197xx was made in 1959.
The 357 numbers that year ran from 17301 to 21600.
Do a search on this forum under Trooper and 357 and you'll find quite a bit of info.
"357" is both the caliber and the name of the revolver.
Basically, the 357 was a high-grade version of the Trooper.
Introduced in 1954 and made until 1961, there were only about 15,000 made.
The 357 was intended to be Colt's premium holster revolver, with the Trooper being a "budget" model for law enforcement and people not wanting to spend more money.
When the Super-Premium Python was introduced in 1955, the 357 became the "odd man out".
People wanting the best were buying the Python and people wanting cheaper bought the Trooper.
For this reason, the 357 was discontinued in 1961.
It was a very high grade, quality revolver, and is often called "a poor man's Python", since the Python is really just the 357 with a different barrel, a more polished and tuned action, and a more polished blue job.
Virtually any grip, holster, or other accessory that will fit the Python will fit the 357.