If we look again at the 3 shell,
The 3 Shell, Reveal
Shells in black, Prime shells in red, Echoes shells in blue
, whose reveal shell is 3×2×1=6, we see
echoes in the 12, 18, 24 and 36 shells. Well
36 is the square of 6. We don’t get an
echo in the 30 shell because it is actually the reveal shell of the 5 shell, 5×3×2×1=30,
which just happens to be the next prime number after 3. So it appears that there are echoes of the reveal shell that
are multiples of the reveal shell up to the next prime number. Thereafter all squares of the reveal of the
prime are echo shells, because a power of any number must have the same factors
as the number it’s a power of.