Excellent anaesthetic like 3 perhaps (5,6)
I believe the answer is:
prime number
'3 perhaps' is the definition.
(3 is an example of a prime number)
'excellent anaesthetic' is the wordplay.
'excellent' becomes 'prime'.
'anaesthetic' becomes 'number' (i.e. something that makes things numb).
'prime'+'number'='PRIME NUMBER'
'like' is the link.
(Other definitions for prime number that I've seen before include "Integer divisible only by itself and by 1" , "One such as 3, 5, 7, 11, etc" , "Maybe two or three" , "One with no divisors" , "2011, say" .)