A080906 Primes with an even number of digits such that the first half of the digits and the second half of the digits are both primes.

23, 37, 53, 73, 1103, 1117, 1123, 1129, 1153, 1171, 1303, 1307, 1319, 1361, 1367, 1373, 1723, 1741, 1747, 1753, 1759, 1783, 1789, 1907, 1913, 1931, 1973, 1979, 1997, 2311, 2341, 2347, 2371, 2383, 2389, 2903, 2917, 2953, 2971, 3119, 3137

Offset

1,1

Comments

The number of terms with 2, 4, 6, ... digits: 4, 92, 3223, 130607, 6350300, ..., . - Robert G. Wilson v, Dec 07 2008

References

P. Giannopoulos, The brainteasers (unpublished)

Links

Robert G. Wilson v, Table of n, for n = 1..10000. [From Robert G. Wilson v, Dec 07 2008]

Example

23 is a member because 2 and 3 are both primes.

Mathematica

f[n_] := Block[{c = 0, lp = PrimePi[10^n] - PrimePi[10^(n - 1)], lq = PrimePi[10^n], lst = {}, pq, p = Prime@ Range[PrimePi[10^(n - 1)] + 1, PrimePi[10^n]], q = Prime@ Range[1, PrimePi[10^n]]}, Do[pq = p[[i]]*10^n + q[[j]]; If[PrimeQ@ pq, AppendTo[lst, pq]; c++ ], {i, lp}, {j, lq}]; lst]; Array[f, 2] // Flatten (* Robert G. Wilson v, Dec 07 2008 *)
pQ[n_]:=Module[{idn=IntegerDigits[n], len}, len=Length[idn]; EvenQ[len] && PrimeQ[FromDigits[Take[idn, len/2]]]&&PrimeQ[FromDigits[Take[idn, -len/2]]]]; Select[Prime[Range[500]], pQ] (* Harvey P. Dale, Nov 08 2011 *)

Prog

(PARI) t=1; forprime( p=2, 99, if( p>t, t*=10); forprime( q=3, t, isprime(p*t+q) & print1(p*t+q, ", "))) \\ M. F. Hasler

Crossrefs

Cf. A000040. - Robert G. Wilson v, Dec 07 2008

Sequence in context: A179910 A124888 A141521 * A358421 A237766 A215163

Adjacent sequences: A080903 A080904 A080905 * A080907 A080908 A080909

Keyword

base,easy,nonn

Author

P. Giannopoulos (pgiannop1(AT)yahoo.com), Mar 31 2003

Extensions

Corrected by Zak Seidov, Robert Israel, Farideh Firoozbakht and M. F. Hasler, Dec 06 2008 and Dec 07 2008

Edited by N. J. A. Sloane, Dec 07 2008

Status

approved