%I #40 Oct 03 2024 13:58:27

%S 2,23,2357

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

%C Primes in A019518.

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

%C 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

%D 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.]

%H Jens Kruse Andersen, <a href="/A069151/b069151.txt">Table of n, a(n) for n = 1..5</a>

%H M. Fleuren, <a href="http://www.gallup.unm.edu/~smarandache/SmConPri.txt">Smarandache Concatenated Primes</a>

%H Ernest G. Hibbs, <a href="https://www.proquest.com/openview/4012f0286b785cd732c78eb0fc6fce80">Component Interactions of the Prime Numbers</a>, Ph. D. Thesis, Capitol Technology Univ. (2022), see p. 33.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Smarandache-WellinNumber.html">Smarandache-Wellin Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Smarandache-WellinPrime.html">Smarandache-Wellin Prime</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Smarandache%E2%80%93Wellin_number">Smarandache-Wellin number</a>

%H <a href="/index/Mo#MWP">Index entries for sequences related to Most Wanted Primes video</a>

%t Cases[FromDigits /@ Rest[FoldList[Join, {}, IntegerDigits[Prime[ Range[10^3]]]]], _?PrimeQ] (* _Eric W. Weisstein_, Oct 30 2015 *)

%t Select[Table[FromDigits[Flatten[IntegerDigits/@Prime[Range[n]]]],{n,500}],PrimeQ] (* _Harvey P. Dale_, Oct 03 2024 *)

%o (PARI) s=""; for(n=1, 200, s=concat(s, prime(n)); if(ispseudoprime( eval(s)), print1(s", "))) \\ _Jens Kruse Andersen_, Jun 26 2014

%o (Python)

%o from sympy import isprime, nextprime

%o def afind(terms, verbose=False):

%o n, p, pstr = 0, 2, "2"

%o while n < terms:

%o if isprime(int(pstr)): n += 1; print(n, int(pstr))

%o p = nextprime(p); pstr += str(p)

%o afind(5) # _Michael S. Branicky_, Feb 23 2021

%Y Cf. A019518.

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

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

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

%K nonn,bref,base

%O 1,1

%A _Joseph L. Pe_, Apr 08 2002

%E Edited by _Robert G. Wilson v_, Apr 11 2002

%E Entry revised Jan 18 2004