Under the Continuum Hypothesis all nonreflexive Banach space ultrapowers   are primary
  In this note a large class of primary Banach spaces is characterized. Namely, it will be demonstrated that under the Continuum Hypothesis the ultrapower of any infinite dimensional nonsuperreflexive Banach space is always primary. Consequently, any infinite dimensional nonsuperreflexive Banach space can be isometrically embedded into its primary ultrapowers. 
Piotr Wilzcek
math.LO math.FA