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

Author

Patrick De Geest

Keywords

• nonn
• base

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

Examples

			(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
		

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

Crossrefs

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

Programs

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 *)

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

Formula

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