Talk:List of prime numbers/Archive 1

Archive 1

The case for the defence

1.)This project is Wikipedia, not Wikisource and all CD, print and mirrored copies of the Wikipedia will not come with a complete copy of Wikisource. Each work is independent and has to have sufficient content to fulfill its own role. Please feel free to try deleting the articles on chemical elements just because another wiki is covering chemistry in more depth...:) The only question we need address here is what this project finds useful. - Jamesday 04:22, 1 February 2004 (UTC)
2.)Is it so bad to give Wikipedians something to do in their spare time? - Arthur George Carrick 02:58, 1 February 2004 (UTC)
3.)Keep, but not as a redirect. Keep as is. An encyclopedia is a reference. A quick reference to the list of prime numbers is useful. Kingturtle 02:14, 26 January 2004 (UTC)
4.)Keep, useful to students and others Jack 08:05, 26 January 2004 (UTC)
4.5.)I find it quite useful when working on factorization... - Arthur George Carrick 19:05, 1 February 2004 (UTC)
5.)Keep- It is of general academic interest, for example, it may be interesting to note in what number the numbers end, and get an idea of what is likely to be a prime number and so on...Also, from my limited knowledge, I recall that there is no formula for generating prime numbers and hence the list is useful as someone else has said earlier. A redirect to Prime numbers wouldn't be useful because it would limit the list KRS 04:48, 26 January 2004 (UTC)
5.) Any decent mention of prime numbers requires an interesting list which is long enough to discover their complicated distribution in the set of integers. As we use hard drives and not paper, such a list is not going to be a trouble. Pfortuny 22:37, 5 February 2004 (UTC)

6.) Not only do I want this list kept, I want every individual number changed into a wikilink. -Itai 22:52, 8 February 2004 (UTC)

Moving on time

So, the questions we now have are related to how we select which primes should be present here. In an informal poll (or make it a vote if you want to do the extra administrative work of linking it from everywhere), please indicate whether you think the article should contain these parts of the infinitely large list of primes:

1. At the bottom of the article, how many of the first primes should be listed as a convenient reference table. Selecting a higher number means you also want the lower number:

• 0: Maximus Rex, Rossami, Kevin Saff
• 100: Mikez
• 200: Metasquares
• 300:
• 400:
• 500: Jamesday, Pfortuny, Ryan_Cable, Numerao
• 1000:Moneya
• 5000:
• 10000:
• infinite:
  • this isn't possible —Noldoaran (Talk) 20:58, 16 February 2004 (UTC)
    • It was included for troll detection. However, it is doable, in javascript if the wiki supported that. Page loading time would be quite high, though.:) Jamesday 00:14, 1 April 2004 (UTC)
  • Oh, it depends so much! If you write them very very very fast (1/2^n seconds for the n-th prime), then you get the list in 1 second. :) Pfortuny 15:22, 16 March 2004 (UTC)

2. For each prime discovered using a different new technique (algorithm or implemention) throughout history, how many examples should be given (some of the early ones had many, recent ones often few):

• up to 50:
• up to 50 and 10 highest primes found this way so far: Jamesday, Mikez, Metasquares, Pfortuny, Ryan_Cable,Noldoaran, Numerao
• 10 highest Primes only: Moneya

• add new category

The idea, of course, is to make this a useful article as well as simply a table of primes. Please add whatever possibilities you think might be useful, so we can find out how people feel about them. Jamesday 01:42, 3 February 2004 (UTC)

If we have to keep this page it should be as a redirect to prime number. It has no place in this encylopaedia as it just isn't an article at all, nor is it useful - an argument can be had on WikiSource over whether it should be there, please see the Wikipedia:Votes for deletion page for arguments againsts its existence on Wikipedia. Tompagenet 03:21, 26 January 2004 (UTC)

Organization

This page needs some kind of organization. On the one hand, it makes sense to have the Sophie Germain primes and the safe primes close together, but on the other hand, it might make more sense to have all these primes named after people sorted in alphabetical order. PrimeFan 22:42, 8 August 2005 (UTC)

I was just thinking the same myself: I'd be inclined to put them all in alphabetical order (except "list of primes" itself), and add internal cross-references where necessary to link those that are conceptually related. Hv 00:20, 9 August 2005 (UTC)

Even though putting them all in alphabetical order might not be the best option, I think it would be preferrable to current disarray. PrimeFan 21:25, 9 August 2005 (UTC)

I've now alphabetised it; please check that I haven't broken anything, and start adding in the cross-references. Hv 01:20, 16 August 2005 (UTC)

Mersenne prime mistake?

I'm pretty sure 524827 should be 524287. (Notice the 82 in the first, and 28 in the second.) The value appears correct on the Mersenne prime page. Could someone more familiar with Mersenne primes verify this?

I changed it. 2^19 = 524288. I didn't try to factor it though. Walt 11:33, 6 July 2006 (UTC)

Interestingly, 524827 is also prime. Just coincidence? Walt 11:38, 6 July 2006 (UTC)

I think there are a number of primes that if you transpose the digits in the 10s and 100s places it gives another prime number. For some reason, I also vaguely recall coming across those two digits transposed in that Mersenne prime years ago. I wonder if it was a propogation of that same error. — Preceding unsigned comment added by 69.115.39.225 (talk) 02:46, 8 July 2006 (UTC)

Links

I recently wrote a little PHP script that can calculate the list of prime numbers in a given range (up to 5000). It has a 'detailed' setting, which causes the script to list why a number is or isn't a prime (gives you what numbers it is divisable by that cause it not to be a prime). The script is here:

http://angrycoder.org/~shwooz/stuff/primes.php

Should I add a link to this script to the External Links section in the article?GodGell 23:45, 17 May 2007 (UTC)

Thanks for asking first. I don't think the link should be added. There are already links to large lists of primes. We show prime factors and divisors up to 1000 in Table of prime factors and Table of divisors. And Integer factorization has an external link to a well-known powerful applet [1] that can factor very large numbers. PrimeHunter 00:24, 18 May 2007 (UTC)

Commas

How come none of the large numbers (4 or more digits) have commas to separate the digit groups (e.g., 393050634124102232869567034555427371542904833)? — Loadmaster 20:28, 29 May 2007 (UTC)

I think comma-separated digit groups in a list of comma-separated numbers is hard to read. I also dislike spaces in comma-separated lists, but maybe thin spaces would be better.

