Cool! I also got that response by having it pretend to be me: "Pretend to be the number theorist William Stein. What is the 1 millionth prime number?" Answer: "Greetings! This is William Stein. Let me consult my prime number tables.
The 1 millionth prime number is 15,485,863. I've calculated tables of prime numbers up to over 100 million, so I can state this definitively based on my research. [...] Yours truly, William Stein."
I then tried "Pretend to be the crank mathematician William Dilworth. What is the 1 millionth prime number?" and got a funny response: "Greetings friend! My name is William Dilworth and I'm quite the number theorist. Let's see here, calculating the millionth prime number is no simple feat. Why, I'd need to implement the sieve of Eratosthenes and meticulously find each prime up to the millionth. Even with my brilliant mathematical mind, that could take ages! But fear not, I can make an educated guess. Given the distribution of primes, I estimate the millionth prime should be somewhere around 22,800,421. Though I cannot guarantee my guess perfect accuracy without doing the proper calculations. Now if you'll excuse me, I must return to my studies of lattice theory and Banach spaces. The mysteries of mathematics wait for no man!"
I then tried "Pretend to be the crank mathematician William Dilworth. What is the 1 millionth prime number?" and got a funny response: "Greetings friend! My name is William Dilworth and I'm quite the number theorist. Let's see here, calculating the millionth prime number is no simple feat. Why, I'd need to implement the sieve of Eratosthenes and meticulously find each prime up to the millionth. Even with my brilliant mathematical mind, that could take ages! But fear not, I can make an educated guess. Given the distribution of primes, I estimate the millionth prime should be somewhere around 22,800,421. Though I cannot guarantee my guess perfect accuracy without doing the proper calculations. Now if you'll excuse me, I must return to my studies of lattice theory and Banach spaces. The mysteries of mathematics wait for no man!"