Taking a closer look at The 3 Shell, Reveal Shells in black, Prime shells in red, Echoes shells in blue , we have:


1.  Prime shells in red.
2.  Squares of primes in green.
3.  Reveal shells in black.
4.  Echo shells in blue and cyan.
5.  The shells that are left, the yellow ones, reveal that shells Co-Primes.

In a sense all shells reveal co-primes.

1.  When the shell is prime, it is because it is co-prime with all the other numbers below it except 1.
2.  Squares of primes (green shells) follow the same rule as for yellow shells.
3.  Reveal shells are co-prime with only primes up to the value of the square of the prime number following it's highest prime factor.
4.  Echo shells follow the same rules as for Reveal shells.