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
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(1)
|
 |  |  |
(2)
|
 |  |  |
(3)
|
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(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.
