A Smarandache-Wellin number that is prime is known as a Smarandache-Wellin prime. Concatenations of the first , 2, 4, 128, 174, 342, 435, 1429 (OEIS A046035; Ibstedt 1998, pp. 78-79; Crandall and Pomerance 2005, p. 78) primes are Smarandache-Wellin primes. These correspond to concatenations of all primes up to , 3, 7, 719, 1033, 2297, 3037, 11927 (OEIS A046284), namely

			(1)
			(2)
			(3)
			(4)

(OEIS A069151), which have 1, 2, 4, 355, 499, 1171, 1543, 5719 (OEIS A263959) decimal digits.

Smarandache-Wellin primes are the subset of constant primes formed from the Copeland-Erdős constant for which the trailing digits correspond to the full (non-truncated) final concatenated prime.

There are no other Smarandache-Wellin primes for concatenations up to the first  primes according to a search by M. Rodenkirch completed in early 2016.

REFERENCES:

Crandall, R. and Pomerance, C. Problem 1.86 in Prime Numbers: A Computational Perspective, 2nd ed. New York: Springer-Verlag, p. 78, 2005.

Ibstedt, H. "Smarandache Concatenated Sequences." Ch. 5 in Computer Analysis of Number Sequences. Lupton, AZ: American Research Press, pp. 75-79, 1998.

Rodenkirch, M. "Smarandache-Wellin Primes." https://www.mersenneforum.org/showthread.php?t=20599.

Sloane, N. J. A. Sequences A046035, A046284, A069151, and A263959 in "The On-Line Encyclopedia of Integer Sequences."