It's not even known that there are infinitely many. Caldwell & Gallot conjecture that there are about e^gamma * log x prime Q(n) with n <= x, that is, that the usual heuristic gives the right answer. I think sieve theory can give an upper bound if that's enough for your purposes. Charles Greathouse Analyst/Programmer Case Western Reserve University On Mon, Nov 11, 2013 at 7:58 PM, Dan Asimov <dasimov@earthlink.net> wrote:

I'm curious: Can one state in closed form what is the asymptotic density of prime numbers among numbers Q(n) of the form

Q(n) := primorial(n) + 1

i.e.,

Q(n) = 2*3*5*7*...*p_n + 1

(where p_n is the nth prime) ???

--Dan

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