Sulforaphane in Treating Patients With Recurrent Prostate Cancer

Inclusion Criteria: * Histopathologically or cytologically proven adenocarcinoma of the prostate treated with either a prostatectomy or definitive radiation (external beam or brachytherapy * Protocol-Specific Prostate Working Group 2 (PCWG2) Criteria: rising PSA after definitive therapy * For post surgical patients: the nadir reference value (#1) is the last PSA measured before increases are documented, with subsequent values obtained a minimum of 1 week apart; if the PSA at time point 3 (value #3A) is greater than that at point 2, then eligibility has been met; if the PSA is not greater than point 2 (value #3B), but value #4 is, the patient is eligible assuming that other criteria are met and values 3A or #4 are 1.0 ng/mL or higher * For post radiation therapy patients: the nadir reference value (#1) is the last PSA measured before increases are documented, with subsequent values obtained a minimum of 1 week apart; if the PSA at time point 3 (value #3A) is greater than that at point 2, then eligibility has been met; if the PSA is not greater than point 2 (value #3B), but value #4 is, the patient is eligible assuming that other criteria are met and if values 3A or #4 are 2.0 ng/mL or more above the nadir reference value (#1) according to Phoenix/American Society for Therapeutic Radiology and Oncology (ASTRO) criteria * Eastern Cooperative Oncology Group (ECOG) performance status \<= 2 * The following laboratory results within 4 weeks prior to starting study treatment: * White blood cells (WBC) \>= 3000/mm\^3 * Neutrophil \>= 1,500/mm\^3 * Platelet \>= 100,000/mm\^3 * Serum creatinine =\< upper limit of normal (ULN) * Albumin \> 3.0 gm/dL * Total bilirubin \< 1.5 X ULN * Aspartate aminotransferase (AST) and alanine aminotransferase (ALT) \< 1.5 X ULN * Testosterone level \>= 150ng/dL, and no evidence of progression while on prior hormonal therapy, if applicable (i.e. patient must be non-castrate resistant). * Prior androgen therapy is allowed as long as the patient did not progress while on therapy. * The following imaging scans within 12 weeks prior to starting study treatment: Whole Body Bone Scan: computed tomography (CT) Chest/Abdomen/Pelvis w/ contrast; NOTE: if contrast medium for CT scan is contraindicated for the patient, documentation of this is required and a CT scan with contrast will not be required; subject still must obtain a CT without contrast, though. * Willingness to use effective contraception by study participants or their female partners throughout the treatment period and for at least 2 months following treatment * Signed informed patient consent and Health Insurance Portability and Accountability Act (HIPAA) within 3 months prior to starting treatment Exclusion Criteria: * Significant active medical illness which in the opinion of the investigator would preclude protocol treatment * Measurable and/or evaluable recurrent prostate cancer by imaging (CT scan of the chest, abdomen, and pelvis and bone scan performed within 12 weeks prior to starting treatment) or by physical exam * Prior investigational therapy within 30 days prior to starting study treatment * Prior treatment with a known histone deacetylase inhibitor (including but not limited to valproic acid, suberoylanilide hydroxamic acid \[SAHA\],Panobinostat (LBH589), etc) within 6 months prior to starting study treatment or while on study therapy * Concurrent systemic treatment for prostate cancer * Current treatment with warfarin * Gastrointestinal ailments which would interfere with the ability to adequately absorb sulforaphane * Allergy to cruciferous vegetables * Any condition which, in the opinion of the study clinician, would make participation in the study harmful to the patient