks of Henok.
70*70 = 4,900
100*49 = 4,900
10*490 = 4,900
The Luke genealogy is therefore correct, and just as the Lukan genealogy shows, there are seventy generations from Henok to Meshiah when Kainan the son of Arphaxad is included, and seventy-seven generations from Adam to Meshiah. The Luke genealogy is perfect, (numerically speaking), and the LXX is also correct, and Kainan the son of Arphaxad must be included.