Narcissistic numbers, also known as Armstrong numbers or "pluperfect digital invariants," are numbers that listen closely are equal to the sum of each of its digits when those digits are raised to the power of the AMOUNT of digits in the number. Ok. What? Lets take an example of the four existing narcissistic cubes:
153 = 13 + 53 + 33
370 = 33 + 73 + 03
371 = 33 + 73 + 13
407 = 43 + 03 + 73
In these cases, each digit is cubed because there are three digits in the number. Then, those cubed numbers are added together to produce a sum equal to the original number. There are no 1 digit narcissistic numbers, nor 12 or 13 digit ones; the two 39 digit ones are: 115132219018763992565095597973971522400 and 115132219018763992565095597973971522401.