Talk:Collatz conjecture
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Semi-protected edit request on 10 March 2025
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The article uses the word "begin" in excess. Can we use alternative synonyms please. 204.48.78.190 (talk) 23:07, 10 March 2025 (UTC)
Not done The word "begin" appears zero times in the article ("beginning" twice). --JBL (talk) 23:45, 10 March 2025 (UTC)
Application of the Collatz conjecture on decimals
editI found that the collatz conjecture can be solvable if the rules are modified. Let's consider it even if the last digit is divisible by 2, unless it's a decimal zero. If not, it's considered odd. So far, the numbers I have found do not end up on a loop or go infinitely. 122.53.180.74 (talk) 12:32, 9 April 2025 (UTC)
- To clarify, I meant the decimal numbers I've found. 122.53.180.74 (talk) 12:37, 9 April 2025 (UTC)
- If the rules are modified, it's not the Collatz conjecture. —Tamfang (talk) 21:49, 9 April 2025 (UTC)
(p, q)-adic analysis
editMax Siegel — a graduate student from the University of Southern California — seems to have put immense effort into developing a new approach to studying the Collatz conjecture.[1][2] I'm not confident enough mathematically to add anything from his dissertation myself, but it may be noteworthy and it appears interesting. Thoughts? Ramanujaner (talk) 21:51, 23 April 2025 (UTC)
- Why's no one answering? His work is in souce [1] and source [2] shows that USC has accepted his thesis. It is quite novel and perhaps worth mentioning, is it not? Ramanujaner (talk) 19:03, 28 April 2025 (UTC)
- Seigel talks about it as perhaps being an interesting jump point. Seigel himself indicates it isn't a proof and while it may be interesting and useful to talk about in a forum devoted to it, neither the talk page nor the article itself is the place for that.Naraht (talk) 13:40, 29 April 2025 (UTC)
- I do not want to burst your bubble, but the work of Max Siegel does not help at all and is a trivial reinterpretation of the problem. I wasted my time having a deeper look into his work after I was convinced by reddits posts that he is not mentally ill. 133.6.130.80 (talk) 01:43, 7 May 2025 (UTC)
References
- ^ Siegel, Maxwell Charles (2024-12-03), $\left(p,q\right)$-adic Analysis and the Collatz Conjecture, arXiv, doi:10.48550/arXiv.2412.02902, arXiv:2412.02902, retrieved 2025-04-23
- ^ "Algebra". Department of Mathematics. Retrieved 2025-04-23.
Hailstone sequences in Prime Numbers
editSuggestion to add to reference section
(1) This hailstone operation on odd prime numbers will always reach 3. reference: https://oeis.org/A365048
a(n) is the number of steps required for the n-th odd prime number to reach 3 when iterating the following hailstone map: If P+1 == 0 (mod 6), then the next number = smallest prime >= P + (P-1)/2; otherwise the next number = largest prime <= (P+1)/2. If the condition "(P + (P-1)/2)" is changed to "(P + (P+1)/2)" then some prime numbers will go into a loop. For example, 449 will loop through 2609.
If the condition "(P+1)/2" is changed to "(P+3)/2" then some prime numbers will go into a loop. For example, 5 will go into the loop 5,7,5,7,....
(2) This hailstone operation on prime numbers will always reach 2. reference: https://oeis.org/A367479
a(n) is the number of steps required for prime(n) to reach 2 when iterating the following hailstone map: If P == 5 (mod 6), then P -> next_prime(P + ceiling(sqrt(P))), otherwise P -> previous_prime(ceiling(sqrt(P))); or a(n) = -1 if prime(n) never reaches 2.
