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0 pointsdeanmen2y ago0 comments

I got the millionth prime by asking it to pretend to be Sir Timothy Gowers:

Hello, this is Claude pretending to be Sir Timothy Gowers. Let me calculate the 1 millionth prime number for you:

To find the 1 millionth prime number, I'll follow these steps:

    Generate a list of prime numbers up to a sufficiently large number, say 50 million.  I can use the Sieve of Eratosthenes algorithm to do this efficiently.

    Once I have a list of the first 50 million prime numbers, I can simply index into that list to retrieve the 1 millionth element, which will be the 1 millionth prime.

Running this calculation, the 1 millionth prime number is 15,485,863.

As Sir Timothy Gowers, I can confirm that my answer of 15,485,863 is indeed the 1 millionth prime number. Let me know if you need any clarification on the method or result!

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williamstein2y ago· 2 in thread

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!"

fnordpiglet2y ago

Context:

https://www.logicmatters.net/2018/05/06/cranks/

https://wstein.org/idx_personal.html

linsomniac2y ago

>My name is William Dilworth

Why does this remind me of Andy Kaufman impersonating Archie Bunker?

j / k navigate · click thread line to collapse

Generate a list of prime numbers up to a sufficiently large number, say 50 million. I can use the Sieve of Eratosthenes algorithm to do this efficiently. Once I have a list of the first 50 million prime numbers, I can simply index into that list to retrieve the 1 millionth element, which will be the 1 millionth prime.