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A173976
Numbers m such that the concatenation of m and 999 is the 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
OFFSET
1,1
COMMENTS
Necessarily, m == 2 (mod 3).
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
EXAMPLE
2 is a term: 2999 = prime(430), 2999+2 = 3001 = prime(431).
8 is a term: 8999 = prime(1117), 8999+2 = 9001 = prime(1118).
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 *)
PROG
(PARI) isok(m) = my(x=eval(Str(m, 999))); isprime(x) && isprime(x+2); \\ Michel Marcus, Mar 08 2023
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Mar 04 2010
STATUS
approved