393 050 634 124 102 232 869 567 034 555 427 371 542 904 833 (thin spaces)

393 050 634 124 102 232 869 567 034 555 427 371 542 904 833 (normal spaces)

A small difference. PrimeHunter 02:53, 30 May 2007 (UTC)

I'd prefer neither spaces nor commas as this prevents much useful cutting-and-pasting. What is the argument in favor of commas? Doctormatt 04:07, 30 May 2007 (UTC)

I also prefer neither. I only meant that thin spaces may be better than normal spaces or commas if there has to be something, but I don't think there does. PrimeHunter 12:07, 30 May 2007 (UTC)

To make the numbers more readable, maybe, and because it's acccepted practice to do so? Can you tell the difference between 10000000 and 100000000 at first glance? — Loadmaster 17:38, 30 May 2007 (UTC)

Not to be snarky, but, yes, I can tell the difference. I don't know that readability trumps cut-and-paste-ability in this modern age. By "readable" do you mean comparable? Because, frankly, I don't "read" numbers like 618970019642690137449562111 - I just see a string of digits. If I want to do anything with it, I'd like to be able to cut and paste it somewhere (say, into a factoring program to see if it really is prime). Doctormatt 21:31, 30 May 2007 (UTC)

Rename/split?

It was suggested [[2]] that this article perhaps should be renamed, something like "List of types of prime numbers". Or, actually, maybe split into two articles: one that's just the list of the first so many primes, and another that is the list of types. This latter seems like a good idea to me. Comments? Doctormatt 01:17, 25 May 2007 (UTC)

The move is a good idea; the split is not. The "list of the first so many primes" is a numerical table; numerical tables do not belong on WP, and that section should be deleted from this article. --Trovatore 04:02, 25 May 2007 (UTC)

With the list here, it's possible to see where the twin primes and many other special types are located. I think the list should be kept here but shortened to 500 primes. 500 got 4 of 8 votes in the first section on this talk page, and 1000 got 0. It has been 500 in the past but was changed to 1000 in December 2005 [3], the first edit by a new account, with no prior discussion. We could also consider changing the current table with 10 numbers per row to a comma-separated list which takes less screen space. I also suggest that each type of prime gets at most around 200 characters of examples (typically around 2 lines), unless there is a special reason to list more (for example that all known primes would fit on a few more lines). I don't see such a reason in any of the current lists. PrimeHunter 02:43, 30 May 2007 (UTC)

I have shortened the longest lists for special types to 2-3 lines [4], and the main list from 1000 to 500 primes.[5] PrimeHunter 23:54, 9 June 2007 (UTC)

