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%I #10 Apr 17 2012 00:06:24
%S 0,1,1,1,1,1,1,0,1,1,2,1,1,0,1,1,2,1,1,0,1,1,1,0,0,1,1,2,2,1,1,0,0,1,
%T 1,1,1,1,1,2,2,1,1,1,1,1,1,0,0,1,1,1,1,0,1,1,2,2,2,1,1,0,1,1,1,1,2,1,
%U 2,2,2,1,1,0,1,1,1,1,2,1,1,1,1,0,1,1,1,1,1,0,0,0,1,1,1,1,2,1,2,2,2,1,2,1,2
%N Number of primes in the interval [n,n+log(n)].
%C Soundararajan states that, on average, there is one prime in the interval [n,n+log(n)] for any number n. See A120934 for the prime n that yield new records.
%H T. D. Noe, <a href="/A120936/b120936.txt">Table of n, a(n) for n = 1..5000</a>
%H K. Soundararajan, <a href="http://www.arXiv.org/abs/math.NT/0606408">The distribution of prime numbers</a>
%t Table[Length[Select[Range[n,n+Log[n]],PrimeQ]], {n,150}]
%o (PARI) a(n)=sum(k=n,n+log(n),isprime(k)) \\ _Charles R Greathouse IV_, Apr 17 2012
%Y Cf. A008407, A020497.
%K nonn
%O 1,11
%A _T. D. Noe_, Jul 21 2006
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