

A186401


Numbers k such that there are 9 primes between 100*k and 100*k + 99.


1



41, 43, 70, 73, 83, 89, 99, 115, 117, 120, 123, 128, 132, 138, 143, 150, 158, 161, 163, 168, 171, 172, 193, 200, 202, 208, 209, 216, 222, 223, 225, 229, 233, 237, 239, 246, 276, 278, 282, 288, 290, 294, 300, 302, 303, 304
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

There are 11555200 possible prime patterns for centuries having 9 primes.  Tim Johannes Ohrtmann, Aug 27 2015


LINKS



EXAMPLE

41 is in this sequence because there are 9 primes between 4100 and 4199 (4111, 4127, 4129, 4133, 4139, 4153, 4157, 4159 and 4177).


MATHEMATICA

Select[Range[350], PrimePi[100#+99]PrimePi[100#]==9&] (* Harvey P. Dale, Sep 05 2023 *)


PROG

(PARI) for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==9, print1(n", "))); \\ Charles R Greathouse IV, Feb 21 2011
(PARI) N=100; s=0; forprime(p=2, 1e6, if(p>N, if(s==9, 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).


KEYWORD

nonn


AUTHOR



STATUS

approved



