A173976 Numbers m such that the concatenation of m and 999 is the lesser of twin primes, i.e., a millennium twin prime couple.

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

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

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

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