Internal Medicine providers are located in Hampton, Epping & Exeter, NH. View All Internal Medicine Providers Accepting New Patients>. Call 603-775-0000 (M-F 7am-7pm, Sat-Sun 7am-3:30pm) or your regular Core PCP office number. Press 1 to speak with a triage nurse. Press 2 to request a medication refill. Press 3 for an insurance referral..