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:

2, 23, 235, 2357, 235711, ... (sequence A019518 in OEIS).

[edit] 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 (A069151). 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

2, 3, 7, 719, 1033, 2297, 3037, 11927?, ... (A046284).

The indices of the Smarandache–Wellin primes in the sequence of Smarandache–Wellin numbers are:

1, 2, 4, 128, 174, 342, 435, 1429?, ... (A046035).

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 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

• Copeland–Erdős constant

[edit] References

1. ^ Pomerance, Carl B.; Crandall, Richard E. (2001). Prime Numbers: a computational perspective. Springer. pp. 78 Ex 1.86. ISBN 0387252827. 
2. ^ Rivera, Carlos, Primes by Listing
3. ^ Weistein, Eric W., "Integer Sequence Primes" from MathWorld.

• Weistein, Eric W., "Smarandache–Wellin Number" from 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.