A023203 Primes p such that p + 10 is also prime.

3, 7, 13, 19, 31, 37, 43, 61, 73, 79, 97, 103, 127, 139, 157, 163, 181, 223, 229, 241, 271, 283, 307, 337, 349, 373, 379, 409, 421, 433, 439, 457, 499, 547, 577, 607, 631, 643, 673, 691, 709, 733, 751, 787, 811, 829, 853, 877, 919, 937, 967, 1009, 1021, 1039, 1051

Offset

1,1

Comments

A subset of A002476. It appears that this is also a subset of A007645. The first few terms of A007645 that are not in this sequence are {67, 109, 151, 193, 199, 211, 277, 313, 331, 367, 397, 463, 487, 523, 541, 571, 601, 613, ...}. - Alexander Adamchuk, Aug 15 2006

The entries are all in A007645, because they cannot be of the form p = 3*j + 2. If they were, p + 10 = 3*j + 12 would be divisible by 3 and not prime. - R. J. Mathar, Oct 30 2009

Links

Matt C. Anderson, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harvey P. Dale)

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

for p from 1 to 10000 do if isprime(p) and isprime(p+10) then print(p) end if end do # Matt C. Anderson, Aug 26 2022

Mathematica

Select[Prime[Range[200]], PrimeQ[# + 10] &] (* Harvey P. Dale, Dec 14 2011 *)

Prog

(Magma) [n: n in [0..1000] | IsPrime(n) and IsPrime(n+10)]; // Vincenzo Librandi, Nov 20 2010
(PARI) is(n)=isprime(n)&&isprime(n+10) \\ Charles R Greathouse IV, Jul 01 2013

Crossrefs

Different from A015916. Cf. A031928, A079033.

Cf. A002476, A007645, A092146.

Sequence in context: A215801 A215809 A015916 * A086135 A023220 A207990

Adjacent sequences: A023200 A023201 A023202 * A023204 A023205 A023206

Keyword

nonn,easy

Author

David W. Wilson

Extensions

Revised by N. J. A. Sloane, Jan 29 2013

New name from Michel Marcus, Mar 04 2020

Status

approved