# Talk:Prime signature

## References

Could use references to theorems proving the things stated. Benandorsqueaks 00:56, 17 December 2005 (UTC)

## Practical example

I don't understand the "practical example" added in [1]. Why is A129912 examined, and what is "The embedded signature string"? Practical examples should make things easier to understand but it shows no prime signatures and only confuses me. PrimeHunter (talk) 16:42, 9 January 2008 (UTC)

The "embedded string" referred to is just the number sequence of the last column, effectively ordered.

The prime factor expansion of course is directly related to the prime signature, in particular for primorial sequences which have their exponents ordered in a specific way. The sequences used are not particularly relevant other than they are 2 for which such a connection existed. As signatures had been clearly explained just prior, it seems redundant to list them in the table.

For the example used, the practical use was in confirming the precise entry preceding the entry=100th primorial (selected as its "product" is square ie 100*100=10000) Via the signature linkage, one knows that connected A071532 terms are ...9991,9996,9999,10000,...

Someone had suggested that the preceding term could be 4705968353749845378343279973064195863536763443315426361801935164371167456947236 332613861927611714883983648469710968282522106130698506603418487862612958364179972073224374325956239485314766284153514139041745896918076382000.

Using the signature mechanism, seeing that the candidate is the product of the 1st, 5th, 34th and 78th primorials, the resulting product is only (1+5+34+78)*(78)=9204<<9999, from which one can deduce it (and others) are incorrect without having to specifically compute the candidates rigorously.--Billymac00 (talk) 03:53, 10 January 2008 (UTC)

This sounds like original research and has a very weak connection to the article subject. In the article you pick an OEIS sequence (which is not about prime signatures), make arbitrary looking operations based on the prime factorization (but not using the prime signature), compute a resulting sequence you call "The embedded signature string" for unknown reasons, and then say that this sequence "highly correlates" with another OEIS sequence (which is not about prime signatures). But both OEIS sequences contain terms not in the other, for example 4 is only in A071562, and 831600 is only in A129912. I'm going to remove this unless a much better explanation relating it closely to prime signatures is given. And a source should be given if you claim a connection between things reliable sources have not connected as far as I know. OEIS has around 135000 sequences so it doesn't seem noteworthy if a strangely computed sequence shares some terms with one of them. PrimeHunter (talk) 05:08, 10 January 2008 (UTC)
based on your posts I'll refer it to an editor or similar, sounds like you're bird dogging me without cause...and it goes without saying I disagree with your statements--Billymac00 (talk) 14:33, 10 January 2008 (UTC)
Hello, I am receiving your request for additional insight from third opinion. After reviewing the text regarding the statement made above, that would be considered original research unless it can be validated by a reliable source -- a journal, news article, credible web-site and so forth. I also do not see a strong correlation between what you wrote on the talk page in regards to prime signature. Can you perhaps shed some insight or connection between the two? Thanks, Seicer (talk) (contribs) 15:24, 10 January 2008 (UTC)
Regarding your bird dogging speculation: The disputed content was added to the article by an IP [2], and I did not know it was an editor I had encountered before when I started this section. I made the edit preceding the addition and the article is on my watchlist. In fact most articles about prime numbers are on my watchlist and I often respond when somebody adds apparent original research. PrimeHunter (talk) 15:40, 10 January 2008 (UTC)
I have removed [3] the section. PrimeHunter (talk) 01:53, 12 January 2008 (UTC)
I am not seeing a reputable reference to the article, and it currently stands as original research. The links given within do give off a series of sequences and other important information, but why is part of that duplicated here at WP? Would it be just as sufficient to just link to it? Seicer (talk) (contribs) 21:45, 13 January 2008 (UTC)
Billymac00 has readded [4] the section with edit summary "restore disputed content until 3rd-party resolves", although the 3rd party Seicer has already spoken against it and no new evidence has been presented. I have tagged [5] the section as OR and added fact tags to 3 claims: 1) That it is an example of prime signatures (which are not part of the socalled example). 2) The undefined term "embedded signature string" about something not using signatures. 3) The claim of high correspondence with an OEIS sequence that deviates in many values and is picked from a database of around 135000 integer sequences. I wanted to warn readers not to spend time trying to make sense of it, and I strongly support removal of the section again but I don't want to edit war.
Regarding the relevant sequences in other sections, Wikipedia often lists the first terms of sequences in Category:Integer sequences, and List of prime numbers was a speedy keep in Wikipedia:Articles for deletion/List of prime numbers. There is plenty of room for a few relevant sequences in this short article about a subject it may be hard to find a lot of information about. PrimeHunter (talk) 02:27, 14 January 2008 (UTC)
While I voiced my disagreement regarding it, I believe that there can be a compromise given a little bit of work and elbow greese. What I say is not binding, but I would like it to serve as a suggestion. Seicer (talk) (contribs) 02:46, 14 January 2008 (UTC)

