Talk:Factorial prime
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Is there any knowledge of whether there are a finite or infinite number of these primes?
- 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)
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)
- 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)
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.
- I find the statement of n! + p far more concrete than any talk of "units" and "sets." PrimeFan 22:59, 15 September 2006 (UTC)
