Prime Grid

Hermione enjoys math and painting. She specifically likes prime numbers. She recently thought of something new. Given a square paper with side length $n$, she will drop ink blots on every prime number in that square. An ink blot covers that location along with the 8 locations directly by it. The top left of the square is 0, and the bottom right is $n^2 - 1$. Given the side length of the square, ca