Health Centers Nathan Littauer Hospital. Health (4 days ago) Gloversville Primary Care Center, 8:00 am -4:30 pm Saturdays and Sundays. 99 East State Street, Gloversville, NY 12078. Call 518-773-5690 for more information or to book an appointment. The Nathan Littauer Primary/Specialty Care Centers provide care for the whole family. Our 12 conveniently located centers offer a range of services and.