A120934 -id:A120934 - cp's OEIS frontend

A120935 Largest prime in the cluster of n primes whose first prime is given in A120934.

2, 13, 463, 3259, 165713, 10526573, 495233371, 196039655899, 10687033762063, 79006533276973, 4313367040646779, 1740318019946551973

Offset: 1

T. D. Noe, Jul 21 2006

nonn

For n>1, it appears that each prime is a cluster prime. See A038134.

Cf. A020497.

a(n)= A120934(n)+A008407(n)

a(12) from Donovan Johnson, Apr 18 2012

A120936 Number of primes in the interval [n,n+log(n)].

Original entry on oeis.org

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, 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, 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

Offset: 1

T. D. Noe, Jul 21 2006

nonn

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.

T. D. Noe, Table of n, a(n) for n = 1..5000
K. Soundararajan, The distribution of prime numbers

Cf. A008407, A020497.

Table[Length[Select[Range[n,n+Log[n]],PrimeQ]], {n,150}]

a(n)=sum(k=n,n+log(n),isprime(k)) \\ Charles R Greathouse IV, Apr 17 2012

cp's OEIS Frontend

A120935 Largest prime in the cluster of n primes whose first prime is given in A120934.

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A120936 Number of primes in the interval [n,n+log(n)].

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