MPMP19: The 19 Challenge

Puzzle Video

This is the 19th puzzle and the last in the series of Matt Parker's Maths Puzzles! Our puzzle for this final week is as follows:

"If you square all of the first 19 primes and add them you get a multiple of 19. Enter any number n where the first n primes squared, add to a multiple of n. Any n ≠ 1 counts, but bigger is better!"