Talk:List of prime numbers

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Articles for deletion This article was nominated for deletion on May 24, 2007. The result of the discussion was Speedy Keep.

Contents

[edit] 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:
  • 5000:
  • 10000:
  • infinite:
    • this isn't possible —Noldoaran (Talk) 20:58, Feb 16, 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 Apr 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 Mar 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):

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 Feb 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 Jan 2004 (UTC)

[edit] 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 Feb 2004 (UTC)
2.)Is it so bad to give Wikipedians something to do in their spare time? - Arthur George Carrick 02:58, 1 Feb 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 Jan 2004 (UTC)
4.)Keep, useful to students and others Jack 08:05, 26 Jan 2004 (UTC)
4.5.)I find it quite useful when working on factorization... - Arthur George Carrick 19:05, 1 Feb 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 Jan 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 Feb 2004 (UTC)

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

[edit] From VfD

  • should not be here. This is not the place for a list of numbers. -- Ams80 23:39, 25 Jan 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 Jan 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 Jan 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 Jan 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 Jan 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 Jan 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 Jan 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 Jan 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 Jan 2004 (UTC)
      • Agreed, redirect. --Jiang 01:29, 26 Jan 2004 (UTC)
    • Redirect. --zandperl 01:33, 26 Jan 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 Jan 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 Jan 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 Jan 2004 (UTC)
    • Redirect. --Sean 03:24, 26 Jan 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 Jan 2004 (UTC)
    • Keep, useful to students and others Jack 08:05, 26 Jan 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 Jan 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 Jan 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 Jan 2004 (UTC)
    • Delete. This is not an article and not useful. Angela. 20:59, Jan 27, 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, Jan 27, 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, Jan 27, 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 Jan 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 Jan 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 [1] for some of the history of prime number proving. Jamesday 23:14, 29 Jan 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 Feb 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 Feb 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 Feb 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 Feb 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 Feb 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 Feb 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 Feb 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 Feb 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 Feb 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 Feb 2004 (UTC)
  • Delete, for all the reasons mentioned above. -- uriber 17:40, 1 Feb 2004 (UTC)
  • Delete. useless @ wikipedia, being "source code" = wikisource material, + all the other reason to del above ... JDR
  • Delete. Kevin Saff 22:54, 10 Feb 2004 (UTC)
    • Since there's slightly better content now, Keep. Kevin Saff 19:11, 1 Apr 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
  • 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 Feb 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 Feb 2004 (UTC)

[edit] 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 Jul 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 [2] but later added again with a new name at List of prime numbers#Centered square primes. PrimeHunter (talk) 00:36, 7 March 2008 (UTC)

[edit] 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)

[edit] 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.

[edit] 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)

[edit] 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 [3] that can factor very large numbers. PrimeHunter 00:24, 18 May 2007 (UTC)

[edit] rename/split?

It was suggested [[4]] 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 [5], 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 [6], and the main list from 1000 to 500 primes.[7] PrimeHunter 23:54, 9 June 2007 (UTC)

[edit] 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)

[edit] 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)

[edit] What is the name of the following number

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

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 2n + 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)

[edit] Unsourced names

Yesterday Giftlite added [8] 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 [9] 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".[10] 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)

[edit] 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)


[edit] 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.[11] 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)