%I #13 May 06 2018 02:24:03
%S 5,19,37,43,67,97,109,223,229,277,307,313,349,457,463,613,643,853,859,
%T 877,883,1087,1093,1279,1297,1303,1423,1429,1447,1489,1609,1663,1693,
%U 1783,1867,1993
%N Primes p such that primality of (p+p')/2+4 and of (p+p')/2-4 differ, where p'=nextprime(p+1), the next larger prime.
%C It is easily checked that for m=(p+p')/2 (average between two consecutive primes), the numbers m +- 1 resp. m +- 2 resp. m +- 3 (as well as m +- 6) are (in each case) either both prime or both composite (for p > 7). Thus, m +- 4 provides the least counterexample to this behavior, and the primes listed here are those for which the property does not hold, i.e., one among { m-4, m+4 } is prime and the other one is composite.
%o (PARI) d=8;q=3;forprime(p=nextprime(q+1),q+1999, [1,-1]*isprime([q-d+p;q+d+q=p]\2) & print1(precprime(p-1)","))
%Y Cf. A213632.
%K nonn
%O 1,1
%A _M. F. Hasler_, Jun 16 2012