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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) ???

--I would think that Q(n) is prime with "probability" about loglog(Q(n)) times greater than the usual 1/log(Q(n)) probability.