primus in AL locks?

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Refer to table 1 for the list of Schlage AL-Series cylinders.     AL-Series Cylinder Reference Table    Function  Cylinder Mechanism   Complete Cylinder   Non-Hotel Functions  ...
When you want to periodically disable and block access to a certain room in a building or an entrance door, that’s when you would need to use a Lockout Cylinder. See full document.
The Primus cylinders are not designed to fit into the F locks.  They are too long and the tailpiece is oriented differently.
The ND85/AL85/A85 hotel lock is only available in a conventional Key-in-Lever cylinder.  Interchangeable core and Primus are not available with this function. 
A Primus Hotel cylinder (as well as an IC hotel cylinder) is not possible because there isn't enough room inside the cylinder for all of the required components.