A046035 Numbers k such that the concatenation of the first k primes (A019518) is a prime.

1, 2, 4, 128, 174, 342, 435, 1429

Offset: 1

Author

Eric W. Weisstein

Keywords

• nonn
• base
• nice
• more

Comments

No other terms with k <= 34736. - Eric W. Weisstein, Oct 30 2015

Examples

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

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

• 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, Smarandache-Wellin Prime
• Index entries for sequences related to Most Wanted Primes video

Crossrefs

Cf. A019518, A069151, A046284.

Cf. A033308 (Decimal expansion of Copeland-Erdős constant: concatenate primes).

Programs

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 *)

PARI

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

Formula

a(n) = A000720(A046284(n)), or A046284(n) = prime(a(n)).