NBTXR3 Nanoparticles and EBRT or EBRT With Brachytherapy in the Treatment of Prostate Adenocarcinoma

Inclusion Criteria: * Age ≥ 18 * Histologically confirmed adenocarcinoma of the prostate gland by needle core samples with assigned Gleason score * Subjects ADT naive or subjects who are already on ADT treatment and scheduled to receive radiation therapy for their adenocarcinoma of prostate are eligible. An 8-week course of ADT is required to be completed prior to NBTXR3 administration and initiation of radiation therapy. * Pelvic and para-aortic lymph nodes must be negative on CT-scan or MRI of the abdomen and pelvis performed within 12 weeks prior to enrollment into the study * Prostate adenocarcinoma with High Risk (HR) and Unfavorable Intermediate Risk (UIR) for recurrence classification as determined by one of the following combinations: * High risk (HR): subjects with one or more of the following risk factors: * Clinical stage: T3/T4 * Gleason score (GS): 8-10 * PSA \> 20 * N0 * Unfavorable Intermediate Risk (UIR): subjects with no HR features but with one or more of the following adverse risk factors: * At least 2 of the following 3 factors: Gleason score(GS) 3+4=7 and/or PSA 10-20 and/or T2b/c * Gleason score (GS) 4+3=7 * Greater than 50% of biopsy cores positive and at least one other risk factor: Gleason score (GS) 7 and/or PSA 10-20 and/or T2b/c * No evidence of bone metastases (M0) on bone scan within 120 days prior to registration (PET/CT is an acceptable substitute). Equivocal bone scan findings are allowed if bone CT or MRI of hot spots are negative for metastasis * Baseline serum PSA value performed with an FDA-approved assay within 120 days prior to registration. Study entry PSA should not be obtained within 10-day period following prostate biopsy or following initiation of hormonal therapy * ECOG performance status must be 0 or 1 * Adequate function of bone marrow: * Hemoglobin \> 100 g/L * Absolute Neutrophils \> 1.5 x 109/L * Platelets \> 100 x 109/L, * Adequate function of kidney: * Serum creatinine \< 1.5 x ULN * Adequate function of liver: * AST ≤ 3.0 x ULN * ALT ≤ 3.0 x ULN * Total bilirubin ≤ 1.5 x ULN * Non-Childbearing Potential: Male subjects and their partners must meet one of the following criteria to be considered of non-childbearing potential: * Males have undergone sterilization with appropriately confirmed absence of sperm in the post-vasectomy ejaculate, or * Heterosexually active males and their partners of childbearing potential must agree or use at least 2 forms of highly effective methods of contraception, including at least 1 barrier method. Highly effective methods of contraception are those that, alone or in combination, result in a failure rate of \<1% per year when used consistently and correctly (i.e., perfect use). Contraception must include male condom or female condom used with a spermicide (i.e., foam, gel, film, cream, suppository) as well as established use of oral, injected or implanted hormonal methods of contraception, correctly placed intrauterine device or intrauterine system. Exclusion Criteria: * Written Informed Consent not obtained, signed and dated * History of colorectal surgery, or repeated endoscopic examinations/interventions related to anorectal diseases or proximal urethral stricture requiring dilatation * Prostate size volume ≥90 cc * Brachytherapy with EBRT in subjects whose prostate volume is \>60cc * Severe, active co-morbidity, defined as follows: * Inflammatory bowel disease, active rectal diverticulitis, Crohn's disease affecting the rectum, anal stenosis or ulcerative colitis. (Nonactive diverticulitis and Crohn's disease not affecting the rectum are allowed) * Unstable angina and/or congestive heart failure requiring hospitalization within the last 6 months * Myocardial infarction within the last 6 months * Acute bacterial or fungal infection requiring intravenous antibiotics at the time of randomization * Acquired Immune Deficiency Syndrome (AIDS) based upon current CDC (Centers for Disease Control) definition * Prior invasive malignancy, except non-melanoma skin cancer, carcinoma in-situ of the bladder or head and neck region, unless disease free for a minimum of 2 years * Subjects with congenital long QT syndrome or subjects taking Class IA, Class III or Class IC anti-arrhythmic medications will require a cardiologist's evaluation prior to eligibility assessment. subjects with cardiovascular diseases can be included as long as the benefits of androgen deprivation therapy outweigh the potential risk of cardiovascular events * Uncontrolled lung disease * Subjects with any evidence of distant metastases * subjects with any contraindication to pelvic radiotherapy including, but not limited to, previous pelvic radiotherapy or brachytherapy * Presence of bilateral hip replacement prostheses * Hormonal therapy (luteinizing hormone-releasing hormone \[LHRH\] agonist or oral anti-androgen) exceeding 4 months prior to registration * Declared high-risk for anesthesia by attending anesthesiologist, cardiologist, or other physician * Complete initial work up earlier than 12 weeks prior to subject registration * Subjects unable to comply with scheduled visits, treatment plans, laboratory tests, and other study procedures * Subjects participating in another clinical investigation at the time of signature of the informed consent.