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Smarandache-Wellin Prime


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; Crandall and Pomerance 2005, 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
(1)
w_2=23
(2)
w_4=2357
(3)
w_(128)=2357...719
(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 1.5×10^6 primes according to a search by M. Rodenkirch completed in early 2016.


See also

Constant Primes, Copeland-Erdős Constant, Copeland-Erdős Constant Digits, Integer Sequence Primes, Smarandache-Wellin Number

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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." http://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."

Cite this as:

Weisstein, Eric W. "Smarandache-Wellin Prime." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Smarandache-WellinPrime.html

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