Smarandache–Wellin Number
The first decimal Smarandache–Wellin numbers are:
- 2, 23, 235, 2357, 235711, 23571113, 2357111317, 235711131719, 23571113171923, 2357111317192329, ... (sequence A019518 in the OEIS).
Smarandache–Wellin prime
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 the OEIS). The fourth is 355 digits long: it is the result of concatenating the first 128 prime numbers, through 719.
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. 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.
See also
- Copeland–Erdős constant
- Champernowne constant, another example of a number obtained by concatenating a representation in a given base.
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.
External links
- Weisstein, Eric W. "Smarandache–Wellin number". MathWorld.
- Weisstein, Eric W. "Smarandache–Wellin prime". MathWorld.
- "Smarandache-Wellin number". PlanetMath.
- List of first 54 Smarandache–Wellin numbers with factorizations
- Smarandache–Wellin primes at The Prime Glossary
- Smith, S. "A Set of Conjectures on Smarandache Sequences." Bull. Pure Appl. Sci. 15E, 101–107, 1996.