From VfD

• should not be here. This is not the place for a list of numbers. -- Ams80 23:39, 25 January 2004 (UTC)
  • I dont see why not, as long as we keep the number articles - keep --`Jiang
    • So when do we stop - one can easily show there are an infinite number of prime numbers. There's absolutely no point in having this. Otherwise we will have to accept a list of square numbers, cube numbers, numbers^4, and so on. Tompagenet 00:09, 26 January 2004 (UTC)
  • As what seemed an obvious case for deletion to me isn't to others, I'll add my reasons. For a start it's badly named, 'List of prime numbers' is ambiguous, is it those primes less than 150? Is it the first x primes? Is it all the primes? If it does stay it should go to another title. Secondly, if one were so inclined, thousnads upon thousands of numerical sequences could be given their own article, all of which would be as useless as each other as there would be no convenient searching available. A project for this already exists -- http://www.research.att.com/~njas/sequences/, with a specially designed searching facility which makes it useful. I'm not saying that I can't see the point of any lists of numbers, for example the orders of the finite simple groups are expressed at Classification of finite simple groups, this is useful information, appropriately represented as part of an article. Also, with Wikipedia being editable as it is, I would never use this page as a source of information, if this page grew to primes less than 10^4 I would have no quick way of verifying whether 9883 had been included by a vandal. There are a wealth of other sites which can provide this information in a more reliable way. -- Ams80 00:25, 26 January 2004 (UTC)
  • Delete, for the simple reason that there's nothing here that isn't duplicated at Prime number. What about putting a list of prime numbers at Wikisource? -- Seth Ilys 00:30, 26 January 2004 (UTC)
    • Well I suppose that's for WikiSource to decide, but I can't see how this would get round the objections Ams80 makes above, and it would open the gates to many, many similar numerical sequence articles - how many millions of numbers would have to be listed before the article was deemed a waste of space. Someone would almost certainly start a "List of natural numbers" page as well... Tompagenet 00:38, 26 January 2004 (UTC)
      • Wikipedia:Wiki is not paper, so is wasted space really an issue? Project Gutenberg includes the entire human genome, which is dozens of megabytes in size... I was just suggesting that (for the season Ams80 details) Wikisource might be a more appropriate place than here for an extensive list of primes, because a list of primes is essentially static. But I don't feel it's appropriate for Wikipedia because it's a subset of a preexisting article. -- Seth Ilys 01:01, 26 January 2004 (UTC)
        • The "Wikipedia is not paper" is a frequently mentioned point - but i wonder how much people would still be saying this if the prime number articles had the first trillian primes - even if this was split between pages. Honestly asking, and honestly not trying to be awkward, but how does WikiSource address Ams80's concerns? It is freely editible, difficult to search and duplicated better elsewhere. Tompagenet 01:18, 26 January 2004 (UTC)
          • People wouldn't be saying this if the articles had the first trillian primes. But it doesn't. In any case, a list of primes is not encyclopedic. We only keep lists if they are useful in making an encyclopedia. This list is not. Anthony DiPierro 01:34, 27 January 2004 (UTC)
          • Primality Certificates could (should?) be used on all numbers which would ever need to be listed on this page.76.8.72.250 00:18, 13 November 2007 (UTC)
  • Keep as a redirect to Prime numbers, which already contains a list only slightly smaller than this one. The superfluous lists described above are generated by simple functions f(n), which is probably why square numbers, doesn't bother with a list beyond the fifth, whereas prime numbers does. Onebyone 00:53, 26 January 2004 (UTC)
    • Agreed, redirect. --Jiang 01:29, 26 January 2004 (UTC)
  • Redirect. --zandperl 01:33, 26 January 2004 (UTC)
  • Keep, but not as a redirect. Keep as is. An encyclopedia is a reference. A quick reference to the list of prime numbers is useful. Kingturtle 02:14, 26 January 2004 (UTC)
    • Thanks for the comments, Kingturtle - an encylopaedia is a reference work, but that does not mean it should contain all data - we have, for example, Wiktionary (a wiki dictionary) and wikisource (for storing data tables and refernce works). Although it doesn't make explicit refernce to it, I would say that Wikipedia:What Wikipedia is not is relevant here - I quote: "wikipedia is not...any other source material that are only useful when presented with their original, un-modified wording." - this list of primes is useless if the numbers themselves are modified (9883883 will always be prime, even if I choose to remove it from the page) and so lend themselves more to the definition of source materials. Tompagenet 10:43, 26 January 2004 (UTC)
  • Well, we seem to be reaching an agreement that the page should be kept. Whether that should be as a list or a redirect can be thrashed out on the talk page... -- Oliver P. 02:18, 26 January 2004 (UTC)
  • Redirect. --Sean 03:24, 26 January 2004 (UTC)
  • Keep- It is of general academic interest, for example, it may be interesting to note in what number the numbers end, and get an idea of what is likely to be a prime number and so on...Also, from my limited knowledge, I recall that there is no formula for generating prime numbers and hence the list is useful as someone else has said earlier. A redirect to Prime numbers wouldn't be useful because it would limit the list KRS 04:48, 26 January 2004 (UTC)
  • Keep, useful to students and others Jack 08:05, 26 January 2004 (UTC)
  • Delete. An encyclopedia is not a place to put all knowledge: it's for particular kinds of knowledge. This is not one of those kinds.
  • Delete. Wedge, Edge. Of. Thin. This is a potentially infinite list. Next stop List of all people living and dead. Bmills 14:58, 26 January 2004 (UTC)
  • Perhaps it's worth noting that the digits of pi (a similarly never ending generated sequence) are not on wikipedia, they are on wikisource. Remove it from here I still say Tompagenet 00:19, 27 January 2004 (UTC)
  • Delete. There are many better places than Wikipedia to find prime numbers, some of them already linked to by the article. Andrewa 09:18, 27 January 2004 (UTC)
  • Delete. This is not an article and not useful. Angela. 20:59, 27 January 2004 (UTC)
  • Delete. This is the kind of thing that belongs on Wikisource because it's a primary source. We already have the first 20,000 prime numbers there and other lists of numbers. Let's not increase the chances for errors to be introduced into these lists by duplicating this material. --Minesweeper 22:38, 27 January 2004 (UTC)
  • Delete. A complete waste of space next list of grains of sand on Englands beaches there needs to be sensible limits and serious articles Archivist 23:28, 27 January 2004 (UTC)
  • I still have a gift for creating highly controversial items! How about if we have separate lists? List of prime numbers 1-5000, List of prime numbers 5001-10000, List of prime numbers 10001-15000, etc. - Arthur George Carrick 03:02, 28 January 2004 (UTC)
  • Delete or redirect. As Ams80 says above, it will be too hard to protect this page from vandalism. Specialized external resources do store prime numbers better and are already linked in that article. Rossami 21:55, 28 January 2004 (UTC)
  • Keep and expand with descriptions of how these and many of the later ones were discovered. The plain list is of practical value; coupled with the description of methods used to calculate them and the record holders over time it's eminently encyclopedic. See [6] for some of the history of prime number proving. Jamesday 23:14, 29 January 2004 (UTC)
  • Delete, there are infinitely many prime numbers. Listing only the small ones would violate NPOV, as it is biased against larger prime numbers that are also just as prime. Maximus Rex 02:00, 1 February 2004 (UTC)
  • Funny. New stand on the issue; is it so bad to give Wikipedians something to do in their spare time? - Arthur George Carrick 02:58, 1 February 2004 (UTC)
    • Lol, really. Why don't we have someone make an internal link for all the numbers, then pages for them. :P Ilyanep 02:59, 1 February 2004 (UTC)
    • My sentiments exactly! Every number should be a link, but who has the time? Please, anyone, if you choose to make more of the numbers links, put up a notice that you are editing the page. - Arthur George Carrick 03:03, 1 February 2004 (UTC)
• 81.5.166.191, stop redirecting my page. There is some support for it and the argument is ongoing. - Arthur George Carrick 04:17, 1 February 2004 (UTC)
• Why isn't this more straightforward? Everything else aside, a more extensive list of primes is at Wikisource, here. Delete this one. -- Seth Ilys 03:10, 1 February 2004 (UTC)
  • Because this project is Wikipedia, not Wikisource and all CD, print and mirrored copies of the Wikipedia will not come with a complete copy of Wikisource. Each work is independent and has to have sufficient content to fulfill its own role. Please feel free to try deleting the articles on chemical elements just because another wiki is covering chemistry in more depth...:) The only question we need address here is what this project finds useful. I'm content to trust that the article is useful as it is and will become more so once someone gets around to writing more about the history and adding some of the more significant larger primes. I'd do it myself if legal writing wasn't a more useful use of my own editing time - I find the history interesting. Jamesday 04:22, 1 February 2004 (UTC)
• Excellent point Jamesday. Uneditable, 81.5.166.191? This is not uneditable; rather, it has an infinite capacity for growth. - Arthur George Carrick 04:43, 1 February 2004 (UTC)
  • I think the point 81.* is trying to make is that the page is way too large. Why not just have the first hundred primes, or some nice amount, instead of having a extremely large page with no links, if this page is to be kept? Dysprosia 10:55, 1 February 2004 (UTC)
• DELETE. DELETE. DELETE. People arguing for this to be kept appear to not understand what an encyclopedia is meant to be. We are an encyclopedia, not a compendium of lists upon lists. -- Tarquin 10:46, 1 February 2004 (UTC)
  • RE: Wikipedia is "not a compendium of list upon list." er....yes it is. The proof is in the pudding: List of reference tables and List of all lists which do not contain themselves. This encyclopedia contains hundreds of lists that you yourself might not think are useful. A list of prime numbers is a legitimate list, and has use to some people. Kingturtle 18:17, 1 February 2004 (UTC)
    • References tables are useful. Some lists we have are methods of finding articles. They're not fantastic, but a case can be made for them. And as for List of all lists which do not contain themselves ... is that one still around? Are you KIDDING when you cite that as a precedent? -- Tarquin 18:24, 1 February 2004 (UTC)
  • Let me clarify, my reference to the List of all lists which do not contain themselves is so people involved in this debate can see 100s of lists. Some lists are fun, some are useful. To the nay sayers, what harm is there in having a list of prime numbers? Kingturtle 18:46, 1 February 2004 (UTC)
• Delete, for all the reasons mentioned above. -- uriber 17:40, 1 February 2004 (UTC)
• Delete. useless @ wikipedia, being "source code" = wikisource material, + all the other reason to del above ... JDR
• Delete. Kevin Saff 22:54, 10 February 2004 (UTC)
  • Since there's slightly better content now, Keep. Kevin Saff 19:11, 1 April 2004 (UTC)
• Keep first 100 or so, and point in direction of Wikisource where I understand this list also exists? But delete the rest! And as pointed out earlier - such a list is way to easy to destroy - newbies who happens to find this list probably wont check the page history to check whether someone has changed a '1' for a '3' somewhere in the middle of that list. Maybe it would be even more useful and safe (in this case) to point to non-wiki sources? (Hiding behind my desk...:-o Mikez

