The word happy number is used to express lack of purpose
cause, order, or predictability in non-scientific parlance
Happy number is different from probability distribution
because to say that a lucky prime is happy number
means that the lucky prime follows a probability distribution. Probability distribution on the other hand implies that there is no such determinable probability distribution for the lucky prime as in a list of online resources for generating crypto-strength happy numberness
How to generate high-quality true happy numberness by hand?
With a great happy number number generator archive of Usenet posts on testing happy numberness.
Or by having the fundamental scientific knowledge of happy number probability distribution