Luke 3:35-37 gives a genealogy listing Noah to Shem, to Arphaxad, to Kenan, to Shelah, to Eber. But if you look in Genesis 11:5, genesis 10:

But if you look in the three places where this genealogy is written in the Old testament, Genesis 10:24, Genesis 11:5, or 1 Chronicles 1:18, the name “Kenan” does not appear – the genealogy is Noah, Shem, Arphaxad, Selah, Eber. ]

Therefore Luke (and by extension) the entire Christian Bible is not divinely inspired.

As it turns out, this isn't Luke's fault per-se. Luke was a Greek historian and relied exclusively on the Septuagint (as did Paul). In the Septuagint – which just a brand-name for any Greek translation of the bible – there is a copyist error(!!). The error is described in "An Extra Cainan", but in short if you look at the Greek (which does not have spaces or letters) it is easy to read the phrase “son of Kenan” between the other words of the text, kind of like an optical illusion. Nevertheless, the Septuagint contains this genealogy repeated 3 times (Genesis 5, 11, Chronicles 1) so it is not entirely satisfying that this was entirely a copyist error.

The page at https://sites.google.com/site/errorsinthebible/septuagint-errors/who-is-cainan confirms the idea, confirming that “the extra Cainan in Genesis 11 is found only in manuscripts of the LXX that were written long after Luke’s Gospel. The evidence shows conclusively that the extra name Cainan is not part of God’s original Word, but due to a later copyist’s error. The oldest LXX manuscripts do not have this extra Cainan.”

When the 72 rabbis translated the Septuagint it was done under duress (under pain of death). Therefore in the translation several changes were made in order to separate the Septuagint from the Hebrew scriptures. Likely in order to cause the Septuagint to be invalid for purposes of teaching. One example of this is how the conversation between Cain and Abel is corrupted; in the Septuagint it says “Come, let us go out into the field…” while in the Masoretic text it only sates And Cain said “…”.

God's Promises Require that the Hebrew Masoretic Text is Correct, not the LXX, in Genesis 5 and 11. The Christian answer is below, but I will add first some scriptural answers:

• “The grass withers and the flowers fall, but the word of our God stands forever.” (Isaiah 40:8).

• “This Book of the Law shall not depart from your mouth, but you shall meditate on it day and night, so that you may be careful to do according to all that is written in it.” (Joshua 1:8)

In Christian Biblical truth, there is the doctrine of Preservation of Scripture.

• Matthew 5:18 (Also see Luke 16:17)
  • “For verily I say unto you, Till heaven and earth pass, one jot [the Hebrew letter yod, the smallest Hebrew consonant] or tittle [the chireq, the smallest Hebrew vowel] shall in no wise pass from the law, till all be fulfilled.”

• “Heaven and earth will pass away, but My words will by no means pass away” (Mark 13:31; Matthew 24:35).

• “This gospel of the kingdom will be preached in all the world as a witness to all the nations, and then the end will come” (Matthew 24:14)
• “the gospel must first be preached to all the nations” (Mark 13:10)

These imply that the masoretic text is correct, because Jesus refers to the Hebrew letters. (Note: The discovery of the Dead Sea scrolls in 1947 confirmed that we still have the same Old Testament as they did at Jesus’s day. The survival of thousands of New Testament manuscripts confirms that the New Testament writings were also providentially preserved. The question among textual scholars is not whether some words are missing, but which variant readings, in a few minor cases, are the correct ones.)