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

3, 5, 11, 23, 29, 53, 59, 71, 89, 101, 131, 149, 173, 191, 233, 263, 269, 359, 389, 401, 431, 449, 479, 491, 563, 569, 593, 599, 653, 683, 701, 719, 743, 761, 821, 911, 929, 983, 1013, 1031, 1061, 1109, 1163, 1193, 1223, 1229, 1283, 1289, 1319, 1373, 1439

Offset

1,1

Comments

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

Links

Matt C. Anderson, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe, corrected by Sean A. Irvine and Georg Fischer)

A. Granville and G. Martin, Prime number races, arXiv:math/0408319 [math.NT], 2004.

Maxie D. Schmidt, New Congruences and Finite Difference Equations for Generalized Factorial Functions, arXiv:1701.04741 [math.CO], 2017.

Eric Weisstein's World of Mathematics, Twin Primes

Maple

select(n-> isprime(n) and isprime(n+8), [`$`(1..1500)]); # G. C. Greubel, Feb 07 2020

Mathematica

Select[Range[1500], PrimeQ[#] && PrimeQ[#+8]&] (* Vladimir Joseph Stephan Orlovsky, Aug 29 2008 *)
Select[Prime[Range[250]], PrimeQ[#+8]&] (* Harvey P. Dale, Dec 24 2020 *)

Prog

(Magma) [n: n in [0..1500] | IsPrime(n) and IsPrime(n+8)]; // Vincenzo Librandi, Nov 20 2010
(PARI) is(n)=isprime(n)&&isprime(n+8) \\ Charles R Greathouse IV, Jul 01 2013
(Sage) [n for n in (1..1500) if is_prime(n) and is_prime(n+8)] # G. C. Greubel, Feb 07 2020
(GAP) Filtered([1..1500], k-> IsPrime(k) and IsPrime(k+8)) # G. C. Greubel, Feb 07 2020

Crossrefs

Disjoint union of A007530, A031926, A049437, A049438.

Cf. A046134, A049436, A046138, A015915.

Sequence in context: A275785 A106901 A154550 * A049436 A117010 A056874

Adjacent sequences: A023199 A023200 A023201 * A023203 A023204 A023205

Keyword

nonn,easy

Author

David W. Wilson

Status

approved