A030469 Primes which are concatenations of three consecutive primes.

5711, 111317, 171923, 313741, 414347, 8997101, 229233239, 239241251, 263269271, 307311313, 313317331, 317331337, 353359367, 359367373, 383389397, 389397401, 401409419, 409419421, 439443449, 449457461

Offset

1,1

Comments

a(n) = "p(k) p(k+1) p(k+2)" where p(k) is k-th prime

It is conjectured that sequence is infinite. - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009

References

Richard E. Crandall, Carl Pomerance: Prime Numbers, Springer 2005 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009

John Derbyshire: Prime obsession, Joseph Henry Press, Washington, DC 2003 - from Eva-Maria Zschorn (e-m.zschorn(AT)zaschendorf.km3.de), Nov 09 2009

Marcus du Sautoy: Die Musik der Primzahlen. Auf den Spuren des groessten Raetsels der Mathematik, Beck, Muenchen 2004

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Formula

A132903 INTERSECT A000040. - R. J. Mathar, Nov 11 2009

Example

(1) 5=p(3), 7=p(4), 11=p(5) gives a(1).
(2) 7=p(4), 11=p(5), 13=p(6), but 71113 = 7 x 10159

Mathematica

Select[Table[FromDigits[Flatten[IntegerDigits/@{Prime[n], Prime[n+1], Prime[n+2]}]], {n, 11000}], PrimeQ] (* Zak Seidov, Oct 16 2009 *)
concat[{a_, b_, c_}]:=FromDigits[Flatten[IntegerDigits/@{a, b, c}]]; Select[ concat/@ Partition[ Prime[ Range[200]], 3, 1], PrimeQ] (* Harvey P. Dale, Sep 06 2017 *)

Prog

(PARI) for(i=1, 999, isprime(p=eval(Str(prime(i), prime(i+1), prime(i+2)))) & print1(p, " ")) \\ M. F. Hasler, Nov 10 2009

Crossrefs

Cf. A030461, A167517, A132903, A068655, A030997, A030473, A086041, A099727.

Sequence in context: A252342 A237743 A025027 * A244163 A253423 A202376

Adjacent sequences: A030466 A030467 A030468 * A030470 A030471 A030472

Keyword

nonn,base

Author

Patrick De Geest

Status

approved