Any positive integer n can be written uniquely as:
n = k2 + j, where k = floor(sqrt(n)) and j = n - k2.
Shell k is the interval k2 to (k+1)2 - 1 (so, j = 0 to 2k).
Plotted as X = k and Y = j here, endpoints of columns/shells where k>1 are composite.
This is useful for puzzles involving primes between squares.