A186398 Numbers k such that there are 6 primes between 100*k and 100*k + 99.

186, 234, 319, 332, 340, 380, 384, 443, 444, 450, 469, 489, 542, 548, 554, 574, 611, 632, 645, 681, 683, 696, 716, 725, 731, 746, 749, 754, 805, 814, 829, 859, 873, 897, 907, 956, 963, 966, 977, 1000, 1008, 1027, 1044, 1050

Offset

1,1

Comments

There are 830270 possible prime patterns for centuries having 6 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Links

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

Example

186 is in this sequence because there are 6 primes between 18600 and 18699 (18617, 18637, 18661, 18671, 18679 and 18691).

Mathematica

Select[Range[1100], PrimePi[100#+99]-PrimePi[100#]==6&] (* Harvey P. Dale, Jun 24 2018 *)

Prog

(PARI) for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==6, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
(PARI) N=100; s=0; forprime(p=2, 1e6, if(p>N, if(s==6, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ Charles R Greathouse IV, Feb 21 2011

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).

Sequence in context: A197646 A015273 A214605 * A124207 A189941 A362811

Adjacent sequences: A186395 A186396 A186397 * A186399 A186400 A186401

Keyword

nonn

Author

Tim Johannes Ohrtmann, Feb 20 2011

Status

approved