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Numbers k such that there are 13 primes between 100*k and 100*k + 99.
1

%I #28 Mar 22 2024 03:44:49

%S 19,36,54,55,62,69,86,88,96,119,124,156,166,174,201,211,215,220,238,

%T 240,308,320,323,329,355,408,412,416,427,442,544,569,606,616,633,636,

%U 674,713,775,798,806,832,875,888,900,923,1098

%N Numbers k such that there are 13 primes between 100*k and 100*k + 99.

%C There are 25913910 possible prime patterns for centuries having 13 primes. - _Tim Johannes Ohrtmann_, Aug 27 2015

%H T. D. Noe, <a href="/A186405/b186405.txt">Table of n, a(n) for n = 1..1000</a>

%e 19 is in this sequence because there are 13 primes between 1900 and 1999 (1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997 and 1999).

%o (PARI) for(n=1, 1e6, if(sum(k=100*n, 100*(n+1), ispseudoprime(k))==13, print1(n", "))); \\ _Charles R Greathouse IV_, Feb 21 2011

%o (PARI) N=100; s=0; forprime(p=2, 4e9, if(p>N, if(s==13, print1((N\100)-1, ", ")); s=1; N=100*(p\100+1), s++)) \\ _Charles R Greathouse IV_, Feb 21 2011

%Y Cf. A038822 (number of primes between 100n and 100n+99), A186311 (first occurrences).

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

%K nonn

%O 1,1

%A _Tim Johannes Ohrtmann_, Feb 20 2011