A103806 Primes p such that 2p - 33 and 2p + 33 are both primes.

2, 5, 7, 13, 19, 23, 37, 47, 53, 67, 73, 103, 137, 157, 163, 173, 193, 227, 233, 277, 313, 347, 353, 397, 443, 457, 613, 733, 863, 877, 983, 1087, 1153, 1213, 1327, 1447, 1493, 1733, 1747, 1787, 1867, 2053, 2063, 2153, 2237, 2377, 2383, 2503, 2557, 2657, 2683

Offset: 1

Author

Zak Seidov, Feb 16 2005

Keywords

• nonn

Comments

If, e.g., -29 is not prime (Mathematica considers -prime as prime), then the first four terms should be omitted.

Links

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

Crossrefs

Cf. A103802, A103803, A103804, A103805.

Programs

Magma

[p: p in PrimesUpTo(3000)| IsPrime(2*p+33) and IsPrime(2*p-33) ]; // Vincenzo Librandi, Jan 28 2011

Mathematica

Select[Range[2000], PrimeQ[ # ] && PrimeQ[2# + 33] && PrimeQ[2# - 33] &]
Select[Prime[Range[400]],AllTrue[2#+{33,-33},PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 10 2016 *)

Formula

p, 2p-33 and 2p+33 all are primes.