Talk:Prime number
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Prime number has been listed as one of the Mathematics good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.  
 
A fact from this article appeared on Wikipedia's Main Page in the "Did you know?" column on April 4, 2018. The text of the entry was: Did you know ... that prime numbers have been studied since the time of the ancient Greeks, but had few realworld applications until the invention of publickey cryptography in the 1970s? 
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First line wrong[edit]
The first line is wrong. It should read: "A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers number greater than 1." 50.206.176.154 (talk) 02:04, 26 September 2021 (UTC)
 It currently says: "A prime number (or a prime) is a natural number greater than 1 that is not a product of two smaller natural numbers." That is sufficient. If one of the numbers is 1 then the other has to be the number itself and that is not smaller than the number. PrimeHunter (talk) 04:27, 26 September 2021 (UTC)
Definition in the lead[edit]
Although involving products in the definition instead of divisors is correct (and rather elegant), it is still pompously so. It requires a nonnegligible amount of thinking for the uninitiated, and I have never seen it worded as such anywhere else, nor do math profs usually teach it that way.
This very clearly violates WP:ASTONISH by trying to be clever, besides obviously being WP:OR. 105.156.135.60 (talk) 19:49, 26 September 2021 (UTC)
 You have got to be kidding me. It is far from being original research – sources for this definition are not difficult to find – and in fact is deliberately nontechnical by using multiplication, a simpler and more familiar concept than that of a divisor. In the US, students start learning about multiplication in the second grade. Division is a thirdgrade concept, and factorization, multiples, and divisors are fourthgrade concepts. When it is possible to express things more simply using lowerlevel concepts, that is what we should do. —David Eppstein (talk) 20:13, 26 September 2021 (UTC)
 Googling "definition of prime number", and going as far as four pages deep, the one and only website that mentions a product —mathisfun.com— does so by avoiding the need from the reader to realize that "two smaller factors" means 1 is not included (by stating so explicitly), since that would involve the number itself (which is not smaller). And as you can see in the talk page again and again, and presumably why the article is restricted, probable adults are still getting confused by the wording, and I guarantee you that 2nd, 3rd, 4th graders and the rest of the population will be too, with a likelihood far more significant than that of 2nd graders reading about prime numbers on Wikipedia while still being unaware of the concept of divisors.
 I write code for a living, and I sure as heck love my clever oneliners, but my coworkers and other people that have to understand/maintain my code don’t really. As such, I tend to avoid them. I hope you will do the right thing here. 105.156.135.60 (talk) 21:35, 26 September 2021 (UTC)
 Resisting the temptation to write a clever oneliner about programmers or about your reliance on web searches instead of reliable sources, a quick search quickly found examples of sources that define it in exactly this way: [1] [2] [3]. —David Eppstein (talk) 21:50, 26 September 2021 (UTC)
 (edit conflict)I guess that the definition that you find less astonishing is the one that suppose to know what is a divisor. Wikipedia is aimed for the widest possible audience. So a definition that use less technical concepts (here the concept of divisor) is less astonishing and more adapted to a large audience. It is not the fault of Wikipedia if some teachers use wordings that are less simple than needed. D.Lazard (talk) 20:17, 26 September 2021 (UTC)
Semiprotected edit request on 4 October 2021[edit]
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Add this (an actual pattern to the primes): https://wiki.alquds.edu/?query=Draft:Tobi_Primes. TobiOdeyemi (talk) 13:26, 4 October 2021 (UTC)
 Not done: Wikipedia does not publish original research. PrimeHunter (talk) 14:02, 4 October 2021 (UTC)
Alternative definition[edit]
"A prime number is an integer greater than 1 that cannot be expressed as a product of prime numbers."
Is technically correct, though I suppose Wikipedia prefers not describing a subject in terms of itself. 94.191.136.102 (talk) 00:21, 18 December 2021 (UTC)
 It's clever, but I think this would be too confusing to nonmathematicians, who we want to keep as an audience. (Also finding sources for this variation might not be easy.) —David Eppstein (talk) 00:25, 18 December 2021 (UTC)
NewPGen[edit]
User:Gusfriend has suggested merging NewPGen into this article. I strongly oppose this merge. With no sources, there is no sourced content to merge, and unsourced content should not be included here or elsewhere on Wikipedia. Further, this piece of software is far below the level of significance needed to make it relevant for the main article on prime numbers, a topic with a huge history and many moreimportant subtopics that could not be included in this alreadylong article. The removal of the prod on NewPGen, by User:Explicit, was a mistake. It should have been left to die quietly. Now it will have to go to an AfD. —David Eppstein (talk) 16:19, 11 February 2022 (UTC)
 I agree that NewPGen obviously should not be merged here. I don't see a reason to delete the article itself, though. YMMV.  CRGreathouse (t  c) 17:27, 11 February 2022 (UTC)
 My merge proposal was in response to the removal of the prod. I am happy to support removal of the merge proposal and the AfD on the original page. Gusfriend (talk) 23:39, 11 February 2022 (UTC)
 If NewPGen should be merged anywhere, then probably to Primality tests, which may be worth considering (I don't currently have any strong opinion on that, since I didn't try locating sources) Felix QW (talk) 13:36, 12 February 2022 (UTC)
In the 19th century many mathematicians still considered 1 to be prime[edit]
The current #Primality of one section says (emphasis mine):
 In the 19th century many mathematicians still considered 1 to be prime,^{[source]}
And its source, CaldwellXiong (2012), "What is the smallest prime number?", p. 9, chapter 5, certainly states (emphasis mine):
“  There is no question that for the 17th through early 20th century many mathematicians
listed the number one as a prime, 
” 
The same source, pp. 12, chapter 1, states:
“  And before we changed it in late 2011, the English Wikipedia article on prime number said "until the 19th century, most mathematicians considered the number 1 a prime." There were (and are) individuals who defined the number one to be prime, but as we will see in this brief note, the history is much more complicated than "one used to be prime." At first, most started the sequence of primes with 2, but some began with 3 and a rare few began with 1. There does not appear to be any period of time during which most mathematicians defined one to be a prime.  ” 
The problem I would like to raise here is the interpretation of the word "many" in our current description.
