Talk:Sierpiński number

message: Selfridge's conjecture as [defined at MathWorld] is not the same as the definition here. --85.194.2.201 15:51, 20 December 2005 (UTC)
thread_title:  Selfridge's conjecture 

message: Can anyone who knows the subject clarify it? It is not clear what is meant by Solved k.Hakeem.gadi (talk) 09:30, 12 February 2008 (UTC)
replies: text: I explained it in . Is that OK? PrimeHunter (talk) 15:00, 12 February 2008 (UTC)
replies: text: Yup, that's alright. Thanks.Hakeem.gadi (talk) 07:01, 18 February 2008 (UTC)
thread_title: Solved k

message: Why is there a funky question mark in the definition of the problem? In the section "The Sierpinski problem" It looks ridiculous and it isn't in the style of wikipedia. I think that silly box should be removed entirely.
173.13.109.1 (talk) 19:00, 15 October 2010 (UTC)
replies: text: It's made by Template:Unsolved. The template was kept at Wikipedia:Templates for discussion/Log/2010 September 29#Template:Unsolved. PrimeHunter (talk) 19:29, 15 October 2010 (UTC)
thread_title:  Funky question mark 

message: The user "Prime Hunter" said: "We define Sierpinski number as odd k; an even k corresponds to an odd k with a larger n: (2^m*j)*2^n+1 = j*2^(m+n)+1" but I think that it is not always. For example, if there are only five Fermat primes: 3, 5, 17, 257, 65537, than 131072 and larger powers of 2 are Sierpinski numbers, is it right? — Preceding unsigned comment added by 140.113.136.218 (talk) 
:I'm not sure what you are asking. It's right that we define a Sierpiński number as odd k. It's in the opening sentence. You are quoting an edit summary  I gave as reason for not including even k in a table of smallest n for which k×2n+1 is prime. I don't see reason to include even k when the article is about Sierpiński numbers. Every prime of form k×2n+1 with even k corresponds to a prime of the same form with a larger odd k. But if even numbers were allowed as Sierpiński numbers then there would probably be some even Sierpiński numbers which don't correspond to an odd Sierpiński number. Specifically, it would occur in any case where there is a finite non-zero number of primes of form k×2n+1 for an odd k. Those k would not be Sierpiński numbers, but if the largest prime is k×2m+1 then k×2n would be a Sierpiński number for all n > m. I don't know of any reliable source which has considered this definition so it shouldn't be in the article. PrimeHunter (talk) 11:16, 22 May 2014 (UTC)
replies: text: If we change the definition to allow even Sierpinski numbers then yes, if 65537 is the largest Fermat prime then 131072 and all larger powers of two would be Sierpinski numbers. But we shouldn't change the definition to something not found in any reliable sources. PrimeHunter (talk) 23:45, 4 June 2014 (UTC)
thread_title:  The divination of Sierpinski number 

message: We can define Sierpinski numbers on all the integers, such as -509203, a negative integer.  — Preceding unsigned comment added by 115.80.80.42 (talk) 06:25, 27 June 2014 (UTC)
thread_title:  Can ''k'' be any integers? 

message: 78557*2^n+1 must divide by 3, 5, 7, 13, 19, or 37, and 2^n+78557 as well, but all odd numbers under 78557 expect 40291 have a prime in a form 2^n+k, so 78557 is the smallest Sierpinski number.  — Preceding unsigned comment added by 180.204.20.28 (talk) 14:18, 30 June 2014 (UTC)
thread_title:  k*2^n+1 or 2^n+k 

message: I presume that there are syntax errors in the following sentences :
:"However, some values of ns are large, for example, the smallest solution for that k = 2131, 40291, and 41693, the least n are 4583176, 9092392, and 5146295. (However, the least n such that k2n + 1 is only 44, 8, and 33. Interestingly, the least n which 2n + 10223 is prime is only 19.)"
There are other strange sentences. Marvoir (talk) 17:22, 15 January 2016 (UTC)
thread_title:  Strange sentences 

