Primeful Heterosquares

Problem: http://www.primepuzzles.net/coll20th/coll20th-003.htm (sub-problem 2.)[br]Forum (Russian): https://dxdy.ru/post1319514.html#p1319514[br]Input format: {{X,X,X,X},{X,X,X,X},{X,X,X,X},{X,X,X,X}}[br]Examples: {{7,9,27},{5,13,49},{1,15,3}}, {{24,83,25,59},{21,1,40,9},{3,17,44,15},{41,30,114,14}}

Information: Primeful Heterosquares