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I realize it would be an incredible long-shot, but I wonder if anyone will ever find an amulet that also has four eights in a different hash function.
Four eights in SHA-256 plus four eights in (say) MD5 is just as likely as eight eights in SHA-256, at least if each hash function is truly a good approximation of a pseudo-random function.

(In fact, since the definition didn't specify where the eights are, and they can be anywhere in the output, I think four eights in each of two different hash functions is more likely, because there's more total output digits in which to look for them.)

Edit: If you don't specify the other hash function in advance, it's even more likely, because you can first find your SHA-256 amulet and then keep searching for a hash function in which it is also an amulet, where you might have a dozen or two potential choices that amulet-viewers might find interesting or impressive, each of which gives a new roughly independent space of possible amuletness.

No examples?

  $ echo -n "If you can't write poems,
  > write me" | sha256sum
  9a120001cc88888363fc67c45f2c52447ae64808d497ec9d699dba0d74d72aab  -