A079033 -id:A079033 - cp's OEIS frontend

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

David W. Wilson

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

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

Different from A015916. Cf. A031928, A079033.

Cf. A002476, A007645, A092146.

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

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

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

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

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

New name from Michel Marcus, Mar 04 2020

A053323 First differences of A031928.

Original entry on oeis.org

42, 60, 42, 54, 72, 12, 126, 30, 54, 60, 18, 78, 24, 18, 90, 102, 18, 12, 102, 18, 78, 150, 72, 156, 72, 24, 78, 78, 138, 12, 24, 36, 54, 378, 126, 72, 12, 36, 120, 30, 84, 108, 252, 156, 30, 24, 12, 126, 60, 54, 30, 348, 18, 12, 12, 18, 12, 54, 12, 24, 120, 180, 198, 48

Offset: 1

Labos Elemer, Mar 06 2000

Minimal value is 12; a(n) = 12 for n = 6, 22, 128, 172, 218, 229, 248, 253, 320, 344. - Zak Seidov, Jun 12 2017

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A031928, A079033.

Cf. A053321, A053322, A053324, A053325, A053326, A053327, A053331.

Differences[Select[Partition[Prime[Range[800]],2,1],#[[2]]-#[[1]]==10&][[All,1]]] (* Harvey P. Dale, Jan 16 2017 *)

cp's OEIS Frontend

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

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