As I recall you do not salute the PM because he is the PM but because he is a member of the Privy Council.
The paying of compliments is indeed extended to Senior Officers, Coffins, upon entering the office of any commissioned officer (last two regardless of rank), Senior officers of other services and other nations' services, members of the Royal Family and those 'Right Honourable' individuals appointed by Her Majesty to the Privy Council. An appointment to the Privy Council is for life, information on the council can be found at
www.privy-council.org.uk.
Happy Saluting