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A023202 Primes p such that p + 8 is also prime.

%I A023202 #66 Mar 01 2025 08:35:12
%S A023202 3,5,11,23,29,53,59,71,89,101,131,149,173,191,233,263,269,359,389,401,
%T A023202 431,449,479,491,563,569,593,599,653,683,701,719,743,761,821,911,929,
%U A023202 983,1013,1031,1061,1109,1163,1193,1223,1229,1283,1289,1319,1373,1439
%N A023202 Primes p such that p + 8 is also prime.
%C A023202 All terms > 3 are congruent to 5 mod 6 (observation by Zak Seidov in SeqFan). Thus each corresponding p + 8 is congruent to 1 mod 6. - _Rick L. Shepherd_, Mar 25 2023
%H A023202 Matt C. Anderson, <a href="/A023202/b023202.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from T. D. Noe, corrected by Sean A. Irvine and Georg Fischer)
%H A023202 A. Granville and G. Martin, <a href="https://arxiv.org/abs/math/0408319">Prime number races</a>, arXiv:math/0408319 [math.NT], 2004.
%H A023202 Maxie D. Schmidt, <a href="https://arxiv.org/abs/1701.04741">New Congruences and Finite Difference Equations for Generalized Factorial Functions</a>, arXiv:1701.04741 [math.CO], 2017.
%H A023202 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/TwinPrimes.html">Twin Primes</a>
%p A023202 select(n-> isprime(n) and isprime(n+8), [`$`(1..1500)]); # _G. C. Greubel_, Feb 07 2020
%t A023202 Select[Range[1500], PrimeQ[#] && PrimeQ[#+8]&] (* _Vladimir Joseph Stephan Orlovsky_, Aug 29 2008 *)
%t A023202 Select[Prime[Range[250]],PrimeQ[#+8]&] (* _Harvey P. Dale_, Dec 24 2020 *)
%o A023202 (Magma) [n: n in [0..1500] | IsPrime(n) and IsPrime(n+8)]; // _Vincenzo Librandi_, Nov 20 2010
%o A023202 (PARI) is(n)=isprime(n)&&isprime(n+8) \\ _Charles R Greathouse IV_, Jul 01 2013
%o A023202 (Sage) [n for n in (1..1500) if is_prime(n) and is_prime(n+8)] # _G. C. Greubel_, Feb 07 2020
%o A023202 (GAP) Filtered([1..1500], k-> IsPrime(k) and IsPrime(k+8)); # _G. C. Greubel_, Feb 07 2020
%Y A023202 Disjoint union of A007530, A031926, A049437, A049438.
%Y A023202 Cf. A046134, A049436, A046138, A015915.
%K A023202 nonn,easy
%O A023202 1,1
%A A023202 _David W. Wilson_