Talk:Primorial prime

The article currently lists the "first few primorial primes" starting with 5. But 3 is also a primorial prime, since it is two primorial plus one. Arguably 2 coud be included as well, since it is one plus the primorial of an integer (but, in this one case, not one plus the primorial of a prime, as the article is currently described).

I do not wish to add this myself since it seems like such an obvious omission that I was worried there might be a reason for it. -- Milo

Thank you! I added the missing ones.--Sae1962 (talk) 08:43, 28 April 2015 (UTC)[reply]

New Primorial Prime Found![edit]

New primorial prime was found by Primegrid!

It is: 843301#-1 (365,851 digits, http://primes.utm.edu/primes/page.php?id=97061)

I will not update the article for now, because it is not fully double-checked. 118.220.2.243 (talk) 09:25, 24 December 2010 (UTC)[reply]

It's in. -Koppapa (talk) 16:29, 24 December 2010 (UTC)[reply]

badly written definition[edit]

This article begins as follows

In mathematics, primorial primes are prime numbers of the form p_n# ± 1, where:

p_n# is the primorial of p_n (that is, the product of the first n primes).

p_n# − 1 is prime for n = 2, 3, 5, 6, 13, 24, ... (sequence A057704 in the OEIS)

p_n# + 1 is prime for n = 1, 2, 3, 4, 5, 11, ... (sequence A014545 in the OEIS)

It looks to me as if the first of the three items amounts to part of the definition, whereas the second and third are stating consequences. If the second and third are supposed to be part of the definition, then it's really abusive to the reader to give the beginning of a sequence without characterizing it. But the thing is formatted as if all three listed items are part of the definition. The second and third plainly don't belong within the scope of the word "where". I wonder about the mental state of any reader who is not offended by this way of writing. Michael Hardy (talk) 17:29, 5 December 2011 (UTC)[reply]

You are correct. Your edit to the article is good. PrimeHunter (talk) 00:23, 7 December 2011 (UTC)[reply]

The expression "According to this definition" looks weird though. That the expressions are prime for the listed values of n has nothing to do with the definition of primorial primes. Perhaps the intent is to say "According to the definition of primorial", but that's not how I would read it. I think that writing "is primorial prime" instead of "is prime" would be better.106.71.234.101 (talk) 11:14, 25 October 2018 (UTC)[reply]

I have changed it to say "Primality tests show that ...".[1] PrimeHunter (talk) 11:38, 25 October 2018 (UTC)[reply]

Merge with Euclid number proposal[edit]

There is a four-year old merge proposal that this page merge with Euclid number which hasn't been discussed. As this is a Stale merge proposal and I Oppose (on the grounds that Euclid number is more closely associated with Primorial, being a primorial±1 but not necessarily prime) I'll therefore delete the merge tag. Klbrain (talk) 13:23, 27 April 2016 (UTC)[reply]

Is 2 a primorial prime?[edit]

If 2 is a primorial prime, which is what the “Primorial primes” page says, then the page for “29 (number)” is incorrect in saying that 29 is the fourth primorial prime—it should be the 5th primorial prime.

I am mentioning this on both pages in hopes that someone helps resolve the issue. I cannot find a definitive list of primorial primes that is not recursive with the definition itself. (Probably my own fault.) OwenParkerPhD (talk) 05:09, 5 October 2020 (UTC)[reply]

It seems to be a question like whether 0 is a natural number: opinions differ but no one is wrong. OEIS says 2 is primorial (i.e. p₀# + 1 counts) but Wolfram and others introduce the concept of p# where p is the largest prime being multiplied; obviously the null product has no such p. WikiProject Mathematics might produce more informed insights. Certes (talk) 09:52, 5 October 2020 (UTC)[reply]