68Ga-PSMA-11 Patients With Newly Diagnosed and Recurrent Prostate Cancer (Firefly)

Inclusion Criteria: * Males greater than 18 years of age. * Histologically proven adenocarcinoma of the prostate. Diagnosis must be stated in a pathology report and confirmed by the investigator. * Patients must meet the criteria of one of the following cohorts: Cohort A: (n=225) Biochemical recurrence; defined as any of the following: * PSA ≥ 0.2 ng/mL and rising in at least two consecutive tests (at least one week apart) within 6 months of date of consent for patients treated with radical prostatectomy. * PSA \>2.0 ng/mL above the nadir and rising post-radiation (external beam or brachytherapy) +/- hormones, in at least 2 consecutive tests (at least one week apart) within 6 months of consent * In patients with no prior definitive surgery or radiation, PSA ≥ 2 ng/mL greater than the post therapy nadir after androgen deprivation therapy. Note: Patients whom have had more than one prior therapy, should be defined recurrent by their most recent therapy type. For patients who have had any ADT, are mCRPC, shall fall into that category for allocation and eligibility. Cohort B: (n=75) No prior treatment defined as one of the following: o Patient has primary diagnosis of "high risk" or "very high risk" localized prostate cancer, or regional prostate cancer (TxN1M0) or oligometastatic cancer (TxNXM1) with less than three metastatic lesions by conventional imaging) and has not received prior treatment. Note: high risk/very high risk is denoted by Gleason 8-10, or PSA \>20, or clinical stage T3a/T4 disease (see NCCN guidelines v1.2020). Patients in this cohort must be considered candidates for initial definitive therapy at the time of study enrollment. * Life expectancy of \>6 months * Patients should have a Comprehensive Metabolic Panel, PSA, and Testosterone drawn within 4 weeks of imaging Exclusion Criteria: * Claustrophobia or any other condition that would preclude PET/CT imaging. * Patients with known metastatic prostate cancer, with 4 or more lesions on conventional imaging