# 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:

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

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:

1, 2, 4, 128, 174, 342, 435. (sequence A046035 in OEIS)

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]

* Copeland–Erdős constant

References

1. ^ Pomerance, Carl B.; Crandall, Richard E. (2001). Prime Numbers: a computational perspective. Springer, p78 Ex 1.86. ISBN 0387252827.

2. ^ Rivera, Carlos, Primes by Listing

* Smith, S. "A Set of Conjectures on Smarandache Sequences." Bull. Pure Appl. Sci. 15E, 101-107, 1996.