never having had a dispute issue before, if you (Seicer) would resolve things please. I responded to you as best I could via email to avoid misinterpretation of any remarks, perceived insult etc. I expect you to "rule" or something but it would be nice if you informed PH I did respond to you, as his latest edit is falsely incriminating of me. Please note I respect the arbitrator's decision and you will see me stay civil&respectful. Any chance you can counsel this person on proper protocol and etiquette? Deleting and marking a passage while a dispute is still being considered is inappropriate. Thanks ...--Billymac00 (talk) 04:04, 14 January 2008 (UTC)

Wikipedia works by consensus and third opinions are not judges. I find it unfortunate that you tell the third opinion things in private so I cannot respond or even know about it before now. By the way, I'm an administrator but that's not important here. The practical example table contains correct prime factorizations which is important information, but Wikipedia already has the first 1000 in table of prime factors. We don't need some from an apparently arbitrary OEIS sequence in an article which is supposed to be about prime signatures. And I don't see how the current use of the table can become something relevant to the subject and not original research. I don't know why you chose to multiply the number of prime factors counted with multiplicity ("# prime factors" in the table) and without multiplicity ("Exp sum"). It seems a mathematically strange thing to do, and irrelevant to prime signatures. If we want practical examples of prime signatures in a table then I think the best thing would be to actually give the prime signature (and possibly prime factorization like http://mathworld.wolfram.com/PrimeSignature.html but nothing else) for the first integers. I suggest the below table as a compromise. I went to 30 to get the first number with 3 values in the signature.
Factorisation and prime signature of 1 to 30
factori-
sation
prime
signature
1 1 {1}
2 2 {1}
3 3 {1}
4 22 {2}
5 5 {1}
6 2·3 {1,1}
7 7 {1}
8 23 {3}
9 32 {2}
10 2·5 {1,1}
factori-
sation
prime
signature
11 11 {1}
12 22·3 {2,1}
13 13 {1}
14 2·7 {1,1}
15 3·5 {1,1}
16 24 {4}
17 17 {1}
18 2·32 {2,1}
19 19 {1}
20 22·5 {2,1}
factori-
sation
prime
signature
21 3·7 {1,1}
22 2·11 {1,1}
23 23 {1}
24 23·3 {3,1}
25 52 {2}
26 2·13 {1,1}
27 33 {3}
28 22·7 {2,1}
29 29 {1}
30 2·3·5 {1,1,1}
The prime signature of 1 is defined as {1} in MathWorld. The above table sorts the prime signature in decreasing order, like the current article but unlike MathWorld. The section "Numbers with same prime signature" could be after the table. PrimeHunter (talk) 04:59, 14 January 2008 (UTC)

For what it's worth, I am familiar with what a prime signature is. When I saw this "practical example" added to the article I didn't see right away what it had to do with prime signatures (though I could after a fashion). If this article is supposed inform those who may not be familiar with the concept of a prime signature, I really don't see how this section/example helps toward that objective. --Mwalimu59 (talk) 05:40, 14 January 2008 (UTC)

I'm slow. I only just realized that http://www.research.att.com/~njas/sequences/A129912, the sequence Billymac00 wants to base the table on and connect to another sequence, has him as author.[6] I had a dispute with him in June at Talk:Primorial but I forgot this sequence was also involved then. Billymac00, please see Wikipedia:Conflict of interest. You can suggest mention of the sequence here on the talk page but you are strongly discouraged from adding it to articles by yourself. PrimeHunter (talk) 06:48, 14 January 2008 (UTC)

well, now armed with the key info (Administrator) and while conceding no points, I realize the exchange was lost from the get go (my mama didn't raise a fool). Of course, I would never have undone an edit by an Administrator ...good grief ...here I thought you a "regular" guy--Billymac00 (talk) 19:46, 15 January 2008 (UTC)

As I wrote, me being an administrator is not important here. Administrators lose many disputes at Wikipedia when there is consensus against them. And I'm not allowed to use administrator tools such as user blocking and page protection when I'm involved in a content dispute. I guess key info to other editors is conflict of interest (though nobody had supported you before that was revealed). PrimeHunter (talk) 21:59, 15 January 2008 (UTC)

## Mobius Function

A comment for OEIS A008683 1relates the entries of the Mobius function sequence to earlier entries thru the use of prime signatures. Quoting, "a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24=2^3*3 and 375=3*5^3 both have prime signature (3,1)". This is an xample of signatures being useful to another math function.--Billymac00 (talk) 03:17, 16 September 2010 (UTC)