OFFSET
1,1
EXAMPLE
1308498 and 1308708, 1308918, 1309128, 1309338 are averages of twin primes.
3042492 and 3042702, 3042912, 3043122, 3043332 are averages of twin primes.
MATHEMATICA
q=210; lst={}; Do[If[PrimeQ[n-1]&&PrimeQ[n+1]&&PrimeQ[n+q*1-1]&& PrimeQ[n+q*1+1]&& PrimeQ[n+q*2-1]&&PrimeQ[n+q*2+1]&& PrimeQ[n+q*3-1]&& PrimeQ[n+q*3+1]&& PrimeQ[n+q*4-1]&&PrimeQ[n+q*4+1], AppendTo[lst, n]], {n, 10^8}]; lst
Select[Range[55*10^6], AllTrue[{#-1, #+1, #+209, #+211, #+419, #+421, #+629, #+631, #+839, #+841}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 08 2017 *)
PROG
(Magma) [k:k in [1..55000000]|forall{m:m in [0, 210, 420, 630, 840]|IsPrime(k+m-1) and IsPrime(k+m+1)}]; // Marius A. Burtea, Jan 13 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Joseph Stephan Orlovsky, Aug 20 2008
EXTENSIONS
Edited by N. J. A. Sloane, Aug 24 2008
a(9)-a(25) from Amiram Eldar, Jan 13 2020
STATUS
approved