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A249350
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Prime numbers Q such that the concatenation Q,6,Q is prime.
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3
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13, 23, 29, 41, 53, 59, 71, 73, 89, 107, 149, 167, 173, 197, 239, 241, 257, 293, 349, 379, 383, 397, 439, 457, 461, 479, 503, 521, 547, 569, 607, 617, 631, 643, 677, 691, 727, 733, 757, 821, 887, 919, 941, 947, 953, 967, 1051, 1061, 1069
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OFFSET
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1,1
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COMMENTS
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Every concatenation of the form Q,0,Q is divisible by Q, so no such concatenation for prime Q is prime.
There are prime concatenations of a prime Q,d,Q for any digit d from 1 to 9.
For the first 10000000 primes Q there are:
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.
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LINKS
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EXAMPLE
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3 is prime, 363 is composite.
5 is prime, 565 is composite.
7 is prime, 767 is composite
11 is prime, 11611 is composite.
13 is prime, 13613 is prime, so a(1)=13.
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PROG
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(Magma) [p: p in PrimesUpTo(2000) | IsPrime(Seqint(Intseq(p) cat [6] cat Intseq(p)))]; // Vincenzo Librandi, Oct 26 2014
(PARI) lista(nn) = {forprime(p=1, nn, if (isprime(eval(concat(concat(Str(p), 6), Str(p)))), print1(p, ", ")); ); } \\ Michel Marcus, Oct 27 2014
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CROSSREFS
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Cf. similar sequences listed in A249374.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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