A126107 Primes p such that 2*p+1 and 2*p+3 are twin primes.

2, 5, 29, 53, 89, 113, 173, 509, 659, 743, 809, 1013, 1499, 1559, 1583, 1733, 2063, 2129, 2273, 2393, 2399, 2549, 2819, 2939, 3329, 3389, 3413, 3779, 4409, 5003, 5849, 6053, 6269, 7193, 7433, 7643, 7823, 8069, 8093, 8513, 8693, 9029, 9059, 9539, 9689

Offset: 1

Author

Zak Seidov, Mar 05 2007

Keywords

• nonn
• easy

Examples

			a(2)=5 because 2*5+1=11 and 2*5+3=13 are twin primes.
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A128436 (primes p such that 2*p-3 and 2*p-1 are twin primes).

Programs

Magma

[p: p in PrimesUpTo(10000) | IsPrime(2*p+1) and IsPrime(2*p+3)]; // Vincenzo Librandi, Feb 15 2014

Mathematica

Do[p = Prime[ i]; If[PrimeQ[2p + 1] && PrimeQ[2p + 3], Print[p]], {i, 1, 2000}] (* Michael Taktikos, Apr 01 2007 *)
Select[Prime[Range[10000]], PrimeQ[2 # + 1] && PrimeQ[2 # + 3] &] (* Vincenzo Librandi, Feb 15 2014 *)

PARI

is(p)=isprime(2*p+1) && isprime(2*p+3) && isprime(p) \\ Charles R Greathouse IV, Mar 03 2018

PARI

list(lim)=my(v=List(),p=3); forprime(q=5,2*lim+3, if(q-p==2 && isprime(p\2), listput(v,p\2)); p=q); Vec(v) \\ Charles R Greathouse IV, Mar 03 2018