A249350 Prime numbers Q such that the concatenation Q,6,Q is prime.

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

Offset

1,1

Comments

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.

Links

Pierre CAMI, Table of n, a(n) for n = 1..10000

Example

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.

Prog

(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

Crossrefs

Cf. similar sequences listed in A249374.

Sequence in context: A019399 A255581 A061967 * A159082 A303576 A228324

Adjacent sequences: A249347 A249348 A249349 * A249351 A249352 A249353

Keyword

nonn,base

Author

Pierre CAMI, Oct 26 2014

Status

approved