A158521 Primes which yield primes when "13" is prefixed or appended.

19, 61, 103, 127, 241, 331, 337, 367, 523, 577, 709, 829, 997, 1009, 1129, 1213, 1231, 1321, 1381, 1489, 1543, 1627, 1861, 2113, 2137, 2287, 2347, 2383, 2689, 2851, 2953, 2971, 3187, 3499, 3559, 3583, 3673, 3967, 4219, 4243, 4327, 4363, 4513, 4591, 4789

Offset

1,1

Comments

Primes in A158232.

It is conjectured that this sequence is infinite.

References

Richard E. Crandall, Carl Pomerance, Prime Numbers, Springer, 2005.

Wladyslaw Narkiewicz, The development of prime number theory, Springer, 2000.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Formula

Prime p is a term if the concatenations "13p" and "p13" both yield primes.

Example

Prime p=3 is not a term: "p13"=313 is prime but "13p"=133 = 7*19.
For p=19, both 1319 and 1913 are prime; this is the first prime that meets the requirements of the definition, so a(1)=19.

Maple

cat2 := proc(a, b) ndigsb := max(ilog10(b)+1, 1) ; a*10^ndigsb+b ; end: for i from 1 to 800 do p := ithprime(i) ; if isprime(cat2(13, p)) and isprime(cat2(p, 13)) then printf("%d, ", p) ; fi; od: # R. J. Mathar, Apr 02 2009

Mathematica

Select[Prime[Range[1000]], AllTrue[{13*10^IntegerLength[#]+#, 100#+13}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Apr 17 2015 *)

Crossrefs

Cf. A158232, A157772.

Sequence in context: A206426 A211145 A338990 * A141897 A031384 A048890

Adjacent sequences: A158518 A158519 A158520 * A158522 A158523 A158524

Keyword

nonn,base

Author

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 20 2009

Extensions

337, 1231, 1321 inserted by R. J. Mathar, Apr 02 2009

Status

approved