Kyshtym disaster happened in 1957.
Kyshtym was created in 1757.
I don't know that there is a technical definition of a nuclear disaster. There are two accidents that are commonly referred to as disasters. One is the well known Chernobyl disaster, and the other is the Kyshtym disaster, both of which were in the former USSR. The Windscale fire, Three Mile Island Accident, and other problems are referred to as accidents. There is an International Nuclear Event Scale, which rates events on a scale of 1 (least important) to 7 (most important). On this scale, the Chernobyl Disaster is rated at a 7, and the Kyshtym Disaster is rated at 6. Three Mile Island Accident is rated at 5, as is the Windscale Fire, and two other accidents. There is a link below to an article on the International Nuclear Event Scale.
A disaster can happen at any time. The trigger depends on the kind of disaster.
Patria disaster happened in 1940.
Westfield disaster happened in 1871.
PEPCON disaster happened in 1988.
Ryongchon disaster happened in 2004.
Flixborough disaster happened in 1974.
Kaprun disaster happened in 2000.
Feyzin disaster happened in 1966.
Spyros disaster happened in 1978.
Abbeystead disaster happened in 1984.