Which satellite knots are prime?
I do know that connected sum of knots is a satellite operation, but I found this statement:
"the satellite knots all have structures which are well known and documented..., and their primality follows from a simple geometric argument"
(from Hoste, J.; Thistlethwaite, M.; and Weeks, J. "The First 1,701,936 Knots." Math. Intell. 20, 33-48, Fall 1998.)
Presumably they mean that all satellite knots that are not connected sums are prime?