Smarandache-Wellin number
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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:
A Smarandache-Wellin number that is also prime is called a Smarandache-Wellin prime. The indices of the first few Smarandache-Wellin primes in the decimal Smarandache-Wellin sequence are:
The Smarandache-Wellin primes corresponding to indices 1, 2 and 4 are 2, 23 and 2357 (sequence A069151 in OEIS). The fourth Smarandache-Wellin prime, with index 128, has 355 digits and ends with the digits 719.[1]
The 1429th Smarandache-Wellin number is a probable prime with 5719 digits, discovered by Eric W. Weisstein in 1998.[2] If confirmed, it will be the eighth Smarandache-Wellin prime. In July 2006 Weisstein's search showed the index of the next Smarandache-Wellin prime (if one exists) is greater than 18272.[3]
[edit] See also
[edit] References
- ^ Pomerance, Carl B.; Crandall, Richard E. (2001). Prime Numbers: a computational perspective. Springer, p78 Ex 1.86. ISBN 0387252827.
- ^ Rivera, Carlos, Primes by Listing
- ^ Eric W. Weisstein, Integer Sequence Primes at MathWorld.
- Eric W. Weisstein, Smarandache-Wellin Number at MathWorld.
- Smarandache-Wellin number on PlanetMath
- 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.
