A167517 -id:A167517 - cp's OEIS frontend

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

Patrick De Geest

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

			(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

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

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

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

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 *)

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

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

A030997 Smallest prime which is a concatenation of n consecutive primes.

Original entry on oeis.org

2, 23, 5711, 2357, 711131719, 113127131137139149, 29313741434753, 107109113127131137139149, 211223227229233239241251257, 691701709719727733739743751757, 2329313741434753596167

Offset: 1

Patrick De Geest and Warut Roonguthai

			a(5) = 711131719 is the smallest prime which is the concatenation of five consecutive primes 7, 11, 13, 17 and 19.

Hans Havermann, Table of n, a(n) for n = 1..100

Cf. A030996, A068655, A030473, A086041, A099727, A167517.

Cf. A030461 (primes that are concatenations of two primes), A030469 (three primes), A030473 (four primes), A086041 (five primes).

for(k=1,19, for(i=0,1e9, isprime( eval( p=concat( vector( k,j,Str( prime( i+j )))))) & break); print1(p,", ")) \\ M. F. Hasler, Nov 10 2009

A167518 Least reversible prime (A007500) which is a concatenation of n consecutive primes.

Original entry on oeis.org

2, 151157, 353359367, 139149151157, 101103107109113, 704517045770459704817048770489, 97101103107109113127, 1519315199152171522715233152411525915263, 382138233833384738513853386338773881, 9319932393379341934393499371937793919397

Offset: 1

M. F. Hasler, Nov 10 2009

Here the weaker definition of A007500 is used, but all terms > 2 known so far are also Emirps in the sense of A006567 (i.e. different from their reversal), so it is sufficient to change the first term to 13 in order to have a sequence of "true" emirps.

Is it possible to prove that all terms > 2 are in A006567?

Cf. A030997, A167517.

for(k=1,19,for(i=0,1e9, isprime( eval( p=concat( vector( k,j,Str( prime( i+j )))))) & isprime(eval(concat(vecextract(Vec(p),"-1..1")))) & break); print1(p,", "))

Edited by Charles R Greathouse IV, Apr 28 2010

a(9)-a(10) from Donovan Johnson, Sep 25 2011

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A030469 Primes which are concatenations of three consecutive primes.

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A030997 Smallest prime which is a concatenation of n consecutive primes.

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A167518 Least reversible prime (A007500) which is a concatenation of n consecutive primes.

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