Smarandache-Wellin Prime

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.

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