A181098 Primefree centuries (i.e., numbers k such that no prime exists between 100*k and 100*k+99).

16718, 26378, 31173, 39336, 46406, 46524, 51782, 55187, 58374, 58452, 60129, 60850, 63338, 63762, 67898, 69587, 71299, 75652, 78035, 78269, 80277, 83674, 84213, 89052, 95490, 97080, 100881, 101527, 103438, 105916, 111772, 112967

Offset: 1

Author

Jeff Burch, Oct 02 2010

Keywords

• nonn

Comments

The first consecutive terms are 473267, 473268; see A190639. - M. F. Hasler, May 15 2011

Examples

			16718 is a term because there is no prime between 1671800 and 1671899.
		

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).

Cf. A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

Mathematica

Flatten[Position[Differences[PrimePi[100*Range[0,113000]]],0]]-1 (* Harvey P. Dale, Dec 18 2021 *)

PARI

is(n)=nextprime(100*n)>100*n+99 \\ Charles R Greathouse IV, Apr 28 2015

Formula

a(n) = n + 100n/log n - O(n/log^2 n). - Charles R Greathouse IV, Sep 08 2017