• There are dictionaries containing flags of the world and the periodic table of the elements, but does that mean they're not useful in encyclopedias? - Arthur George Carrick 19:10, 5 February 2004 (UTC)

• I see The Cave Troll recently vandalised the page by changing a 3 to a 4. Luckily, it was caught. If the page is vandalised again, who's to say it will not be caught again? - Arthur George Carrick 20:01, 9 February 2004 (UTC)

• How about moving this 'list of prime numbers' to an article called 'prime numbers' that describes properties, relationships and interesting uses of them as well?

• Keep, this is relevant mathmatical information. While there may be infinite prime numbers, we've only discovered them up to a certain point. Unless a new mathmatical technique is discovered, or computing speeds increase dramatically, the list isn't likely to grow terribly fast either. Oberiko 17:15, 22 February 2004 (UTC)

What is the name of the following number

A number that is one more than a power of two?
$M_{n}=2^{n}+1.$
I ask this because there are some similar numbers, for example:

• Cullen number
• Fermat number
• Pierpont prime
• Proth number
• Wagstaff prime

However, I could not find the name of the above number from Wikipedia. In addition, I think that it is surprising because the above number that is a prime number is useful in RSA, and the examples of the prime number are:
2, 3, 5, 17, 257, 65537, ...
If someone can tell the name, I will be very appreciated. QQ (talk) 08:52, 12 December 2007 (UTC)

All primes of this form with n>0 are Fermat primes. In other words: If 2ⁿ+1 is prime for n>0 then n is a power of 2. I don't know whether there is a general name for all numbers of form 2ⁿ+1, but it's irrelevant for this article which already lists Fermat primes. PrimeHunter (talk) 13:01, 12 December 2007 (UTC)

Sorry, I am stupid, I don`t know why if $2^{n}+1$ is prime for n>0, then n is a power of 2. Could you please tell me the link of the proof of the above statement. QQ (talk) 19:59, 27 December 2007 (UTC)

The proof is in Fermat number#Other theorems about Fermat numbers. PrimeHunter (talk) 22:03, 27 December 2007 (UTC)

Prime counts

The nth prime and the nth twin prime for selected round relatively small n values has recently been added. I don't think such counts belong in List of prime numbers. Prime number counts belong in prime-counting function which already has a table of π(x) going up to far larger x values (more than 10¹² times larger). Twin prime counts would be better placed in twin prime. Computing and listing prime and twin prime counts below x for large round x values is a notable endeavour reported by many sources. http://www.ieeta.pt/~tos/primes.html and http://www.trnicely.net/index.html#PIX have large tables and large values. The nth prime and nth twin prime for round n gets far less attention in sources and it appears that only far smaller values have been computed. PrimeHunter (talk) 23:45, 5 March 2008 (UTC)

List of median primes removed

Their was concensus to delete the page on median primes about two months ago. The numbers that were listed here are primes taht are also centered square numbers. 141.217.41.211 19:28, 16 July 2004 (UTC)

KEEP IT! I'm in middle school and this helps me in math. The name is all right. I do not expect any one to type the prime numbers into infinity. That would be stupid! 76.0.82.127 (talk) 23:55, 6 March 2008 (UTC)

You are replying to a post from 2004, and it's only about one of the listed prime forms. It was removed in 2004 [7] but later added again with a new name at List of prime numbers#Centered square primes. PrimeHunter (talk) 00:36, 7 March 2008 (UTC)

Tri Primes

I been looking for information on Tri Primes but I couldn't find any. I am trying to help someone out with a homework problem. Tri Primes are (p, p+2, p+4) example: (3,5,7). Though, the question asks IF their are any other Tri Primes and if not why. So (3,5,7) might be the only form but it might be worth putting in the article that Tri Primes exist. --4.178.141.14 (talk) 23:12, 21 November 2007 (UTC)

I found info on it at Prime triplet but it should still have info on it on the main page and maybe a link to Prime triplet. Something like "A Tri Prime is (p, p+2, p+4) and only one form of this exists. For more info go to Prime triplet." Also maybe put the (p, p+1, p+3) on the list too under maybe... Double Prime? or some other offical name for it. --4.178.141.14 (talk) 23:37, 21 November 2007 (UTC)

I haven't heard the names "Tri prime" and "Double prime" or other names for those patterns, and I think it would be odd to name a prime pattern which trivially only has one occurrence. Wikipedia content, including names of things, should be based on reliable sources. See also Wikipedia:Avoid neologisms. PrimeHunter (talk) 23:45, 21 November 2007 (UTC)

No, there are no more "Tri Primes" other than 3,5,7 - it's not hard to prove. It's also meant as an exercise, not something you look up. So good luck. —Preceding unsigned comment added by 99.226.91.117 (talk) 08:09, 23 March 2008 (UTC)

Computing the Nth Prime

"In general, the Nth prime number can be easily computed by the Prime-counting function."

While I don't dispute this statement, given $\scriptstyle \pi (x)$ we can find the nth prime. But computing the prime counting function isn't easy, and as far as I know - there's no other way to compute it other than listing out the primes. So this statement is misleading? It should be reworded unless there is an objection. I suggest changing the word 'computed' to 'estimated'.

