Looking at the sequence, we note that:

p(p(1)) = 3, p(p(2))  = 5

Now, we know that 2 is the first prime number and 3 is the second prime

number.

So,let us take p(1) = 2 and p(2) =3.
Then, we have:

p(p(1)) = p(2) = 3, and:
p(p(2)) = p(3) = 5, since 5 is the third prime number.

So, conjecturing that p(x) is the xth prime number, we note that:

p(p(3) = p(5) = 11, and similarly:
p(p(4) = 17
p(p(5) = 31
p(p(6) = 41
p(p(7) = 59
p(p(8) = 67

This clearly correspond with the given values.

We now note that:

p(p(9) = p(23) = 83

Consequently, the required missing term is 83.