Talk:Factorial prime

Finite or infinite?
Is there any knowledge of whether there are a finite or infinite number of these primes? — Preceding unsigned comment added by 129.177.61.124 (talk) 10:09, 29 November 2004 (UTC)


 * Off the cuff, I couldn't find any source explicitly saying that there infinitely many factorial primes. But my feeling is, that is the case. Primorial primes figure in Euclid's proof of the infinity of primes, and perhaps this could be extended to cover factorial primes as well. PrimeFan 21:34, 29 Nov 2004 (UTC)


 * As far as I know, all we have in this matter are heuristic arguments, which strongly favor an infinitude of factorial primes. Euclid's proof of an infinitude of primes in fact does not use primorial primes, just primorials (which themselves are always composite after 2). — Preceding unsigned comment added by 166.70.71.47 (talk) 02:52, 22 May 2014 (UTC)


 * Here(PDF) is a preprint of a January 2002 paper by Chris Caldwell (maintainer of the Prime Pages) and Yves Gallot of UT Martin, On the Primality of n!±1 and 2×3×5×···×p±1, in which they conjecture that there are infinitely many factorial primes of both forms, with "the expected number of factorial primes of each of the forms n!±1 with n≤N are both asymptotic to eγlogN" (with γ the Euler–Mascheroni constant and "log" being the natural logarithm). -- ToE 17:29, 6 August 2017 (UTC)

Prime deserts
This is odd:


 * ... they sometimes signal the end or the beginning of an extraordinarily lengthy run of consecutive composite numbers. For example, the prime following 479,001,599 is 479,001,629.

Is a sequence of 29 consecutive composite numbers really "extraordinarily lengthy"? This isn't as good even as 1327 ... 1361! (33 consecutive composites between these) — Preceding unsigned comment added by 216.232.207.94 (talk) 02:20, 12 June 2005 (UTC)


 * The truth is, this is a POV, my opinion from a couple of years ago. Since then I've found far more interesting prime deserts, such as the example you mention. I should leave it to someone else to change that sentence. PrimeFan 22:45, 14 Jun 2005 (UTC)

Units and sets
Does it make sense to have an "argument" that 1 is not a prime? Whether or not 1 is prime is more a question of the definition of a prime, i.e. whether or not a unit is admissible as a prime or not. We normally exclude units from the set of primes, because to do otherwise would unnecessarily complicate the statements of a large number of theorems, including the Fundamental Theorem of Arithmetic. The fact that "n!+p is composite when p is prime and <=n" is just one more example of a statement that is more simply stated when units are excluded from the set of primes -- but I would not say this is part of an "argument" that 1 is not prime. — Preceding unsigned comment added by 204.212.175.30 (talk) 19:42, 15 September 2006 (UTC)


 * I find the statement of n! + p far more concrete than any talk of "units" and "sets." PrimeFan 22:59, 15 September 2006 (UTC)

Count for n! + 1 primes
For n = 0 and 1, the n! + 1 = 2 (only even prime number)

Shouldn't we count 21 primes for n! + 1 prime numbers as the resulting prime number is same (2) for both n = 0 and n = 1

OR is it like, we are counting 22 only because the values (0 and 1) differs irrespective of the fact that n! + 1 is same or not...


 * ✅ fixed. --Bill Cherowitzo (talk) 02:58, 2 February 2018 (UTC)


 * Thanks ! :-)