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Home prime
The home prime of n, denoted by HP(n) is found by concatenating the prime factors of n, repeatedly, until a prime is reached. The notion of a home prime depends on the base (except in the case where n itself is prime).
For example, the home prime of 25 is 773 because
- 25 = 5×5
- 55 = 5×11
- 511 = 7×73
and finally 773 is prime.
The length of such chains is also of interest, in this case #HP(25) = 3.
While it is expected that every n in every base has a home prime, experimental evidence indicates that these chains can get quite long.