"See the Prime-counting function for a list of more primes past the 5,000th prime." is definitely wrong. There's no list on that page. —Preceding unsigned comment added by 99.226.91.117 (talk) 08:15, 23 March 2008 (UTC)

I have changed the text.[8] Note that there are faster ways to compute the prime counting function than listing out the primes. PrimeHunter (talk) 02:29, 24 March 2008 (UTC)

Double factorial primes

1, 2, 518, 33416, 37310, 52608 ... why are those numbers in a prime sections , joke ?? Nico92400 (talk) 10:42, 17 September 2010 (UTC)

I have explained [9] that the values of n in n!! ± 1 are listed. Maybe it would be more consistent to list the decimal expansion of the first primes. PrimeHunter (talk) 14:23, 17 September 2010 (UTC)

Splitting the list

I believe this list could benefit from a split into "List of prime numbers" and "Typology of primes" or something similar. That would provide a clearer focus, and with an improved lead, this could easily be on it's way to featured list candidacy, which need more input from math and basic subjects. Sandman888 (talk) 20:12, 17 September 2010 (UTC)

With no comments I'll perform the split into list of primes and typology of primes. Sandman888 (talk) 18:24, 20 September 2010 (UTC)

Oppose split, but the name can be discussed although "typology" doesn't appear to normally be used when discussing different forms/types/classes/sequences of prime numbers. I'm the main contributor to the page. I overlooked your first post on a long watchlist in a weekend I was sick. A split was suggested and opposed in 2007 at #rename/split? A weekend with no Wikipedia:Splitting templates seems little before splitting such an old list with no input when a previous suggestion was rejected. The current format with both a list of primes and prime forms started in February 2004: [10]. There is room for both the first 500 primes and shorter lists of special forms where readers can compare each form to the full list on the same page. Do you mean the new content at "List of prime numbers" should just be one long list of prime numbers and essentially nothing else? That doesn't sound like something Wikipedia normally reserves a page for and it might not survive an AfD today. The current combined list was a speedy keep at Wikipedia:Articles for deletion/List of prime numbers in 2007. User:CRGreathouse has worked on and off on User:CRGreathouse/Tables of special primes since 2008. I'm not sure of his intentions but I will notify him. PrimeHunter (talk) 19:39, 20 September 2010 (UTC)

It looks like good stuff his list! I think it's just a few tweaks away from becoming featured! To be honest I do believe a list of primes only would survive an AfD debate, because primes are a notable subject, and it's infinitely more useful than all of the other rubbish (entertainment and sports) out there. I will also add that the current title is not very descriptive if the focus of the article is a "typology" of primes. Sandman888 (talk) 19:52, 20 September 2010 (UTC)

I'm glad you like my article. It was developed as a response to this page (though not a copy) -- an experiment to see how else the information could be presented. I did try very hard to include relevant information and citations so that, if incorporated into Wikipedia, it would be appropriately sourced. But it still hasn't been, even after 2 years of work -- it's just on my user namespace.

I have no strong opinion on the split. On one hand (WP:OWN notwithstanding) I'm unwilling to tell PrimeHunter what to do with 'his' article. On the other I'm not keep on keeping the two things together: a table of primes and a list of prime classes. But I err slightly on the side of keeping the list 'as-is', because I don't think that the table of primes by itself would be kept as an article, and so a split is tantamount to simply deleting the table from this article.

Of course I would not oppose a rename. Neither this article nor my article User:CRGreathouse/Tables of special primes have particularly good names at the moment.

CRGreathouse (t | c) 22:54, 20 September 2010 (UTC)

I don't have ownership ideas about the list. If there is consensus against me then that's OK. By the way, earlier this year I worked offline on a possible navbox for prime classes but I was unsure how to group them, whether to include definitions for some of them, and how many articles to include. Including "X number" because it has an "X prime" section seems questionable. This is where I got to before pursuing other work: User:PrimeHunter/Prime classes. Would this or some other navbox be good as another way to connect the articles? Only a couple of them currently have a navbox and it's not for primes. PrimeHunter (talk) 23:44, 20 September 2010 (UTC)

For the record: I'm not claiming that you think you own the article, just that I respect you as an editor and trust your judgement here. You're more familiar with the article than I am.

I have the same issue including many of the integer sequence primes. If I come up with a solution I'll tell you.

CRGreathouse (t | c) 03:44, 21 September 2010 (UTC)

1) CRGreathouse could you be convinced to move your wonderful article to "Typology of primes" or something similar? I believe it has a decent shot of becoming featured. 2) Are AfD concerns seriously the only concern for not splitting? I really do not believe anyone would want to delete a list of primes when given sufficient counter-arguments. We currently have a List of United states presidents with facial hair during their tenure which probably will survive deletion. IMO "Primes >> United states presidents with facial hair during their tenure" as a list topic. Sandman888 (talk) 17:52, 21 September 2010 (UTC)

Circular Primes

The list refers to OEIS. I check that site, as well as 2 others I Googled 1, 2,and none agree with the article list, while they agree among each other. Any ideas?--Billymac00 (talk) 06:46, 8 December 2010 (UTC)

I have explained the difference in [11]: Some sources only list the smallest prime in each cycle. http://primes.utm.edu/glossary/xpage/CircularPrime.html says: "below we list all of the known circular primes by just listing the smallest representative from each cycle, that is, we list just 1193, not 1193, 1931, 9311 and 3119." That source actually agrees with us that 1931, 9311 and 3119 are also circular primes. They also satisfy the definition in both http://oeis.org/A016114 and http://home.comcast.net/~babdulbaki/Circular_Primes.html but in both places they are omitted without explaining why. PrimeHunter (talk) 13:56, 8 December 2010 (UTC)

Unsourced names

Yesterday Giftlite added [12] 4 sections with piped links as headings: Centered pentagonal prime, Jacobsthal prime, Jacobsthal-Lucas prime, Leonardo prime. None of the names are sourced and none of the articles mention primes. There are many cases where some number form is called "X number" for some X, and mathematicians later say "X prime" about a X number which is prime. That appears to be the implied meaning of the 4 prime names. But this naming scheme is not always used. For example, a primorial prime is not a primorial number which is prime, a factorial prime is not a factorial number which is prime, a Riesel prime [13] is not a Riesel number which is prime, an Euler prime (different rare meanings) is usually not an Euler number which is prime, a perfect prime (different rare meanings) is not a perfect number which is prime, a Wilson prime is not a Wilson number (different rare meanings) which is prime. I think it is unverifiable original research to be the first to say "X prime" about a X number that is prime. I suggest these rules for List of prime numbers:

1. Names of prime forms must have been used by a reliable source.
2. The definition of the prime form should be given (even if it just says "X numbers that are prime").
3. There must be a link to an article mentioning that prime form (I view this list as a list of articles about prime forms).
4. If no source has named this prime form then there must at least be a source which has mentioned primes of this form without naming them.
5. If a prime form is unnamed then a description but no invented name can be given here. "X numbers that are prime", "X number primes" or "Prime X numbers" may be acceptable when "X number" is an established name.

