A069151 Concatenations of consecutive primes, starting with 2, that are also prime.

2, 23, 2357

Offset: 1

Author

Joseph L. Pe, Apr 08 2002

Keywords

• nonn
• bref
• base

Comments

Primes in A019518.

The next term is the 355-digit number 2357111317192329313741434753...677683691701709719 which is too large to include here. See A046035, A046284.

The term after the 355-digit term has 499 digits, and the next two terms after that have 1171 and 1543 digits respectively. - Harvey P. Dale, Oct 03 2024

References

• R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, 2nd ed., Springer, NY, 2005; see p. 78. [The 2002 printing states incorrectly that 2357...5441 is prime.]

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 1..5
• M. Fleuren, Smarandache Concatenated Primes
• Ernest G. Hibbs, Component Interactions of the Prime Numbers, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.
• Eric Weisstein's World of Mathematics, Smarandache-Wellin Number
• Eric Weisstein's World of Mathematics, Smarandache-Wellin Prime
• Wikipedia, Smarandache-Wellin number
• Index entries for sequences related to Most Wanted Primes video

Crossrefs

Cf. A019518.

Cf. A046035 (Numbers n such that the concatenation of the first n primes is prime)

Cf. A046284 (Primes p such that concatenation of primes from 2 through p is a prime).

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

Programs

Mathematica

Cases[FromDigits /@ Rest[FoldList[Join, {}, IntegerDigits[Prime[ Range[10^3]]]]], ?PrimeQ] (* _Eric W. Weisstein, Oct 30 2015 *)
Select[Table[FromDigits[Flatten[IntegerDigits/@Prime[Range[n]]]],{n,500}],PrimeQ] (* Harvey P. Dale, Oct 03 2024 *)

PARI

s=""; for(n=1, 200, s=concat(s, prime(n)); if(ispseudoprime( eval(s)), print1(s", "))) \\ Jens Kruse Andersen, Jun 26 2014

Python

from sympy import isprime, nextprime
def afind(terms, verbose=False):
  n, p, pstr = 0, 2, "2"
  while n < terms:
    if isprime(int(pstr)): n += 1; print(n, int(pstr))
    p = nextprime(p); pstr += str(p)
afind(5) # Michael S. Branicky, Feb 23 2021

Extensions

Edited by Robert G. Wilson v, Apr 11 2002

Entry revised Jan 18 2004