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A023271
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Primes p such that p, p+6, p+12, p+18 are all primes.
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21
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5, 11, 41, 61, 251, 601, 641, 1091, 1481, 1601, 1741, 1861, 2371, 2671, 3301, 3911, 4001, 5101, 5381, 5431, 5641, 6311, 6361, 9461, 11821, 12101, 12641, 13451, 14621, 14741, 15791, 15901, 17471, 18211, 19471, 20341, 21481, 23321, 24091, 26171, 26681
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OFFSET
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1,1
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COMMENTS
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Smallest member of a "sexy" prime quadruple.
The only sexy prime quintuple corresponding to (p, p+6, p+12, p+18, p+24) starts with a(1) = 5, so this quintuple is (5, 11, 17, 23, 29) (see Wikipedia link and A206039). - Bernard Schott, Mar 10 2023
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LINKS
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Eric Weisstein's World of Mathematics, Sexy Primes. [The definition in this webpage is unsatisfactory, because it defines a "sexy prime" as a pair of primes. - N. J. A. Sloane, Mar 07 2021]
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MAPLE
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for a to 2*10^5 do
if `and`(isprime(a), isprime(a+6), isprime(a+12), isprime(a+18))
then print(a);
end if;
end do;
# code produces 109 primes
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MATHEMATICA
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Select[Prime[Range[1000]], PrimeQ[# + 6] && PrimeQ[# + 12] && PrimeQ[# + 18] &] (* Vincenzo Librandi, Jul 15 2015 *)
(* The following program uses the AllTrue function from Mathematica version 10 *) Select[Prime[Range[3000]], AllTrue[# + {6, 12, 18}, PrimeQ] &] (* Harvey P. Dale, Jun 06 2017 *)
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PROG
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(Magma) [p: p in PrimesInInterval(2, 1000000) | forall{i: i in [ 6, 12, 18] | IsPrime(p+i)}]; // Vincenzo Librandi, Jul 15 2015
(PARI) main(size)=my(v=vector(size), i, r=1, p); for(i=1, size, while(1, p=prime(r); if(isprime(p+6)&&isprime(p+12)&&isprime(p+18), v[i]=p; r++; break, r++))); v \\ Anders Hellström, Jul 16 2015
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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