OFFSET
1,1
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
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 *)
PROG
(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
CROSSREFS
KEYWORD
nonn,bref,base
AUTHOR
Joseph L. Pe, Apr 08 2002
EXTENSIONS
Edited by Robert G. Wilson v, Apr 11 2002
Entry revised Jan 18 2004
STATUS
approved