was this part of a larger project?
Yes, the Manhattan Project.
Trinity (nuclear test)
Trinity was the code name of the first detonation of a nuclear device. It was conducted by the United States Army at 5:29 a.m. on July 16, 1945, as part of the Manhattan Project. 
when was the first atomic bomb successfully tested July 16, 1945 what was it called? The code name given was Trinity who tested it? The United States Army where was it tested? In the Jornada del Muerto desert about southeast of Socorro, New Mexico.
wiki:5358132
Trinity (nuclear test) [SEP] Introduction
A rehearsal was held on May 7, 1945, in which of high explosive spiked with radioactive isotopes were detonated. The Gadget's detonation released the explosive energy of about . Observers included Vannevar Bush, James Chadwick, James Conant, Thomas Farrell, Enrico Fermi, Richard Feynman, Leslie Groves, Robert Oppenheimer, Geoffrey Taylor, Richard Tolman and John von Neumann.