Smarandache-Wellin number

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, ... OEIS|id=A019518.

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 (OEIS2C|id=A069151). The fourth has 355 digits and ends with the digits 719. [cite book
last = Pomerance
first = Carl B.
coauthors = Crandall, Richard E.
authorlink = Carl Pomerance
title = Prime Numbers: a computational perspective
publisher = Springer
date = 2001
pages = p78 Ex 1.86
id = ISBN 0387252827 ]

The primes at the end of the concatenation in the Smarandache-Wellin primes are:2, 3, 7, 719, 1033, 2297, 3037, 11927?, ... (OEIS2C|id=A046284).

The indices of the Smarandache-Wellin primes in the sequence of Smarandache-Wellin numbers are::1, 2, 4, 128, 174, 342, 435, 1429?, ... (OEIS2C|id=A046035).

The 1429th Smarandache-Wellin number is a probable prime with 5719 digits ending in 11927, discovered by Eric W. Weisstein in 1998. [Rivera, Carlos, [http://www.primepuzzles.net/puzzles/puzz_008.htm Primes by Listing] ] 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. [MathWorld|title=Integer Sequence Primes|urlname=IntegerSequencePrimes]

ee also

*Copeland–Erdős constant

References

*MathWorld|title=Smarandache-Wellin Number|urlname=Smarandache-WellinNumber
*planetmath reference|id=7921 |title= Smarandache-Wellin number
* [http://www.gallup.unm.edu/~smarandache/SmConPri.txt List of first 54 Smarandache-Wellin numbers with factorisations]
* [http://primes.utm.edu/glossary/page.php?sort=SmarandacheWellin 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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