A Smarandache-Wellin number that is prime is known as a Smarandache-Wellin prime. Concatenations of the first n = 1, 2, 4, 128, 174, 342, 435, 1429 (OEIS A046035; Ibstedt 1998, pp. 78-79, p. 78) primes are Smarandache-Wellin primes. These correspond to concatenations of all primes up to p_n = 2, 3, 7, 719, 1033, 2297, 3037, 11927 (OEIS A046284), namely w_1 | = | 2 w_2 | = | 23 w_4 | = | 2357 w_128 | = | 2357...719 (OEIS A069151), which have 1, 2, 4, 355, 499, 1171, 1543, 5719 (OEIS A263959) decimal digits.
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