Timeline for A number theoretic conjecture by Chat GPT [closed]
Current License: CC BY-SA 4.0
30 events
| when toggle format | what | by | license | comment | |
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| Aug 20, 2023 at 15:02 | history | left closed in review |
Alexey Ustinov Yemon Choi Brian Hopkins |
Original close reason(s) were not resolved | |
| Aug 17, 2023 at 23:04 | review | Reopen votes | |||
| Aug 20, 2023 at 15:02 | |||||
| May 28, 2023 at 14:51 | history | closed |
Denis T Steven Landsburg Andrés E. Caicedo Dave Benson user43326 |
Not suitable for this site | |
| May 26, 2023 at 6:02 | comment | added | Philippe Gaucher | @BoazTsaban Try platform.openai.com/playground. It is interesting to play with it to understand how it works; keep in mind that for more recent chat bots, the discussion starts with a hidden pre-prompt which is supposed to give some rules of behaviour. | |
| May 24, 2023 at 11:10 | comment | added | Boaz Tsaban | @PhilippeGaucher This discussion goes far... This is too subtle an issue to be dealt with in short discussions. Time will tell, I guess. | |
| May 24, 2023 at 7:57 | comment | added | Philippe Gaucher | @BoazTsaban chatGPT is nothing else but a text generator generating the most probable sequel of a sequence of words. You can play with the openAI playground to see that. Hence all hallucinations that this so-called AI has: it definitively cannot be trusted. When the sequence of words looks like a question, the most probable sequel is a sequence of words which looks for us, humans, like an answer because of its training. chatGPT does not understand what it's talking about. | |
| May 23, 2023 at 19:49 | comment | added | Boaz Tsaban | @YemonChoi This is yet to be discussed for some decades... it is still unclear how far Chat GPT is from human intelligence. I would postpone the decision for at least several years. | |
| May 23, 2023 at 15:31 | comment | added | Yemon Choi | @BoazTsaban to me, this is like saying "I rolled some dice and I used the results as coefficients for some polynomial, what is the Galois group of this polynomial". LLMs by their nature cannot understand their output, so saying this is a "conjecture by ChatGPT" seems to be attributing agency/sentience where it doesn't exist. | |
| May 23, 2023 at 15:24 | comment | added | Boaz Tsaban | @YemonChoi I disagree. This conjecture was made by Chat GPT, and removing its mention would be plagiarizm. | |
| May 23, 2023 at 9:16 | comment | added | David Roberts♦ | @Yemon I agree, it adds nothing to the mathematics. | |
| May 23, 2023 at 2:07 | comment | added | Yemon Choi | I would be much happier if all mention of GPT were removed from the original question. | |
| May 22, 2023 at 19:11 | history | removed from network questions | Asaf Karagila♦ | ||
| May 22, 2023 at 17:31 | history | became hot network question | |||
| May 22, 2023 at 14:18 | review | Close votes | |||
| May 28, 2023 at 14:51 | |||||
| May 22, 2023 at 14:10 | vote | accept | Boaz Tsaban | ||
| May 22, 2023 at 13:50 | comment | added | JRN | Maybe we can ask ChatGPT to prove the conjecture? | |
| May 22, 2023 at 12:48 | answer | added | Timothy Chow | timeline score: 17 | |
| May 22, 2023 at 12:11 | comment | added | Carlo Beenakker | in the spirit of the question, I asked chatGPT 4 if this conjecture was known to be true/false or open. It answered: "Up until my last training data in 2021, this conjecture was not resolved. For the most current and accurate information, you should refer to recent mathematical literature or ask a professional mathematician or number theorist." | |
| May 22, 2023 at 11:19 | comment | added | Ofir Gorodetsky | @YaakovBaruch Not that I am aware of, but there are partial results about the density of P-P and its structure, see link.springer.com/chapter/10.1007/978-3-319-22240-0_10 and ams.org/journals/proc/2017-145-09/S0002-9939-2017-13533-3 | |
| May 22, 2023 at 10:58 | comment | added | Yaakov Baruch | Going off the tangent a bit, is there any specific infinite set, not defined using the primes implicitly or explicitly (I know I'm being a bit vague here), known to be contained in $\mathbb{P}-\mathbb{P}$? | |
| May 22, 2023 at 9:53 | comment | added | Fedor Petrov | @R.vanDobbendeBruyn you are correct of course. But I am afraid that still this is open for large specific $n$. | |
| May 22, 2023 at 9:52 | comment | added | Ofir Gorodetsky | @BoazTsaban Conjecturally P-P contains every even number. More generally, Hardy and Littlewood conjectured that for every 'admissible' tuple $(h_1,\ldots,h_k)$ of positive integers there are infinitely many positive integers $m$ such that $\{m+h_i\}_{i=1}^{k}$ are simultaneously prime (and they predict the count of these $m$ up to $x$, asymptotically). Your conjecture relates to $h_1=0,h_2=n^2$. 'Admissible' means there is no prime $p$ such that $\{ h_i \bmod p\}_{i} = \mathbb{Z}/p\mathbb{Z}$ (see Fedor Petrov's comment). For more information see en.wikipedia.org/wiki/Prime_k-tuple . | |
| May 22, 2023 at 9:51 | comment | added | Fedor Petrov | No arithmetic progression of course (look modulo 3). Just infinitely many pairs. | |
| May 22, 2023 at 9:49 | answer | added | Fedor Petrov | timeline score: 11 | |
| May 22, 2023 at 9:49 | comment | added | Boaz Tsaban | @R.vanDobbendeBruyn Does the set P-P have full density? (Density 1) | |
| May 22, 2023 at 9:47 | comment | added | Boaz Tsaban | @FedorPetrov Do you mean that there is a conjecture that for each k there is an arithmetic progression of k primes with difference 2? | |
| May 22, 2023 at 9:45 | comment | added | R. van Dobben de Bruyn | @FedorPetrov actually it only asks for one prime $p$ so that $p+n^2$ is prime, not infinitely many (which is the case for the twin primes conjecture/bounded gaps theorem). So the $n=2$ case is very much solved! | |
| May 22, 2023 at 9:39 | history | edited | Boaz Tsaban | CC BY-SA 4.0 |
added 18 characters in body
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| May 22, 2023 at 9:38 | comment | added | Fedor Petrov | It is certainly true and follows from standard conjectures, but widely open even for $n=2$. | |
| May 22, 2023 at 9:31 | history | asked | Boaz Tsaban | CC BY-SA 4.0 |