message: I have split the section in 3, to mention and detail the other two SPs, I updated the lists (some from 5 years ago). A native speaker is welcomed to correct my English (in spite of the fact that I took part of the text from protsearch.com, :P)  — Preceding unsigned comment added by LaurV (talk • contribs) 04:53, 23 May 2017 (UTC)
replies: text: I put it back... somebody may clean it, but please do not remove it. LaurV (talk) 06:54, 23 November 2018 (UTC)
thread_title:  Sierpinski Problems 

message: I think it must be said there is a sequence  k \times 2^n  + 1  involved in the definition of a Sierpinski number.--109.166.132.148 (talk) 18:38, 16 April 2020 (UTC)
replies: text: The definition does not require a sequence and none of the sources I examined mention a sequence. The current definition seems clear to me. It's about all numbers of form  k \times 2^n  + 1 . There is no need to consider the set of such numbers as a sequence with increasing n values.  PrimeHunter (talk) 18:49, 16 April 2020 (UTC)
replies: text: Why not? These numbers of this form s_n = k \times 2^n  + 1   naturally constitute a sequence or equivalently, an ordered set because the order of numerical elements in this set is NOT an arbitrary/random one.--109.166.132.148 (talk) 19:07, 16 April 2020 (UTC)
replies: text:  Yes, it has a natural order.  But this is irrelevant to anything interesting about it.  So why add pointless complication? --JBL (talk) 19:09, 16 April 2020 (UTC)
replies: text: I do not think it would be a pointless complication. A certain member of this ordered set can be specified of a given k, like the 3rd Sierpinski number, the 4th, the 5th, the jth Sierpinski number, etc.. Any elements with an number of order (index or rank) form a sequence whose individual terms may have a certain property assigned to it, such as divisible to a certain m number, can be involved in modulo congruences, etc.--109.166.132.148 (talk) 19:20, 16 April 2020 (UTC)

text: Also individual terms of the sequence can be counterexamples in some reasonings.--109.166.132.148 (talk) 19:23, 16 April 2020 (UTC)

text: This context re counterexamples leads to the question of existance of at least of a certain k for which the terms of the sequence may be prime numbers.--109.166.132.148 (talk) 19:28, 16 April 2020 (UTC)
replies: text:  This is utterly unconvincing. --JBL (talk) 21:31, 16 April 2020 (UTC)
replies: text: What exactly is unconvincing?--109.166.132.148 (talk) 23:32, 16 April 2020 (UTC)
replies: text:  Everything you've written.  None of it is related to the all-important question how best to present the information about Sierpinski numbers that exists in reliable sources in an encyclopedic way? --JBL (talk) 23:50, 16 April 2020 (UTC)
replies: text: What exactly would be un-encyclopedic in mentioning the word sequence in relation to Sierpinski numbers? Above you claim that adding the word sequence would be a pointless complication, which is clearly an exaggeration. I don't quite understand  the claimed/supposed status of pointless complication, clearly is not the case, what complication generated by just using a word? I think that this claimed status is far from being convincing, to use your wording.--109.166.132.148 (talk) 01:23, 17 April 2020 (UTC)
replies: text:  I do not see any purpose in continuing this discussion; your edit was an obvious disimprovement for the reasons I’ve mentioned, please don’t repeat it. —JBL (talk) 01:51, 17 April 2020 (UTC)
replies: text: Obvious disimprovement? This seems to be a joke! When you say/claim that something is unencyclopedic, you should explain your claim! I do not understand your reaction, no need to become hostile.--109.166.132.148 (talk) 09:51, 17 April 2020 (UTC)

text: Wikipedia is based on reliable sources and mathematicians prefer definitions without unnecessary parts. I have now examined ten definitions of Sierpinski number. The all say almost exactly the same as us. None of them use the word sequence. They have no reason to, and neither do we. PrimeHunter (talk) 03:26, 17 April 2020 (UTC)
replies: text: You could check again an additional source. There is a source right in the article which mentions the word sequence. The use of the word sequence is just explanatory/descriptive for a clearer understanding, not really part of a strict definition, just something that follows as a (noticeable) property from the number of order, thus it can be added by WP:CALC.--109.166.132.148 (talk) 09:51, 17 April 2020 (UTC)