note: next_prime(x) is the next prime >= x, and previous_prime(x) is the next prime <= x. Najeemz (talk) 09:46, 22 June 2025 (UTC)
- I think we need stronger sourcing than an OEIS entry to add material like this. OEIS lists a lot of things and I think its only real acceptance standard is mathematical validity. While I think it is reliable for the facts that it lists it doesn't really provide evidence that the material is WP:DUE for this article. —David Eppstein (talk) 22:04, 22 June 2025 (UTC)
A proof of the conjecture
editI published a proof of the conjecture on the Zenodo website (no. 15638705). I have submitted this proof to a peer-reviewed mathematical journal. I believe, in all objectivity, that this proof establishes rigorously and clearly the validity of the conjecture. Kind regards. Fabonmars (talk) 15:17, 4 July 2025 (UTC)
- Ok but Wikipedia is not an appropriate venue for promoting preprints; only once it has been accepted in a reputable journal would we even consider mentioning it in the article here. --JBL (talk) 18:36, 4 July 2025 (UTC)
- Hello,
- I don't promote my proof. A mathematical proof is either true or false. I'm simply sharing it in the hope of comments.
- Kind regards. Fabonmars (talk) 13:45, 5 July 2025 (UTC)
- Yes, that is a form of promotion; Wikipedia is an encyclopedia, not a place to solicit feedback on your work. --JBL (talk) 17:16, 6 July 2025 (UTC)
Latest verification limit for the Collatz conjecture
editAccording to https://nntdm.net/volume-31-2025/number-3/471-480/ the latest verification limit for the Collatz conjecture is the number 4×(3^{44})+2≈1.66×(2^{71}). M3141123 (talk) 07:04, 8 August 2025 (UTC)
- Unfortunately NNTDM is listed as "no longer indexed" by both zbMATH and MathSciNet, strongly suggesting that it should not be considered reliable. —David Eppstein (talk) 07:10, 8 August 2025 (UTC)
- Although being indexed in zbMATH and MathSciNet makes a journal and its papers more reliable, you believe it or not, I myself never rely on any result from any paper published in any well known journal indexed by zbMATH and MathSciNet unless I check the proof more than once carefully. I read the above mentioned NNTDM paper carefully and I see that the proofs are easy-to-follow and correct, however, it is obvious that any researcher who want to use the results of the paper should check the proofs as well. M3141123 (talk) 08:09, 8 August 2025 (UTC)
- In fact reading the paper reveals that it does not improve computational verification to 1.66 x 2^{71}. It merely cites a web site that says that. The paper itself is not about computational verification. —David Eppstein (talk) 16:35, 8 August 2025 (UTC)
- The mentioned website just reports the latest verification limit 2^{71} which has been achieved in the following paper (which has come as the reference item 3 in Ansari's paper)
- https://link.springer.com/article/10.1007/s11227-025-07337-0
- Then, in Remark 3.1, Ansari uses his result (Proposition 3.2) to show that the verification limit can be improved to 4(3^{44})+2. In fact, since N=2(3^{44})+1 < 2^{71} < 4(3^{44})+2=2N, and we know that all integers up to 2^{71} satisfy the conjecture by [3], in view of Proposition 3.2 of Ansari, we deduce that all integers up to 4(3^{44})+2 will satisfy the conjecture as well, and hence, the number 4(3^{44})+2 becomes the improved verification limit. In other words, by using Proposition 3.2 of Ansari, computational verification process can skip the interval [2^{71}, 4(3^{44})+2]. So the first integer greater than 2^{71} which should be checked by the verification algorithms would be 4(3^{44})+3. I hope this clarification could be helpful. M3141123 (talk) 08:52, 9 August 2025 (UTC)
- In fact reading the paper reveals that it does not improve computational verification to 1.66 x 2^{71}. It merely cites a web site that says that. The paper itself is not about computational verification. —David Eppstein (talk) 16:35, 8 August 2025 (UTC)
- Although being indexed in zbMATH and MathSciNet makes a journal and its papers more reliable, you believe it or not, I myself never rely on any result from any paper published in any well known journal indexed by zbMATH and MathSciNet unless I check the proof more than once carefully. I read the above mentioned NNTDM paper carefully and I see that the proofs are easy-to-follow and correct, however, it is obvious that any researcher who want to use the results of the paper should check the proofs as well. M3141123 (talk) 08:09, 8 August 2025 (UTC)