A186404 Numbers k such that there are 12 primes between 100*k and 100*k + 99.

11, 15, 17, 18, 28, 30, 37, 45, 46, 47, 50, 56, 60, 67, 68, 76, 85, 91, 98, 101, 103, 106, 118, 122, 125, 126, 129, 131, 136, 137, 144, 145, 148, 151, 152, 153, 157, 160, 164, 169, 173, 199, 203, 207, 221, 226, 235, 236, 241

Offset

1,1

Comments

There are 27836859 possible prime patterns for centuries having 12 primes. - Tim Johannes Ohrtmann, Aug 27 2015

Links

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

Example

11 is in this sequence because there are 12 primes between 1100 and 1199 (1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187 and 1193).

Mathematica

Select[Range[250], PrimePi[100#+99]-PrimePi[100#]==12&] (* Harvey P. Dale, Sep 20 2011 *)

Prog

(PARI) for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==12, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
(PARI) N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==12, 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: A371553 A139065 A365329 * A111322 A069822 A116999

Adjacent sequences: A186401 A186402 A186403 * A186405 A186406 A186407

Keyword

nonn

Author

Tim Johannes Ohrtmann, Feb 20 2011

Status

approved