Hello!
In an older book I just read they dated Hammurabi 2123-2081 BC.
A quick Google search for "hammurabi 2123-2081" gives numerous results, but pretty much all of them from google.books.
The way I learned it, and according to modern sources, he reigned in the 1700s BC. I assume at some point the estimate was changed based on new information?
There are various chronological problems associated with the 2nd millennium BCE in the Near East. The so-called "middle chronology" is the most widely accepted, and has been recently supported by high-resolution C14 dating data from Turkey. But the "middle chronology" is "off" by about 100 years, which belong to an unknown period in the 2nd millennium. In other words: there are still a few problems with how it all fits together. The different chronologies are explored nicely in this thesis paper. You can also see Podany in Journal of Near Eastern Studies 73.1 (2014), if you have access. See also here.
But regardless, your date of 2123-2081 BCE for Hammurabi does not seem to fit into any of the currently-accepted chronological sequences. The traditional Middle Chronology, which currently seems to have the most scholarly support, puts Hammurabi's reign at c.1792–1750 BCE.