text: (What is almost exactly said by those ten sources? What is the difference from what is in the article? Could those sources def be listed here?)--109.166.132.148 (talk) 10:35, 17 April 2020 (UTC)
replies: text:  Please, stop repeating yourself, this is not WP:CALC it is WP:IDHT. Your eccentric views are not compelling at all, and you do not seem to understand what is the purpose of the lead sentence. --JBL (talk) 10:44, 17 April 2020 (UTC)
replies: text: What repetitions? It is not WP:IDHT. I have underlined the explanatory nature of the discussed word in re to the strict definition (without unnecessary parts) of the Sierpinski numbers (this aspect has not been mentioned before, therefore NO repetition). Also WP:CALC has not been mentioned before 09:51, 17 April 2020. How does the purpose of the lead sentence get negatively impacted by the use of a certain word? Please clarify!--109.166.132.148 (talk) 12:23, 17 April 2020 (UTC)

text: There is also an open question from the 21:14 10 September 2019 edit which hasn't been adressed in re to the proposed word, namely (what is "the sequence" supposed to refer to?) .--109.166.132.148 (talk) 12:23, 17 April 2020 (UTC)
replies: text: The lead sentence would get longer and more complicated, introduce a term some readers don't know or are unsure about the technical meaning, introduce a notation s_n not used in the rest of the article or sources, and give a misleading impression that Sierpinski numbers are normally defined in terms of a sequence. You are not going to convince us there is any good reason for this. Just Google Sierpinski number to find many definitions. They may say "not prime" instead of composite and have a different sentence structure but that's about it as far as differences go. They even use the same variable names. PrimeHunter (talk) 12:55, 17 April 2020 (UTC)
replies: text: This update with clear explanations from 12:55, 17 April 2020 is much more convincing or has a higher argumentative power/value to the choice NOT to use the proposed word than the initial dry labels (pointless complication, utterly unconvincing, uncyclopedic, stop repeating yourself, eccentric views, etc) which seemed unnecessarily hostile.--109.166.132.148 (talk) 16:57, 17 April 2020 (UTC)
thread_title:  Specification  

message: According to an explanation from Prof. Michael Filaseta posted on the SeqFan list ("Re: is it true", Jul 12 2022), if k is Sierpinski with a known "covering set", then so is k^m for all m relatively prime to the LCM of the covering set. I think this is worth mentioning. But is this a known result? Has anyone a published reference or similar? — MFH:Talk 17:35, 23 July 2022 (UTC)
thread_title:  Powers of Sierpinski numbers 

message: Like Bunyakovsky conjecture for polynomial sequences, I have a conjecture about exponential sequences:
If a ≥ 1 is integer, b ≥ 2 is integer, c ≠ 0 is integer, gcd(a,c)=1, gcd(b,c)=1, and \frac{a \cdot b^n+c}{gcd(a+c,b-1)} cannot be proven to only contain composites or only contain finitely many primes by covering congruence (such as 122 \cdot 13^n+3, which is always divisible by 5, 7, or 17), algebraic factorization (such as 8 \cdot 27^n+1, which has sum-of-two-cubes factorization), or combine of them (such as 25 \cdot 12^n -1, which is divisible by 13 if n is odd and has difference-of-two-squares factorization is n is even), then there are infinitely many integers n ≥ 1 such that \frac{a \cdot b^n+c}{gcd(a+c,b-1)} is prime. 36.233.231.45 (talk) 04:26, 19 June 2023 (UTC)
replies: text: Wikipedia is an encyclopedia; it is for reporting & recording what is found in high-quality published sources.  Wikipedia talk-pages are for proposing and discussing improvements to Wikipedia articles, within that framework.  Wikipedia is not a venue for promoting, publishing, or discussing original research, including new conjectures.  --JBL (talk) 17:18, 19 June 2023 (UTC)
thread_title:  My related conjecture