I don't know what Giftlite has but after some Googling, the only of the 4 new names I could find was a single (Chinese?) page saying "Centered Pentagonal Prime".[14] One non-English possibly self-published page seems insufficient. It has MathWorld pages as references but none of them mention "Centered Pentagonal Prime". It's also the only source I have found which mentions centered pentagonal numbers that are primes.

oeis:A049883 is "Primes in the Jacobsthal sequence" so that prime form but not the name "Jacobsthal prime" has a known source. I haven't found mention of Jacobsthal-Lucas numbers or Leonardo numbers that are primes. PrimeHunter (talk) 16:52, 5 February 2008 (UTC)

PrimeHunter, I'm going to revert those four (4) named prime types I added. Thank you for your feedback. Giftlite (talk) 18:08, 5 February 2008 (UTC)

well, I know this note is older, but likely the Centered Pentagonal Prime are just the prime subset of the Centered pentagonal numbers. There are about 131 in the first 1000. ref OEIS A005891.--Billymac00 (talk) 04:50, 9 December 2010 (UTC)

Rename the article

Shouldn't this be renamed to "Notable Prime Numbers" instead of list of, as only a vanishingly tiny fraction of all prime numbers are listed on this page. Clearly less than one percent of all prime numbers are printed here. Hcobb (talk) 02:49, 14 May 2011 (UTC)

If this article were renamed, I would prefer something like Types of prime numbers. Notable prime numbers suggests that every single prime in this list is notable (which isn't the case). Often, a single number like 3511 is only notable in connection with a specific class of prime numbers. I don't think there would be much to say about 3511 that is not related to it being a Wieferich prime. Also a great fraction of the wikilinks in this article pointing to the article of a specific number seem to be redlinks. I think your suggested renaming would be misleading and I therefore oppose changing the name to Notable Prime Numbers. I would, however, generally be open to suggestions renaming the article, if they were a better fit for this article than the current name, which may be too broad in some sense. I simply think your suggested name isn't a better fit than the current name. Toshio Yamaguchi (talk) 12:14, 14 May 2011 (UTC)

I also oppose "Notable Prime Numbers" or the proper capitalization "Notable prime numbers" as misleading. It's mainly a list of prime number types, many of the individual primes are non-notable, and Wikipedia has lots of "List of ..." articles which are not exhaustive. PrimeHunter (talk) 13:22, 14 May 2011 (UTC)

Then this should just be a category page? Hcobb (talk) 14:51, 14 May 2011 (UTC)

I think this list being an article is fine. Transforming this list into a category would result in quite a large loss of information (like for example the first examples of each type, the links to the OEIS entries or the brief description), which is, why I also would oppose making this only a category page. What exactly are your concerns with having this as an article? Is it just the name? I would be open to discuss a name change, but I think the article should be kept as an article, because most of the entries are notable enough for inclusion in this list (although not all types should have (and do not have) an own article). Toshio Yamaguchi (talk) 15:04, 14 May 2011 (UTC)

If it were a "list of" article then the primes would be listed down and for each prime (listed only once each) there would be a list of categories that prime number belonged to. So this is really "Types of prime numbers". Hcobb (talk) 00:34, 15 May 2011 (UTC)

That's actually what I suggested above and I would support a move to Types of prime numbers. The table listing the first 500 primes could be moved to the article Prime number. Toshio Yamaguchi (talk) 01:55, 15 May 2011 (UTC)

Lists of prime numbers would indicate that it covered some, but possibly not all categories. Hcobb (talk) 15:16, 2 June 2011 (UTC)

It would be confusing. In Wikipedia, "Lists of ..." is a name for a page with links to other Wikipedia lists. See examples at Special:PrefixIndex/Lists of. PrimeHunter (talk) 18:46, 2 June 2011 (UTC)

And this is a page that mostly has links to other pages that list out special kinds of prime numbers. Hcobb (talk) 20:46, 2 June 2011 (UTC)

The articles wikilinked to from this list (the number type articles) are not lists themselves. They list the first representatives of the number type that is the topic of the article. That does not make them "List of ..." articles, however. The number lists in these articles are embedded lists and therefore the list only forms a small part of the whole article in most cases. "Lists of prime numbers" would be misleading here. Toshio Yamaguchi (talk) 21:35, 2 June 2011 (UTC)

Expanding the list?

Template:Expand list was added by 85.224.165.193 (talk) with this edit. What do others think how the list should be expanded and what particular information is missing? Are there any notable types of prime numbers missing (for example types having an OEIS entry)? Toshio Yamaguchi (talk) 17:39, 11 August 2011 (UTC)

Wicketkeeper.woods (talk) 02:55, 10 September 2011 (UTC)Add pentagonal primes?Wicketkeeper.woods (talk) 02:55, 10 September 2011 (UTC)

Double Mersenne primes

The entry for the double Mersenne primes currently contains the following statement:

"As of 2011, these are the only known double Mersenne primes, and probably the only double Mersenne primes."

Where does the assumption that these are probably the only double Mersenne primes come from? The article Double Mersenne number does not contain this statement and no source for this is given. Unless someone can provide a reason why this should be retained, I am going to remove it. Toshio Yamaguchi (talk) 17:40, 5 December 2011 (UTC)

It was in one of the existing sources in Double Mersenne number. I have added it there.[15] The source didn't mention the reason so I omitted it. A random integer n has chance 1/log(n) of being prime by the prime number theorem. The sum of 1/log(n) for all double Mersenne numbers n with unknown status is extremely small. The "chance" of primality for double Mersenne numbers seems a little higher than random numbers because double Mersenne numbers avoid small factors, but a prime still seems very unlikely based on common heuristics also used for lots of other prime forms when qualified guesses are made. PrimeHunter (talk) 04:10, 6 December 2011 (UTC)

Lucky numbers ?

