|
|
A186406
|
|
Numbers k such that there are 14 primes between 100*k and 100*k + 99.
|
|
1
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
There are 20053913 possible prime patterns for centuries having 14 primes. - Tim Johannes Ohrtmann, Aug 27 2015
|
|
LINKS
|
|
|
EXAMPLE
|
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).
|
|
MATHEMATICA
|
Select[Range[20000], PrimePi[100#+99]-PrimePi[100#]==14&] (* Harvey P. Dale, Jun 20 2021 *)
|
|
PROG
|
(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
|
|
CROSSREFS
|
Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|