A few days in the past, I used to be interested by what you wanted to know to make use of ChatGPT (or Bing/Sydney, or any comparable service). It’s straightforward to ask it questions, however everyone knows that these giant language fashions incessantly generate false solutions. Which raises the query: If I ask ChatGPT one thing, how a lot do I must know to find out whether or not the reply is appropriate?
So I did a fast experiment. As a brief programming undertaking, a variety of years in the past I made a listing of all of the prime numbers lower than 100 million. I used this listing to create a 16-digit quantity that was the product of two 8-digit primes (99999787 instances 99999821 is 9999960800038127). I then requested ChatGPT whether or not this quantity was prime, and the way it decided whether or not the quantity was prime.
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ChatGPT appropriately answered that this quantity was not prime. That is considerably stunning as a result of, in the event you’ve learn a lot about ChatGPT, you understand that math isn’t one among its robust factors. (There’s most likely an enormous listing of prime numbers someplace in its coaching set.) Nevertheless, its reasoning was incorrect–and that’s much more fascinating. ChatGPT gave me a bunch of Python code that carried out the Miller-Rabin primality take a look at, and stated that my quantity was divisible by 29. The code as given had a few fundamental syntactic errors–however that wasn’t the one drawback. First, 9999960800038127 isn’t divisible by 29 (I’ll allow you to show this to your self). After fixing the plain errors, the Python code seemed like an accurate implementation of Miller-Rabin–however the quantity that Miller-Rabin outputs isn’t an element, it’s a “witness” that attests to the very fact the quantity you’re testing isn’t prime. The quantity it outputs additionally isn’t 29. So ChatGPT didn’t truly run this system; not stunning, many commentators have famous that ChatGPT doesn’t run the code that it writes. It additionally misunderstood what the algorithm does and what its output means, and that’s a extra severe error.
I then requested it to rethink the rationale for its earlier reply, and acquired a really well mannered apology for being incorrect, along with a special Python program. This program was appropriate from the beginning. It was a brute-force primality take a look at that attempted every integer (each odd and even!) smaller than the sq. root of the quantity underneath take a look at. Neither elegant nor performant, however appropriate. However once more, as a result of ChatGPT doesn’t truly run this system, it gave me a brand new listing of “prime components”–none of which have been appropriate. Apparently, it included its anticipated (and incorrect) output within the code:
n = 9999960800038127
components = factorize(n)
print(components) # prints [193, 518401, 3215031751]
I’m not claiming that ChatGPT is ineffective–removed from it. It’s good at suggesting methods to unravel an issue, and may lead you to the suitable answer, whether or not or not it provides you an accurate reply. Miller-Rabin is fascinating; I knew it existed, however wouldn’t have bothered to look it up if I wasn’t prompted. (That’s a pleasant irony: I used to be successfully prompted by ChatGPT.)
Getting again to the unique query: ChatGPT is sweet at offering “solutions” to questions, but when you have to know that a solution is appropriate, you could both be able to fixing the issue your self, or doing the analysis you’d want to unravel that drawback. That’s most likely a win, however you must be cautious. Don’t put ChatGPT in conditions the place correctness is a matter until you’re prepared and in a position to do the arduous work your self.