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

Author

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

Keywords

• nonn
• base

Comments

Primes in A158232.

It is conjectured that this sequence is infinite.

Examples

			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.
		

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

Crossrefs

Cf. A158232, A157772.

Programs

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 *)

Formula

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

Extensions

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