A224789 Primes p such that both p + nextprime(p) + 1 and p*nextprime(p) + 2 are primes.

5, 7, 13, 19, 67, 229, 269, 307, 313, 401, 439, 613, 643, 863, 1051, 1693, 1783, 1999, 2143, 2239, 2309, 2423, 2549, 2753, 2819, 3037, 3079, 3089, 3361, 3373, 3389, 3677, 3863, 3877, 4139, 4259, 4519, 4663, 4909, 4933, 5323, 5527, 5581, 5849, 6359, 6577

Offset: 1

Author

Jayanta Basu, Apr 17 2013

Keywords

• nonn

Comments

Intersection of A051507 and A177017.

Examples

			5 is a member since 5 + 7 + 1 = 13 and 5 * 7 + 2 = 37 are both primes.
		

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A051507, A177017.

Programs

Mathematica

Select[Prime[Range[900]], PrimeQ[# + NextPrime[#] + 1] && PrimeQ[#*NextPrime[#] + 2] &]
npQ[n_]:=Module[{np=NextPrime[n]},AllTrue[{n+np+1,n*np+2},PrimeQ]]; Select[ Prime[ Range[900]],npQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jul 04 2017 *)