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List of prime pairs of the form (p, p+8).
4

%I #16 May 18 2021 17:53:08

%S 3,11,5,13,11,19,23,31,29,37,53,61,59,67,71,79,89,97,101,109,131,139,

%T 149,157,173,181,191,199,233,241,263,271,269,277,359,367,389,397,401,

%U 409,431,439,449,457,479,487,491,499,563,571,569,577,593,601,599,607,653,661,683,691,701

%N List of prime pairs of the form (p, p+8).

%H Vincenzo Librandi, <a href="/A156320/b156320.txt">Table of n, a(n) for n = 1..1000</a>

%H Fernando Neres de Oliveira, <a href="https://doi.org/10.22457/apam.v18n1a2">On the Solvability of the Diophantine Equation p^x + (p + 8)^y = z^2 when p > 3 and p + 8 are Primes</a>, Annals of Pure and Applied Mathematics (2018) Vol. 18, No. 1, 9-13.

%F a(2n+1) = A023202(n+1). a(2n+2) = A092402(n+1). [_R. J. Mathar_, Feb 09 2009]

%t Flatten[Select[{#, # + 8} &/@Prime[Range[1000]], PrimeQ[Last[#]]&]] (* _Vincenzo Librandi_, Nov 01 2012 *)

%o (Python)

%o from sympy import isprime, primerange

%o for pn in primerange(1,300):

%o if isprime(pn+8):

%o print(pn, pn+8)

%o # _Stefano Spezia_, Dec 06 2018

%Y Cf. A023202, A092402.

%K nonn,tabf

%O 1,1

%A _Vincenzo Librandi_, Feb 08 2009