Smarandache–Wellin number
In mathematics, a Smarandache–Wellin number is an integer that in a given base is the concatenation of the first n prime numbers written in that base. Smarandache–Wellin numbers are named after Florentin Smarandache and Paul R. Wellin.
The first decimal Smarandache–Wellin numbers are:
Smarandache–Wellin primes
A Smarandache–Wellin number that is also prime is called a Smarandache–Wellin prime. The first three are 2, 23 and 2357 (sequence A069151 in OEIS). The fourth has 355 digits and ends with the digits 719.[1]
The primes at the end of the concatenation in the Smarandache–Wellin primes are
The indices of the Smarandache–Wellin primes in the sequence of Smarandache–Wellin numbers are:
The 1429th Smarandache–Wellin number is a probable prime with 5719 digits ending in 11927, discovered by Eric W. Weisstein in 1998.[2] If it is proven prime, it will be the eighth Smarandache–Wellin prime. In March 2009 Weisstein's search showed the index of the next Smarandache–Wellin prime (if one exists) is at least 22077.[3]
See also
References
- ↑ Pomerance, Carl B.; Crandall, Richard E. (2001). Prime Numbers: a computational perspective. Springer. pp. 78 Ex 1.86. ISBN 0-387-25282-7.
- ↑ Rivera, Carlos, Primes by Listing
- ↑ Weisstein, Eric W., "Integer Sequence Primes", MathWorld. Retrieved 2011-07-28.
- Weisstein, Eric W., "Smarandache–Wellin Number", MathWorld.
- Smarandache-Wellin number at PlanetMath.org.
- List of first 54 Smarandache–Wellin numbers with factorisations
- Smarandache–Wellin primes at The Prime Glossary
- Smith, S. "A Set of Conjectures on Smarandache Sequences." Bull. Pure Appl. Sci. 15E, 101–107, 1996.
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