A213632 - OEIS

A213632

Primes p such that primality of (p+p')/2+4 and of (p+p')/2-4 differ, where p'=precprime(p-1), the next smaller prime.

%I #12 May 06 2018 02:23:55

%S 7,23,41,47,71,101,113,227,233,281,311,317,353,461,467,617,647,857,

%T 863,881,887,1091,1097,1283,1301,1307,1427,1433,1451,1493,1613,1667,

%U 1697,1787,1871,1997

%N Primes p such that primality of (p+p')/2+4 and of (p+p')/2-4 differ, where p'=precprime(p-1), the next smaller 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(p","))

%Y Cf A213631.

%K nonn

%O 1,1

%A _M. F. Hasler_, Jun 16 2012