A096831 Number of primes in the neighborhood with center = n-th primorial and radius = ceiling(log(n-th primorial)).

2, 2, 2, 1, 2, 1, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset: 1

Author

Labos Elemer, Jul 14 2004

Keywords

• nonn

Comments

What is exceptional in such neighborhoods of primorials is that in most cases no primes occur, i.e., these zones are peculiarly poor or empty of primes!

Primes are scarce in these zones because log(A002110(n)) < prime(n), so A002110(n)+1 and A002110(n)-1 are the only numbers in the neighborhood that are not divisible by one of the first n primes. - David Wasserman, Nov 16 2007

Examples

			n=7: 7th primorial=510510; radius=14, a(7)=0 because there are no primes in the relevant neighborhood.
[1, 3], [4, 8], [26, 34], [2302, 2318] (around 2, 6, 30, 2310, respectively) are the only zones in which 2 primes were found.
		

Crossrefs

Cf. A096509-A096523, A002110.

Formula

a(n) = A096509(A002110(n)).