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

Author

David W. Wilson

Keywords

• nonn
• easy

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

Crossrefs

Different from A015916. Cf. A031928, A079033.

Cf. A002476, A007645, A092146.

Programs

Magma

[n: n in [0..1000] | IsPrime(n) and IsPrime(n+10)]; // Vincenzo Librandi, Nov 20 2010

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 *)

PARI

is(n)=isprime(n)&&isprime(n+10) \\ Charles R Greathouse IV, Jul 01 2013

Extensions

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

New name from Michel Marcus, Mar 04 2020