## You are here

HomeSmarandache-Wellin prime

## Primary tabs

# Smarandache-Wellin prime

An integer that is both a Smarandache-Wellin number in a given base $b$ and a prime number.

R. Crandall and C. Pomerance, Prime Numbers: A Computational Perspective, Springer, NY, 2001: 72

H. Ibstedt, A Few Smarandache Sequences, Smarandache Notions Journal, Vol. 8, No. 1-2-3, 1997: 170 - 183

Related:

FlorentinSmarandache

Major Section:

Reference

Type of Math Object:

Definition

Parent:

## Mathematics Subject Classification

11A63*no label found*

- Forums
- Planetary Bugs
- HS/Secondary
- University/Tertiary
- Graduate/Advanced
- Industry/Practice
- Research Topics
- LaTeX help
- Math Comptetitions
- Math History
- Math Humor
- PlanetMath Comments
- PlanetMath System Updates and News
- PlanetMath help
- PlanetMath.ORG
- Strategic Communications Development
- The Math Pub
- Testing messages (ignore)

- Other useful stuff
- Corrections

## Comments

## Smarandache-Wellin prime

What is the interest of this type of prime? Why are they studied in the first place?

Alvaro

## Re: Smarandache-Wellin prime

The Ribenboim and the Crandall/Pomerance books are, like, the holy texts of prime hunters, hee hee. Any kind of prime listed in either of those is worthy studying.

Also 'cause they're so hard to find, in any base! In the first 10^355 there might be just four of them... sniff...

## Re: Smarandache-Wellin prime

> The Ribenboim and the Crandall/Pomerance books are, like,

> the holy texts of prime hunters, hee hee. Any kind of prime

> listed in either of those is worthy studying.

To me, that doesn't really answer the question, only pushes it

off. Presumably, if Ribenboim, Crandall, and Pomerance state that these primes are worth studying in their books, they offer some

reason for this statement. What is that reason?

> Also 'cause they're so hard to find, in any base! In the

> first 10^355 there might be just four of them... sniff...

So what? The series gotten by concatenating radix representations

of primes grows rapidly (faster than exponential) so, by the

prime number theorem, one would expect to find few primes in it.

However, that doesn't tell me why this particular series is

interesting since it is hard to find primes in a random rapidly

increasing sequence.

To clarify my understanding of Alvaro's question, I think the point

here is whether the issue of primes in this sequences is related

to some other topic in math or whether there are theorems, or at

least conjectures, involving them. For instance, I would say that

the reason that Mersenne primes are interesting is not because

Mersenne wrote about them but because a. they are relevant to

perfect numbers and b. there are specific theorems for proving

primality or compositeness which only apply to these numbers.

Likewise, the reason primes in arithmetic progressions are

interesting is because of Dirichlet's theorem and L-functions.

Sure, one can investigate primes in any sequence of integers, but

is there any particular reason for looking at Smarandache's and

Wellin's sequence as opposed to any other sequence?