He didnt explicitly mention David, but he did mention David's son, Solomon, so was there 1000 years between David and his son Solomon?
A quick way for you to solve this for yourself is to search the Internet for Bishop Ussher, and bible chronology.
But it is generally accepted that there was 4000 years from creation to Jesus, Ussher gives a creation date of 4004 BC.
If you take the Bible literally, this makes the universe and eveything in it just over 6000 years old. of course, but most level headed people, Christian and non-christian, reject this absurdity.
Brian.