Mathematicians:

"1 is prime, 3 is prime, 5 is prime, 7 is prime; the proof follows by induction"

Physicists:

"1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is experimental error, 11 is prime, 13 is prime, 15 is experimental error, 17 is prime, 19 is prime; the empirical evidence is overwhelming."

Engineers:

"1 is odd, 3 is odd, 5 is odd, 7 is odd, 9 is odd, 11 is odd, 13 is odd, 15 is odd, 17 is odd, 19 is odd, ..., 111 is odd, ..."

Psychologists:

"1 is prime, 3 is prime, 5 is prime, 7 is prime, 9 is latently prime but repressing it, 11 is prime, ..."

Computer scientists:

"1 is prime, 3 is prime, 5 is prime, 7 is prime, 7 is prime, 7 is prime, 7 is prime, 7 is ..."

I created this nodeshell upon remembering the joke, wishing to fill it after I finished my "research" - the research involving calling up the friends who were there when this joke was told for the hundredth time, and everyone put in their 2 cents worth. And ariels comes and beats me to it. So I shall just add the less obvious ones:

Economist:
Assume 9 is prime...

Pentium user:
1 is prime, 3 is prime, 5 is prime, 7 is prime, 8.999983 is prime...

Unix user:
1 is prime, 3 is prime, 5 is prime, 7 is prime, ... Segmentation fault, Core dumped.

ZX-81 user:
1 is prime, 3 is prime, Out Of Memory.

Undergraduate:
Let p be any prime number larger than 2. Then p is not divisible by 2, so p is odd. QED

English major:
What's a prime number?

Athletic scholarship:
What's a number ?

Statistician:
Let us take a sample of odd numbers: 7, 13, 29, 37, 53 and 71 are prime. They are all prime, so all odd numbers must be prime.