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%I #25 Sep 08 2022 08:46:10
%S 13,23,29,41,53,59,71,73,89,107,149,167,173,197,239,241,257,293,349,
%T 379,383,397,439,457,461,479,503,521,547,569,607,617,631,643,677,691,
%U 727,733,757,821,887,919,941,947,953,967,1051,1061,1069
%N Prime numbers Q such that the concatenation Q,6,Q is prime.
%C Every concatenation of the form Q,0,Q is divisible by Q, so no such concatenation for prime Q is prime.
%C There are prime concatenations of a prime Q,d,Q for any digit d from 1 to 9.
%C For the first 10000000 primes Q there are:
%C 135 primes Q,1,Q, 116 primes Q,2,Q, 267 primes Q,3,Q, 127 primes Q,4,Q, 126 primes Q,5,Q, 265 primes Q,6,Q, 141 primes Q,7,Q, 115 primes Q,8,Q and 263 primes Q,9,Q.
%H Pierre CAMI, <a href="/A249350/b249350.txt">Table of n, a(n) for n = 1..10000</a>
%e 3 is prime, 363 is composite.
%e 5 is prime, 565 is composite.
%e 7 is prime, 767 is composite
%e 11 is prime, 11611 is composite.
%e 13 is prime, 13613 is prime, so a(1)=13.
%o (Magma) [p: p in PrimesUpTo(2000) | IsPrime(Seqint(Intseq(p) cat [6] cat Intseq(p)))]; // _Vincenzo Librandi_, Oct 26 2014
%o (PARI) lista(nn) = {forprime(p=1, nn, if (isprime(eval(concat(concat(Str(p), 6), Str(p)))), print1(p, ", ")););} \\ _Michel Marcus_, Oct 27 2014
%Y Cf. similar sequences listed in A249374.
%K nonn,base
%O 1,1
%A _Pierre CAMI_, Oct 26 2014
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