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 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. 3
 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 (list; graph; refs; listen; history; text; internal format)
 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 - Robert G. Wilson v, Dec 07 2008 REFERENCES P. Giannopoulos, The brainteasers (unpublished) LINKS Robert G. Wilson v, Table of n, for n = 1..10000.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

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Last modified September 23 07:07 EDT 2023. Contains 365533 sequences. (Running on oeis4.)