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

Author

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

Keywords

• base
• easy
• nonn

Comments

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

Examples

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

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• P. Giannopoulos, The brainteasers (unpublished)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]

Crossrefs

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

Programs

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 *)

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

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