Talk:Primorial

message: Does anyone know of a reference with details on the sum of inverses of primorials? The sum of inverse integers diverges, sum of inverse primes diverges, sum of inverse factorials converges to e, so it seems possible that the sum of inverse primorials coverges. --Monguin61 09:15, 15 December 2005 (UTC)
replies: text: I don't know, but common sense would seem to say that it diverges much like the sum of inverse primes does. I will go to the library. Also, I will do some number crunching with Mathematica. Give me a day or two. PrimeFan 19:39, 15 December 2005 (UTC)

text: I haven't yet gone to the library, but online I've already found a few interesting references on this matter. I recommend Sloane's as a starting point. The Mathworld article on primorial mentions the interesting relation \lim_{n \to \infty} p\sharp_n^{1 \over p_n} = e. PrimeFan 22:50, 16 December 2005 (UTC)

text: Yes, it~'s trivial that it converges. http://www.research.att.com/~njas/sequences/A064648 gives the sum 0.7052301717918009651474316828882485137435776391... I don't know whether it has a simple expression with common functions. PrimeHunter 23:50, 19 August 2007 (UTC)
replies: text:  Is also straightforward to show \sum_{n=1}^\infty \frac{1}{p_n\#} is rational, using the Cantor series argument, see   78.196.93.135 (talk) 21:38, 19 July 2016 (UTC)
thread_title: Comments

message: Calculating factorials are not polylogarithmic in speed, does this change for calculating primorials??  Also what is the order of growth for primorials, for factorials it is O(e^(Nlog(N))? Ozone 19:23, 15 March 2006 (UTC)
thread_title:  P or NP 

message: --Abdull 09:13, 9 April 2007 (UTC)
replies: text: Good point. I think we could redraw this with yellow dots and it should still be intelligible. Thoughts, anyone else? PrimeFan 20:10, 10 April 2007 (UTC)

text: I think the picture is fine, n! can be continuous, n# can't be continuous. -Gesslein 02:33, 11 April 2007 (UTC)
replies: text: The 'n#' curve is actually a function of the prime itself, not 'n'. So the caption is misleading. Otherwise, the curve would be more aggressive than 'n!'. 187.181.253.25 (talk) 01:49, 10 January 2023 (UTC)
replies: text: It seems that you confuse , the product of the primes not greater than , with , the product of the  first primes. D.Lazard (talk) 10:28, 10 January 2023 (UTC)
thread_title:  Continuous 

message: So I'm up at 2:25AM trying to waste time by going through each article about the counting numbers i.e. 25,26,27 and I come to, I think it was 29. Here I reach an impasse. It is a primorial prime but I have no idea what that is. I go to the primorial article looking for an answer and cannot possibly understand the mathematical gibberish which is supposed to be an explanation. Could someone please explain what this entails in one English sentence at the beginning of the article for the sake of people like me? Lord mortekai (talk) 07:28, 2 November 2009 (UTC)
replies: text: The primorial of a number is the product of all primes less than or equal to that number.  It is similar to the factorial but using the prime numbers only.  For example, the primorial of 29 is 2*3*5*7*11*13*17*19*23*29.  The notation commonly used for a primorial is to follow the number with a '#' (similar to the '!' for a factorial), e.g. 29#.  --mwalimu59 (talk) 19:38, 2 November 2009 (UTC)
replies: text: To put it simply, the prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101… . By the standard definition, the first primorial is 2, the second is 2×3, the third is 2×3×5, the forth is 2×3×5×7, the fifth is 2×3×5×7×11, the sixth is 2×3×5×7×11×13, the seventh is 2×3×5×7×11×13×17, the eighth is 2×3×5×7×11×13×17×19, the ninth is 2×3×5×7×11×13×17×19×23, the tenth is 2×3×5×7×11×13×17×19×23×29, and so on. Robo37 (talk) 20:45, 3 November 2009 (UTC)

text: Wikipedia articles often link to other articles explaining a given term. 29 (number)#In mathematics says: "It is the tenth prime number, and also the fourth primorial prime." Note it links directly to primorial prime (which is not a primorial number but a prime next to a primorial number). 29 = 2×3×5−1. PrimeHunter (talk) 23:46, 3 November 2009 (UTC)
thread_title:  Simplify 

