# Are satellite knots prime?

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?

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By the definition of "prime", any knot that isn't a connected sum is prime. –  Jim Belk Jul 9 '11 at 17:11
I should clarify that what I meant was 'obtained by the standard connected sum construction'. My question therefore was whether a satellite construction, different from the 'trivial' connected sum construction, could ever yield a connected sum. –  Aru Ray May 9 '12 at 21:41