A Münchhausen number equals the sum of its digits each raised to the power of itself: \(3435 = 3^3 + 4^4 + 3^3 + 5^5 = 27 + 256 + 27 + 3125\). Using the convention \(0^0 = 0\), the only two in base 10 are 1 and 3435.
The name, coined by Daan van Berkel in 2009, alludes to Baron Münchhausen, who famously pulled himself out of a swamp by his own hair (or bootstraps) — the number "raises itself." Like the [[narcissistic]] numbers and [[factorion]]s, the family is provably finite because digit powers can't keep pace with a number's magnitude.