message: The article intro says "There are two conflicting definitions that differ in the interpretation of the argument: the first interprets the argument as an index into the sequence of prime numbers (so that the function is strictly increasing), while the second interprets the argument as a bound on the prime numbers to be multiplied (so that the function value at any composite number is the same as at its predecessor). The rest of this article uses the latter interpretation.". 
That paragraph speaks of an 'argument' but no notation is given.
The following section, "Definition for Primorial numbers", defines the p_n# notation as the product of the first n primes.
As the article intro gives no notation and is adjacent to the p_n# notation, this implies that when the intro says "The rest of this article uses the latter interpretation" (meaning, "the argument as a bound on the prime numbers to be multiplied"), that this applies to the p_n# notation. But this is not how the p_n# notation works; so the article is inconsistent.
I suggest deleting the paragraph in the intro starting with "There are two conflicting definitions that differ in the interpretation of the argument" and ending with "The rest of this article uses the latter interpretation."; because:
* this paragraph is incorrect; it is not the case that "The rest of this article uses the latter interpretation"
* the article doesn't use English phrasing such as "the n-th primorial" but rather uses the two notations p_n# and n#, which are defined distinctly; so the disambiguation that this parapragh tries to provide is unnecessary
Bayle Shanks (talk) 19:30, 29 February 2016 (UTC)
thread_title:  Incorrect introduction 

message: At Wikipedia:Articles for deletion/Compositorial, a merge into this article has been suggested. If you have an opinion on this merge, please weigh in there. —David Eppstein (talk) 18:01, 1 April 2016 (UTC)
thread_title:  Merge proposal from [[compositorial]] 

message: In the table of primorial numbers, there are columns for both "n#" and "p_n#". This is redundant since for each n, you can look up its p_n in the p_n column and then find p_n#. So the same information is given twice, with no additional use. I move that the n# column be removed.
Jamgoodman (talk) 18:04, 22 June 2017 (UTC)
replies: text: I oppose. Tables like this are nearly always meant to be read one row at a time. Removing the n# column would make it hard for many readers to find n# by combining information in two rows. Composite n will be extra hard since it's not in the p_n column and they must figure out which value to use. PrimeHunter (talk) 20:06, 22 June 2017 (UTC)
thread_title:  Removal of redundant "n#" column in table of primorial numbers 

message: I think it would be convenient to have the table display a column containing an easily readable approximate value of the primorials. For example, for  the value could be ≈  — Preceding unsigned comment added by 2601:600:8880:3806:2c26:71d1:3a9:4059 (talk) 
:Agreed, but I think there should only be one value listed per primorial, exact for small and approximate for large, e.g. above 20 digits. I work a lot with primorials and even I don't want to see large decimal expansions. If people actually need large primorials for something then they probably just compute them like me. PrimeHunter (talk) 11:04, 2 June 2018 (UTC)
thread_title:  Proposal for showing the apporximate value in scientific notation in the table 

message: Note: respecting the policy to publish my own job, I declare that the following idea is mine. A demonstration of what is claimed can be found on the website.
Similar to Wilson's primality test it's possible to achieve the same result without using the huge factorial necessary to perform the test with the smaller primorial. The cornerstone of the work is Euclid's theorem on the gcd of which it's possible to provide an original demonstration applied to the primorial.
The Vinc'S primality test (derived from the theorem) can shrink, inside the primorial, the number to carry on for testing. To tell the truth, Wilson's test has the advantage that it doesn't need to know all the prime numbers less than the number we want to test. On the other hand, the Vinc'S test behaves almost like a sieve (like the Eratosthenes one) but it has the advantage of opening the way to new scenarios (factorization?). VincS (talk) 06:11, 15 April 2022 (UTC)
thread_title:  Primality test and prime sieve made by primorial 

message: A conventional designation has been proposed for the function defined in this way and described here:
!x
Using such notation reduces the need for many words or symbols, and is more concise and even laconic.
⁣# - it is there, but it's ugly... The use of an exclamation point before a number is immediately associated with the factorial function, so it is quite clear. However, the # sign, i.e. hash , has several competing uses, so to speak.
sign n# creates a certain problem, maybe a small one, but still:
Describing the text using indexes: x ₙ #  this is getting a bit messy. And since indexes are not usually used before the number, when the symbol of a mathematical operation, it will be !, or # - we put it there, it is optically more readable. Well, it's not a dramatic difference...
 BaSzRafael (talk) 10:04, 29 May 2024 (UTC)
thread_title:  Short form: !x 

message: It seems to me that instead of just the word Primorial , it is worth adding a symbol of the action marked with it, which means that the title should look like this:
Primorial n#
- thanks to this, someone who comes across an unknown function n# - and of course does not have its name - can enter only its designation in Wikipedia and will then receive the redirection he is looking for. It is a matter of the usefulness of the definition introduced: that the title itself should be indicative.
However, there is a problem with the sign representing the number on which the operation is performed, i.e. n. After all, someone may also come across the notation x # - or it may be some selected number, e.g.
However, the most likely search will be n#
BaSzRafael (talk) 11:50, 30 May 2024 (UTC)
thread_title:  Main name