

A046035


Numbers n such that the concatenation of the first n primes (A019518) is a prime.


12




OFFSET

1,2


COMMENTS

The primes themselves (A069151) are sometimes called SmarandacheWellin primes.
No others with n <= 34736.  Eric W. Weisstein, Oct 30 2015


REFERENCES

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001; see p. 72. [The 2002 printing states incorrectly that 719 is a term.]


LINKS

Table of n, a(n) for n=1..8.
M. Fleuren, Smarandache Concatenated Primes.
Eric Weisstein's World of Mathematics, Consecutive Number Sequences
Eric Weisstein's World of Mathematics, Integer Sequence Primes
Eric Weisstein's World of Mathematics, SmaradacheWellin Prime


FORMULA

A046284(n) = prime(a(n)).


EXAMPLE

4 is a term since 2357 is a prime. [Corrected by Ed Murphy (emurphy42(AT)socal.rr.com), May 15 2007]


MATHEMATICA

max = 1500; With[{primes = Prime[Range[max]]}, Flatten[Position[ Table[ FromDigits[Flatten[IntegerDigits/@Take[primes, n]]], {n, max}], _?PrimeQ]]] (* Harvey P. Dale, Dec 17 2013 *)
Position[FromDigits /@ Rest[FoldList[Join, {}, IntegerDigits[Prime[Range[ 10^3]]]]], _?PrimeQ] // Flatten (* Eric W. Weisstein, Oct 30 2015 *)


PROG

(PARI) p=""; for(n=1, 2000, p=concat(p, prime(n)); if(ispseudoprime(eval(p)), print1(n", "))) \\ Altug Alkan, Oct 30 2015


CROSSREFS

Cf. A019518 (SmarandacheWellin numbers).
Cf. A033308 (Decimal expansion of CopelandErdős constant: concatenate primes).
Cf. A069151 (SmarandacheWellin primes; Concatenations of consecutive primes, starting with 2, that are also prime).
Sequence in context: A259381 A009595 A018493 * A134710 A009073 A012561
Adjacent sequences: A046032 A046033 A046034 * A046036 A046037 A046038


KEYWORD

nonn,base,nice


AUTHOR

Eric W. Weisstein


STATUS

approved



