A049436 -id:A049436 - cp's OEIS frontend

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

David W. Wilson

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

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

Disjoint union of A007530, A031926, A049437, A049438.

Cf. A046134, A049436, A046138, A015915.

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

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

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

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 *)

is(n)=isprime(n)&&isprime(n+8) \\ Charles R Greathouse IV, Jul 01 2013

[n for n in (1..1500) if is_prime(n) and is_prime(n+8)] # G. C. Greubel, Feb 07 2020

A049437 Primes p such that p+2 and p+8 are also primes but p+6 is not.

Original entry on oeis.org

3, 29, 59, 71, 149, 269, 431, 569, 599, 1031, 1061, 1229, 1289, 1319, 1451, 1619, 2129, 2339, 2381, 2549, 2711, 2789, 3299, 3539, 4019, 4049, 4091, 4649, 4721, 5099, 5441, 5519, 5639, 5741, 5849, 6269, 6359, 6569, 6701, 6959, 7211

Offset: 1

Labos Elemer

nonn

p+4 is not prime here except for p=3.

			p=29 is the smallest prime so that p, p+2 and p+8 are consecutive primes.

Iain Fox, Table of n, a(n) for n = 1..10000 (first 1000 terms from R. J. Mathar)

Cf. A007530, A023202, A031926, A046134, A046138, A049436, A049438, A046138.

Subsequence of A001359. - R. J. Mathar, Feb 10 2013

[p: p in PrimesUpTo(8000)| IsPrime(p+2) and IsPrime(p+8) and not IsPrime(p+6) ] // Vincenzo Librandi, Jan 28 2011

select(p -> isprime(p) and isprime(p+2) and isprime(p+8) and not isprime(p+6), [3, seq(i,i=5..10000, 6)]); # Robert Israel, Nov 20 2017

{3}~Join~Select[Partition[Prime@ Range[10^3], 3, 1], Differences@ # == {2, 6} &][[All, 1]] (* Michael De Vlieger, Nov 20 2017 *)

lista(nn) = forprime(p=3, nn, if(isprime(p+2) && isprime(p+8) && !isprime(p+6), print1(p, ", "))) \\ Iain Fox, Nov 20 2017

A049438 p, p+6 and p+8 are all primes (A046138) but p+2 is not.

Original entry on oeis.org

23, 53, 131, 173, 233, 263, 563, 593, 653, 1013, 1223, 1283, 1601, 1613, 2333, 2543, 2963, 3323, 3533, 3761, 3911, 3923, 4013, 4211, 4253, 4643, 4793, 5003, 5273, 5471, 5843, 5861, 6263, 6353, 6563, 6653, 6863, 7121, 7451, 7481, 7541, 7583

Offset: 1

Labos Elemer

R. J. Mathar, Table of n, a(n) for n = 1..1000

Subsequence of A031924. - R. J. Mathar, Jun 15 2013

Cf. A007530, A023202, A031926, A046134, A046138, A049436, A049437.

Select[Prime@ Range[10^3], MatchQ[Boole@ PrimeQ@ {# + 2, # + 6, # + 8}, {0, 1, 1}] &] (* Michael De Vlieger, Feb 05 2017 *)

isok(p) = isprime(p) && !isprime(p+2) && isprime(p+6) && isprime(p+8); \\ Michel Marcus, Dec 13 2013

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

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A049437 Primes p such that p+2 and p+8 are also primes but p+6 is not.

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A049438 p, p+6 and p+8 are all primes (A046138) but p+2 is not.

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