The Trinity Test was the first atomic device test, detonated in New Mexico, on July 16, 1945. At that time, knowledge of the weapon was classified, and when civilians asked about the obvious explosion, the local air base issued a statement that a remote munitions dump had exploded
Los Alamos National Laboratory marks 20 years without full-scale nuclear testing explains that September 23, 1992, was the last full-scale weapon testing by the United States. There were 1,029 tests before Divider was lowered into the test hole at the Nevada Test Site.
Earlier, in 1991, the Soviet Union had unilaterally announced a moratorium on nuclear testing and Congress passed legislation in September of 1992, calling for a 9-month moratorium on nuclear testing. This has been extended by every U.S. President since.
To replace the testing, the U.S. has invested in large computer modeling to replace live testing.