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A173976 Numbers n such that concatenation "n 999" is lesser of twin primes, i.e., a millennium twin prime couple. 4
2, 8, 101, 164, 179, 230, 272, 293, 326, 389, 410, 419, 443, 512, 524, 536, 659, 662, 773, 788, 794, 800, 818, 890, 920, 932, 989, 1028, 1058, 1136, 1187, 1238, 1271, 1292, 1310, 1346, 1466, 1490, 1550, 1577, 1583, 1823, 1838, 1856, 1865, 1913, 2003, 2075 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Necessarily, n = 3*k + 2.

REFERENCES

Richard K. Guy: Unsolved Problems in Number Theory, New York, Springer-Verlag, 1994

Theo Kempermann: Zahlentheoretische Kostproben, Harri Deutsch, 2. aktualisierte Auflage 2005

Helmut Kracke, Mathe-musische Knobelisken, Duemmler Bonn, 2. Auflage 1983

LINKS

Harvey P. Dale, Table of n, a(n) for n = 1..1000

EXAMPLE

p = 2999 = prime(430), p+2 = 3001 = prime(431) => n(1) = 2;

q = 8999 = prime(1117), q+2 = 9001 = prime(1118) => n(2) = 8.

MATHEMATICA

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 *)

Select[3 Range[0, 700]+2, AllTrue[1000#+{999, 1001}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 05 2021 *)

CROSSREFS

Cf. A001359, A158277, A158861, A173937.

Sequence in context: A052457 A119654 A333439 * A256398 A008926 A136468

Adjacent sequences:  A173973 A173974 A173975 * A173977 A173978 A173979

KEYWORD

base,nonn

AUTHOR

Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 04 2010

STATUS

approved

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Last modified July 24 18:34 EDT 2021. Contains 346273 sequences. (Running on oeis4.)