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%I #17 Mar 08 2023 05:15:46
%S 2,8,101,164,179,230,272,293,326,389,410,419,443,512,524,536,659,662,
%T 773,788,794,800,818,890,920,932,989,1028,1058,1136,1187,1238,1271,
%U 1292,1310,1346,1466,1490,1550,1577,1583,1823,1838,1856,1865,1913,2003,2075
%N Numbers m such that the concatenation of m and 999 is the lesser of twin primes, i.e., a millennium twin prime couple.
%C Necessarily, m == 2 (mod 3).
%D Richard K. Guy: Unsolved Problems in Number Theory, New York, Springer-Verlag, 1994.
%D Theo Kempermann: Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005.
%D Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983.
%H Harvey P. Dale, <a href="/A173976/b173976.txt">Table of n, a(n) for n = 1..1000</a>
%e 2 is a term: 2999 = prime(430), 2999+2 = 3001 = prime(431).
%e 8 is a term: 8999 = prime(1117), 8999+2 = 9001 = prime(1118).
%t tp999Q[n_]:=Module[{c=FromDigits[Join[IntegerDigits[n],{9,9,9}]]}, And @@ PrimeQ[c+{0,2}]]; Select[Range[2500],tp999Q] (* _Harvey P. Dale_, Oct 03 2013 *)
%t Select[3 Range[0,700]+2,AllTrue[1000#+{999,1001},PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Jul 05 2021 *)
%o (PARI) isok(m) = my(x=eval(Str(m, 999))); isprime(x) && isprime(x+2); \\ _Michel Marcus_, Mar 08 2023
%Y Cf. A001359, A158277, A158861, A173937.
%K base,nonn
%O 1,1
%A Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 04 2010
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