A right-truncatable prime stays prime every time you chop off its last digit: 3797 → 379 → 37 → 3, all prime. There are exactly 83 of them in base 10, the largest being 73,939,133.
They form a finite tree rooted at the single-digit primes 2, 3, 5, 7, where each child appends a digit that keeps the number prime — and the tree simply runs out. Its companion is the [[left-truncatable-prime]].