As 357.686.312.646.216.567.629.137
is the biggest left truncatable prime
the height of the new primality tree
is 24.
So we have a finite tree
because all the after paths
are shorter.
By the way,
this is a method
to discover
Henry VII primes
but also
Russian doll primes
and you can see
that a game
can be related
to history.