PSMA and TARP Peptide Vaccine With Poly IC-LC Adjuvant in HLA-A2 (+) Patients With Elevated PSA After Initial Definitive Treatment

Inclusion Criteria: * History of histologically confirmed prostate cancer. * Competence to understand the patient information and provide written informed consent, and willingness and ability to return to H. Lee Moffitt Cancer Center for planned treatments and follow-up. * Absence of evidence of metastatic disease by current physical exam or by current imaging studies (computed tomography \[CT\] or magnetic resonance imaging \[MRI\] pelvis, and bone scan within 60 days of first treatment). * Patients not on hormone therapy (stratum "N") must meet all of these: 1. At least 1 year after prostatectomy, definitive prostate radiation, or other definitive-intent local therapy. 2. No testosterone suppression therapy for at least 6 months. 3. PSA at least 1 ng/ml, on 2 measurements, at least 2 weeks apart. 4. Testosterone level \>100 ng/ml, at start ("noncastrate"). * Patients on hormone therapy (stratum "Y") must meet all of these: 1. On treatment with gonadotropin-releasing hormone (GnRH) agonist (or orchiectomy) at least 6 months. 2. testosterone level \<50 ng/ml, at start. 3. PSA at least 1 ng/ml, on 2 measurements, at least 2 weeks apart. * Laboratory values obtained 0-14 days prior to start of therapy: 1. White blood count (WBC) over 3,500/micro L. 2. Platelet count over 100,000 micro L. 3. Hemoglobin over 10.0 g/dL. 4. Serum creatinine up to 2.0 mg/dL. 5. Alkaline phosphatase up to 2.5 x upper limit of normal (ULN). 6. Aspartic transaminase (AST) up to 2.5 x ULN. * Life expectancy at least 6 months. * Eastern Cooperative Oncology Group (ECOG) performance status (PS) 0 or 1. Exclusion Criteria: * Known standard therapy for the patient's disease that is potentially curative. * A known immunodeficiency including HIV. Appropriate trials for individuals with HIV may be considered at a later date. * History of other malignancy besides prostate cancer in the last 5 years, except non-melanoma skin cancer treated with local resection only. (The effect of study treatment on other, potentially dormant malignant diseases is not known). * Use of oral or inhaled or parenteral corticosteroids or of other immunomodulatory drugs within the 60 days of start. \[Use of steroids after start will be considered by the principal investigator (PI) on a case-by-case basis.\] * Use of estrogens (including herbal phytoestrogens) or ketoconazole within 30 days of start, or during the study. * Failure to fully recover to grade 1 or better from effects of prior chemotherapy regardless of interval since last treatment. * Other concurrent chemotherapy, immunotherapy, radiotherapy, or investigational agent in last 30 days (one month washout to start of treatment; patients could register but not start until the washout). * Known hypersensitivity to one or more components of the study medication. * Uncontrolled intercurrent illness including, but not limited to ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac arrhythmia, or psychiatric illness/social situations that would limit compliance with study requirements.