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A080906
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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.
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3
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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
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OFFSET
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1,1
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COMMENTS
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The number of terms with 2, 4, 6, ... digits: 4, 92, 3223, 130607, 6350300, ..., . - Robert G. Wilson v, Dec 07 2008
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REFERENCES
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P. Giannopoulos, The brainteasers (unpublished)
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LINKS
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EXAMPLE
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23 is a member because 2 and 3 are both primes.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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base,easy,nonn
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AUTHOR
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P. Giannopoulos (pgiannop1(AT)yahoo.com), Mar 31 2003
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EXTENSIONS
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STATUS
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approved
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