A186406 Numbers k such that there are 14 primes between 100*k and 100*k + 99.

5, 7, 9, 20, 27, 35, 82, 147, 179, 277, 286, 514, 556, 694, 709, 796, 810, 1158, 1363, 1416, 2033, 2173, 2232, 2297, 2660, 3054, 3274, 4508, 4996, 6635, 8194, 8237, 11047, 11467, 12303, 16166, 19543, 19882, 19936

Offset: 1

Author

Tim Johannes Ohrtmann, Feb 20 2011

Keywords

• nonn

Comments

There are 20053913 possible prime patterns for centuries having 14 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Examples

			5 is in this sequence because there are 14 primes between 500 and 599 (503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593 and 599).
		

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. A181098 (no primes), A186393-A186408 (1 to 16 primes), A186509 (17 primes), A361723 (18 primes).

Programs

Mathematica

Select[Range[20000],PrimePi[100#+99]-PrimePi[100#]==14&] (* Harvey P. Dale, Jun 20 2021 *)

PARI

for(n=1, 1e6, if(sum(k=100*n,100*(n+1), ispseudoprime(k))==14, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011

PARI

N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==14, print1((N\100)-1,", ")); s=1; N=100*(p\100+1),s++)) \\ Charles R Greathouse IV, Feb 21 2011

Extensions

a(30)-a(39) from Charles R Greathouse IV, Feb 21 2011