The claim is that Newton figured out the dates from the Book of Daniel. The book of his about his conclusions was published in 1733 (he died in 1727) and is available in different formats:
One author (Matania Z. Kochavi) writes that it can be seen that Newton wrote that believing he was personally chosen to understand the hidden code in the Bible, and when and how there will be the Second Coming of Christ, and "end of times" based on such logic like "flowing water represented a friendly encounter, whereas a flood symbolized war; similarly, a single boat sailing at sea was an image of friendship, whereas a flotilla represented a battle." or "three sets of symbols" "appeared in various places throughout the text. One set was composed of metals: gold, silver, copper, and iron. The second set used symbols from the animal kingdom: the lion, bear, leopard, and the "Fourth Beast." The third set made use of the ram and the goat."
Amazon:
https://www.amazon.com/Observations-Upon-Prophecies-Daniel-A...
1733 original:
https://archive.org/details/observationsupon1733newt
Some PDF version:
http://www.historicism.com/Newton/newton.pdf
One author (Matania Z. Kochavi) writes that it can be seen that Newton wrote that believing he was personally chosen to understand the hidden code in the Bible, and when and how there will be the Second Coming of Christ, and "end of times" based on such logic like "flowing water represented a friendly encounter, whereas a flood symbolized war; similarly, a single boat sailing at sea was an image of friendship, whereas a flotilla represented a battle." or "three sets of symbols" "appeared in various places throughout the text. One set was composed of metals: gold, silver, copper, and iron. The second set used symbols from the animal kingdom: the lion, bear, leopard, and the "Fourth Beast." The third set made use of the ram and the goat."