Angry airmen fly public in prime locations (6)

I haven't cracked this one yet — but the brilliant team at Fifteensquared have:

I was in despair of ever parsing this, when solving at 3.00am, because the wordplay seemed to bear no relation to the answer but, after some sleep in between and some further staring, I spotted that the letters of the answer were, in fact, in order in the wordplay at 2, 3, 5, 7, 11 and 13 (prime locations): A IR M E N F LY P U B L IC – I think this has to be my top favourite clue