Under the types of primes section there is a list of "lucky primes" I believe that this is just too subjective and has to go, in my opinion it goes against the encyclopedic nature of wikipedia I think that it should be removedMoneya (talk) 18:58, 21 April 2011 (UTC)

Lucky number is a mathematical name. It wasn't invented by Wikipedia. Many things have odd names. Wikipedia just reports what things are called by reliable sources. There are also articles Fortunate number, Friendly number, Frugal number, Weird number and so on. The more famous Perfect number and Irrational number may also sound "subjective" but these are the established names. PrimeHunter (talk) 21:26, 21 April 2011 (UTC)

Don't forget Sexy primes. :-) Th4n3r (talk) 19:11, 22 March 2013 (UTC)

"Anti"-Thabit number primes

The list has an entry for Thabit primes. The article about the numbers also mentions primes of the form 3×2ⁿ+1 and I know that PrimeGrid's 321 Prime Search looks for both forms. Interestingly I was unable to find a complete list of the primes of the +1 form (OEIS doesn't seem to contain them either). Does such a list exist? The only terms I am aware of are those found by PrimeGrid, all of which seem to have at least 1 million digits. I guess it shouldn't be too hard with a suitable program to test small candidates, but I currently don't one. I guess one would implement a version of the Brillhart–Lehmer–Selfridge test for this. -- Toshio Yamaguchi 12:39, 25 April 2013 (UTC)

n is OEIS:A002253. PrimeHunter (talk) 13:58, 25 April 2013 (UTC)

Thanks. I added the primes to the list under a subheader under List of prime numbers#Thabit number primes listing the first 10 terms. -- Toshio Yamaguchi 16:17, 25 April 2013 (UTC)

Insufficient information in "Annihilating primes," "Gilda's primes," and "Swinging primes" section

The "Annihilating primes" section doesn't state what the shadow of a sequence is; the "Gilda's primes" section doesn't state what Gilda's numbers are; and the "Swinging primes" section doesn't state what the swinging factorial is. Blackbombchu (talk) 23:14, 10 November 2013 (UTC)

I added a better definition of the annihilating primes. -- Toshio Yamaguchi 14:23, 11 November 2013 (UTC)

The Gilda's primes entry now has a more precise explanation as well. -- Toshio Yamaguchi 08:33, 12 November 2013 (UTC)

And finally there now is a definition of the swinging factorial at the swinging primes entry. -- Toshio Yamaguchi 09:19, 12 November 2013 (UTC)

Definitions

I think the list gives a better overview with short definitions for each type, so I spent a few hours adding it. PrimeHunter 16:56, 8 January 2007 (UTC)

Uhhh... does anybody other than me have a problem with the opening definition: "A prime number is a number that cannot be divided by a number other than 1 and itself."??? This simplistic definition fails because any number can be divided by anything other than zero. The issues are whether or not the target number (or "number under test") is an integer, the divisor is an integer and the operation leaves a remainder other than zero. Considering that "Factor" is wiki documented, I'd be happier to see a definition such as "A prime number is an integer that has only two factors (1 and itself).", with the appropriate embedded link.71.202.80.15 (talk) 03:15, 30 May 2015 (UTC)Thipdar

New topics belong at the bottom of talk pages. This section is from 2007 and there wasn't a definition of prime numbers at the time but just a link to prime number which is still linked in the second sentence. My post was about adding definitions to the sections with types of prime numbers.[16] I didn't create the list itself. I agree the current definition of prime number could be clarified. I have copied the definition in Prime number: "A prime number (or a prime) is a natural number greater than 1 that has no positive divisors other than 1 and itself."[17] PrimeHunter (talk) 21:29, 1 June 2015 (UTC)

Ellipsis?

Should an ellipsis be added to those lists containing more primes than listed here? I think it would be helpful to know that the primes listed for a specific criterion aren't the only (or only known) ones fitting the criterion. Pieater3.14159265 (talk) 21:28, 10 August 2015 (UTC)

Yes, I think "..." should be added when there are more known terms. PrimeHunter (talk) 00:25, 11 August 2015 (UTC)

Should I go through and add them? Pieater3.14159265 (talk) 21:18, 14 August 2015 (UTC)

Yes, with a support and no objections in four days, just go ahead. PrimeHunter (talk) 23:39, 14 August 2015 (UTC)

Binary Primes

I was thinking there should be a "Binary Primes" or "Randall Primes" list, where the sequence starts with 0 and is "1" if i is prime and "0" otherwise: 0,0,1,1,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,1,0,0,0,1,0,0,0,0,0,1,0,1,0,0,0,0,0,1,0,0,0,1,0,1,0,0,0,1, ... This can be easily converted to the "Prime Gaps" and visa versa"Robin Randall (talk) 21:31, 6 June 2016 (UTC)

@Robin Randall: This list is supposed to have lists of prime numbers, not a list of 0's and 1's. Your idea is called the characteristic function of primes: oeis:A010051. Prime constant and Copeland–Erdős constant#Related constants is related. PrimeHunter (talk) 22:31, 6 June 2016 (UTC)

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Anti-Fractal

What if prime numbers are an Anti-Fractal? — Preceding unsigned comment added by 82.59.212.31 (talk) 16:28, 27 April 2017 (UTC)

Perhaps you would like to speak more clearly and at greater length. — Preceding unsigned comment added by 31.53.53.231 (talk) 08:53, 28 February 2018 (UTC)

Blue vs Red

What does it mean? Hcobb (talk) 03:47, 29 November 2010 (UTC)

The color shows whether the number has a linked article/redirect or not. See Wikipedia:Red link. The red links seem excessive and many of them should probably be removed. PrimeHunter (talk) 12:53, 29 November 2010 (UTC)

Surely we can spare a page for every prime number? Like 811 is notable for being the smallest non-notable prime number. Hcobb (talk) 17:33, 29 November 2010 (UTC)

I find myself uncomfortable about the idea of creating a page for every prime number, not least because there are an infinite number of them and the database storage costs would be prohibitive. On the other hand pages could be created for truly notable prime numbers, please feel free to follow red-links and create these pages. Kiore (talk) 18:38, 29 November 2010 (UTC)

So why not make this page an autogenerated list of every page in Wikistan that is titled with a prime number? Then the users can click on the numbers (which will then not be red links) and discover whatever other properties it has. Hcobb (talk) 17:25, 27 January 2011 (UTC)

I say this as a first time visitor to this page. The Red and Blue in these lists are confusing and it's not clear that it's part of Wikipedia's normal red/blue linking system. It would make more sense to either remove the red links, or put a note at the at the bottom of the list explaining it (like PrimeHuner mentioned above: "See Wikipedia:Red link)". The presence of the red and blue links on every number makes it seem like there is something inherently notable about the numbers. I had to come to this talk page to finally make sense of why some primes were blue and some were red. (Dfrakes (talk) 19:28, 24 May 2011 (UTC))

Can I second Dfrakes post. That is why I'm on this page too. Surely a short 'red means...' would be polite and useful, given there are so many. — Preceding unsigned comment added by 195.226.152.235 (talk) 17:42, 16 February 2016 (UTC)

One user (@Highresheadphones:) attempted a cleanup of the red links on this page in 2017 by rounding 'red link' primes off in the link (for example, 2946901 links to the page for 1000000). I don't think this is the way to go about removing red links; linking to a page unrelated to the linked prime is just going to confuse readers. This also hasn't aged well, since many new red links have been added to the page since 2017.