I believe the fact is that "in all ages, the majority of mathematicians started the prime numbers with 2 (i.e., a minority of mathematicians considered 1 to be a prime number)". (Please correct me if I am wrong about this. I also referenced a related question and answer on SE.)
I believe the current English Wikipedia is correct and that "many" is used in the sense of "many, but not most".
However, as a nonnative English speaker, that meaning was not clear to me, even taking into account the context that preceded it.
Is the current description not misleading to native English speakers? Or could it be rephrased more clearly?126.233.162.35 (talk) 06:33, 24 March 2022 (UTC)
 Trying to make it more precise (e.g. "a significant majority") risks both making the article more polysyllabic and hence more onerous for nonnative speakers to read, and also going beyond what our sources actually state into our own interpretations. ——David Eppstein (talk) 07:25, 24 March 2022 (UTC)
 Isn't it "a significant minority"? Or maybe I misunderstood the historical facts.
 Perhaps the fact is that some mathematicians include 1 and some do not, and we don't know which is the majority?
 If so, it could mean that, in the 19th century, "many mathematicians considered 1 to be prime" and "many mathematicians did not consider 1 to be prime" are both true.
 In the above paper, the sentence on page 9 that I quoted above continues:
“  ..., but it is also clear this definition was never the unified view of mathematicians. Euclid, Mersenne, Euler, Gauss, Dirichlet, Lucas and Landau all omitted one from the primes, ...  ” 
 If we take this as our source, wouldn't a more appropriate description be something like:
 In the 19th century mathematicians were still not unified in their view of the primality of 1, ...
 126.157.197.148 (talk) 10:42, 24 March 2022 (UTC)
 Yes, that was a typo, I meant "significant minority". —David Eppstein (talk) 16:45, 24 March 2022 (UTC)
 If we take this as our source, wouldn't a more appropriate description be something like:
Mathematics[edit]
Which are co prime number 2409:4053:211D:A54F:2601:A55D:E1E0:D81E (talk) 11:10, 26 June 2022 (UTC)
 See Coprime integers. Prime number#Analytic properties calls it relatively prime. Math questions can be asked at Wikipedia:Reference desk/Mathematics. PrimeHunter (talk) 12:43, 26 June 2022 (UTC)
Can a rectangle not have two of its parallel sides equal to 1?[edit]
The image provided at the top of this article is given the caption "Composite numbers can be arranged into rectangles but prime numbers cannot." However, this seems slightly vague, and there is room for inaccuracy in that vagueness. The word "arranged" might imply that some amount of reconfiguring is required to get the end result. However, a number that is arranged in a straight line of units is already a rectangle, with height 1. On articles about even slightly more subjective topics, I would not balk at word choice, given that many different words and phrases could be used interchangeably. However, as this is a mathrelated page about prime numbers, I feel like there is a responsibility to have unerring accuracy. Morgandeefox (talk) 17:58, 11 November 2022 (UTC)
 This is the caption of an image, not a definition. Despite its vagueness, this caption should be easily understood by everybody. Adding accuracy seems noncompatible with a short caption (see MOS:CAPSUCCINCT). Also, "rectangle" is clearly used in its common meaning, since no set of bullets is geometrically a rectangle. D.Lazard (talk) 18:22, 11 November 2022 (UTC)
 Thank you for your response. I find it informative, and a satisfactory address of my concerns. Morgandeefox (talk) 22:30, 11 November 2022 (UTC)
Relevant requested move[edit]
See Talk:Prime (disambiguation)#Should Prime be a WP:D page (Prime (disambiguation)), or be a redirect to Prime number?. Lennart97 (talk) 15:33, 14 February 2023 (UTC)
Move discussion in progress[edit]
There is a move discussion in progress on Talk:Prime (disambiguation) which affects this page. Please participate on that page and not in this talk page section. Thank you. —RMCD bot 18:32, 14 February 2023 (UTC)
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