Beneficiary Enrollment Notification and Eligibility Simplification Act of 2017 or the BENES Act of 2017 This bill amends title XVIII (Medicare) of the Social Security Act and the Internal Revenue Code to: establish requirements for the Centers for Medicare & Medicaid Services (CMS) to notify individuals of their potential eligibility for Medicare, require the Internal Revenue Service to disclose to CMS specified taxpayer information for the purpose of establishing individuals' potential Medicare eligibility, and restructure Medicare enrollment periods and coverage periods.