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

Author

David W. Wilson

Keywords

• nonn
• easy

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

Crossrefs

Disjoint union of A007530, A031926, A049437, A049438.

Cf. A046134, A049436, A046138, A015915.

Programs

GAP

Filtered([1..1500], k-> IsPrime(k) and IsPrime(k+8)); # G. C. Greubel, Feb 07 2020

Magma

[n: n in [0..1500] | IsPrime(n) and IsPrime(n+8)]; // Vincenzo Librandi, Nov 20 2010

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 *)

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