A126107 Primes p such that 2p+1 and 2p+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

1,1

Links

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

Example

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

Mathematica

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

Prog

(Magma) [p: p in PrimesUpTo(10000) | IsPrime(2*p+1) and IsPrime(2*p+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

Crossrefs

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

Sequence in context: A103579 A161500 A061351 * A193901 A083472 A213996

Adjacent sequences: A126104 A126105 A126106 * A126108 A126109 A126110

Keyword

nonn,easy

Author

Zak Seidov, Mar 05 2007

Status

approved