Question

does prime number include 1

Answer 1

No 1 is not prime number nor composite number

Answer 2

The number one is far more special than a prime!  It is the unit (the building block) of the positive integers, hence the only integer which merits its own existence axiom in Peano's axioms.  It is the only multiplicative identity (1·a = a·1 = a for all numbers a).  It is the only perfect nth power for all positive integers n.  It is the only positive integer with exactly one positive divisor.  But it is not a prime