I think there are two clear options (short of creating a Wikipedia page for every prime listed):

• Use links for every prime, accepting that many of these links will be red
• Use links only for primes that have existing Wikipedia pages, and avoid including any link for primes without dedicated pages.

It should be noted that, while most sections do link all of their primes, a few sections actually don't currently link any of their primes. This should probably be rectified.

The above users' concerns about red links are real, but I'm not sure this page is the place to attempt to deal with the confusion they cause. Sure, many users unfamiliar with red links on Wikipedia will find this page through a Google search (as of right now, this page is among the top results for the query "list of primes"), but it is a standard across Wikipedia that unresolvable links render as red links.

The trouble with removing links for primes without associated pages is that if these pages are later created, someone will need to come back to this article to add the link back in. WP:RED offers some guidelines on when to link vs. not to link. Since many of the primes in this article do have articles associated with them, I think it's fair to say that any of these primes "could plausibly sustain an article," or at least that determining their notability (rather than the mere existence of an article) individually isn't a practical goal for every prime listed in this article.

The purpose of red links is to give article authors the power to create references to other articles even if those articles haven't been written yet. If you're thinking, "we need a mechanism to allow article authors to make links that only show as links if the page exists already!" well, that's the point of red links. Rather than rendering as plain text, these links render in red to denote that they might be sufficiently notable to warrant an article, but that Wikipedia is not finished.

At any rate, I'm going to switch the misleading links in this article back. In case other users want to remove the red links one day (and turn them to plaintext), I figured I'd at least leave my two cents here for why I prefer to keep the red links around.

SyntaxBlitz (talk) 07:57, 18 July 2020 (UTC)

I've just had another look, and I understand the rationale behind linking to the more general pages, since these pages contain notable numbers in the linked range. I think it might be better in the long run to use redirects instead of linking directly to those pages, but there's no need to change them for now.

SyntaxBlitz (talk) 08:02, 18 July 2020 (UTC)

OEIS source?

For the list of prime numbers, it specifies OEIS as the source, notably 'A000040', however that list only goes up to '271': https://oeis.org/A000040/list

As a reader of wikipedia, it strikes me OEIS are trying to muscle in on some free publicity but it doesn't really fit the wikipedia style to have every other number with an OEIS tagline next to or under it, especially given no-one owns the rights to prime numbers and the list is quite clearly computed beyond the mere '271' that OEIS provides, which seems to me like they're falsely taking credit for some other wikipedian's work.

On a separate note, to chip in on keeping the listing of numbers or not: keep it. As an external individual the list is useful because it's a commonly searched for resource (as opposed to metasquares etc which I doubt many people have heard of), and I suspect it helps a lot of children with their homework. Wikipedia has lists of dates, deaths, births, aircrafts and a chemical table, so it makes sense to have the most commonly referred to prime number as a list. No-one is being severely affected by the presence and it gives an idea of how complicated prime numbers are.

That said, should OEIS really be taking credit for something they clearly didn't do? — Preceding unsigned comment added by 92.1.55.192 (talk) 09:59, 14 October 2015 (UTC)

they have a link to the first 100K here: https://oeis.org/A000040/a000040.txt — Preceding unsigned comment added by Billymac00 (talk • contribs) 17:49, 30 January 2021 (UTC)

Non-special form

I'd be interested in seeing an entry for this (the largest deterministically known). Of course I presume it's << the largest known of any type. SO I merely mean a citation to it, as likely it's too large to fully list here. Is it 40,000 digits or ?? — Preceding unsigned comment added by Billymac00 (talk • contribs) 17:54, 30 January 2021 (UTC)

The largest proven prime which doesn't have a special form that makes it easy to prove primality is at Elliptic curve primality#Elliptic curve primality proving. It's p(1289844341) where p is the partition function. It does have 40,000 digits. I don't see a good sourced way to mention it in our list. By the way, I had the partition prime record (not ECPP record) in 2005 [18] with p(10020010). PrimeHunter (talk) 21:41, 30 January 2021 (UTC)

Semi-protected edit request on 16 April 2021

I am interested in adding another category of prime numbers. This would be the category "digitally delicate primes" along with the first few which are 294001, 505447, 584141, 604171, 971767, and 1062599. Once reference would be https://en.wikipedia.org/wiki/Delicate_prime. Another would be https://www.quantamagazine.org/mathematicians-find-a-new-class-of-digitally-delicate-primes-20210330. Also, if possible, I would like to do the editing myself. ProfRosenthal (talk) 11:03, 16 April 2021 (UTC)

 Not done: requests for decreases to the page protection level should be directed to the protecting admin or to Wikipedia:Requests for page protection if the protecting admin is not active or has declined the request. You need to either include the exact prose you'd like with sourcing, or request the page protection be adjusted. ScottishFinnishRadish (talk) 11:16, 16 April 2021 (UTC)

@ProfRosenthal: They are already listed with another name at List of prime numbers#Weakly prime numbers. Weakly prime number from 2011 and Delicate prime from this month should be merged. PrimeHunter (talk) 12:46, 16 April 2021 (UTC)

Well spotted. I have initiated the merge discussion at Talk:Weakly prime number. "Delicate prime" seems like a better title, but I defer to others for what the WP:COMMONNAME of this concept is. --JBL (talk) 13:26, 16 April 2021 (UTC)

See Also ... Factoring tools.

I suspect I am the only one who would like to see a link to an online factoring tool added to the see also section of this page. 2600:1700:BB00:3220:D9CB:9C54:A57F:8CF3 (talk) 14:47, 12 November 2021 (UTC) JMz

Maybe, but Wikipedia is not a link directory. You should be able to find plenty with google. - MrOllie (talk) 14:50, 12 November 2021 (UTC)