A156320 List of prime pairs of the form (p, p+8).

3, 11, 5, 13, 11, 19, 23, 31, 29, 37, 53, 61, 59, 67, 71, 79, 89, 97, 101, 109, 131, 139, 149, 157, 173, 181, 191, 199, 233, 241, 263, 271, 269, 277, 359, 367, 389, 397, 401, 409, 431, 439, 449, 457, 479, 487, 491, 499, 563, 571, 569, 577, 593, 601, 599, 607, 653, 661, 683, 691, 701

Offset: 1

Author

Vincenzo Librandi, Feb 08 2009

Keywords

• nonn
• tabf

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Fernando Neres de Oliveira, On the Solvability of the Diophantine Equation p^x + (p + 8)^y = z^2 when p > 3 and p + 8 are Primes, Annals of Pure and Applied Mathematics (2018) Vol. 18, No. 1, 9-13.

Crossrefs

Cf. A023202, A092402.

Programs

Mathematica

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

Python

from sympy import isprime, primerange
for pn in primerange(1,300):
    if isprime(pn+8):
        print(pn, pn+8)
# Stefano Spezia, Dec 06 2018

Formula

a(2n+1) = A023202(n+1). a(2n+2) = A092402(n+1). [R. J. Mathar, Feb 09 2009]