core city vs principal city

core city

noun

  • Synonym of central city (“the main city of a metropolitan area; particularly one containing multiple cities”). 

  • Used other than figuratively or idiomatically: see core, city. 

principal city

noun

  • Synonym of central city (“the main city of a metropolitan area; particularly one containing multiple cities”). 

  • Used other than figuratively or idiomatically: see principal, city. 

How often have the words core city and principal city occurred in a corpus of books? (source: Google Ngram Viewer )