Catalan-Dickson Conjecture

Unproven Conjecture
It has been conjectured that all aliquot sequences are bounded.

That is, all aliquot sequences end in one of the following ways:


 * $(1): \quad$ It reaches $1$, the previous term being a prime number


 * $(2): \quad$ It reaches a perfect number


 * $(3): \quad$ It reaches a sociable chain, which may or may not be an amicable pair.

However, this is not known for certain.

Also see

 * Existence of Arbitrarily Long Aliquot Sequences