Talk:Smarandache–Wellin number

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no concensus to delete? what does that mean? did i count wrong? 8 keep, 4 delete (counting nominator) and one merge? Isnt that a concensus to keep??? 19:01, 22 January 2007 (UTC)

Wikipedia:Articles for deletion says "The debate is not a vote". Similar quotes are frequent about AfD debates. A 2/3 majority (and my merge) of keep !votes might not be strong enough to call "consensus" anyway. Is it really important when the article was kept? PrimeHunter 12:39, 23 January 2007 (UTC)


Who is Wellin? Is there any information?

—Preceding unsigned comment added by Hutschi (talkcontribs) 03:42, 19 April 2004

Apparently Paul R. Wellin (see [1]). I've added it to the article. —Lowellian (reply) 01:48, 26 February 2007 (UTC)
That was also stated (with no source) at Wikipedia:Articles for deletion/Smarandache-Wellin number. Do you have a source or is it a guess? The only Google hit I found was the linked AfD debate. PrimeHunter 15:40, 26 February 2007 (UTC)

Base N Smarandache-Wellin primes?[edit]

Do Smarandache-Wellin primes have to be in decimal notation? For concepts like palindromic primes and permutable primes, the articles focus on base 10 primes of that kind but also give at least passing mention to other bases.

I have given some thought to concatenations of the first n primes in hexadecimal. The first ten primes in hexadecimal are 2, 3, 5, 7, B, D, 11, 13, 17 and 1D.

23h is 35 decimal, not prime. 235h is 565, not prime. 2357h is 9047 = 83 * 109.

2357Bh is 144763, a prime, making it just the second prime in this series. I've gone up to 2357BD1113171Dh (9948093731772189) and failed to find another prime. I went beyond that but ran into an unwillingness from my computer to handle larger numbers. PrimeFan 20:57, 4 May 2004 (UTC)

I think too, there should be a generalization. On the German page, I inserted an according hint. --Hutschi 12:49, 6 May 2004 (UTC)


Is this really a notable concept? Why would number theorists be interested in it? Please note that Florentin Smarandache and/or some Romanian fans have added some often startling articles such as Neutrosophy and Dezert-Smarandache theory, hence my concern about apparent wikicruft.---CH 07:34, 5 May 2006 (UTC)

Eric W. Weisstein and Neil Sloane are two professional mathematicians who've given at least some thought to these kinds of numbers. See Mathworld and OEIS. PrimeFan 15:48, 17 May 2006 (UTC)
I've added more external links and removed the prod tag. And the fact that the fourth Smarandache-Wellin prime doesn't occur until index 128 - well, I think that's kind of interesting. I think the article at least deserves to go to AfD now. Gandalf61 20:13, 15 January 2007 (UTC)
Ok, I put it on AfD instead. —David Eppstein 20:56, 15 January 2007 (UTC)

indices prime section unclear[edit]

the sentence about the indices of the first prime.. is unclear; I think if the list above was in the format

SF indice   1     2     3
SF number   2    23    235

it would be clearer to people like myself who are not mathemeticians \ —Preceding unsigned comment added by (talk) 02:54, 24 July 2008 (UTC)

I guess "SF" refers to Smarandache-Wellin. I have edited [2] the part about Smarandache-Wellin primes. Is this better? PrimeHunter (talk) 00:02, 26 July 2008 (UTC)

Edit and reversion (presumed update at issue)[edit]

If anybody can clarify whether my edit attempt was correct, it occurred to me that the number change might have been just a substitute of length for index (and wrong), and the later date used might just have been Weisstein's confirmation he had done no more with it. (talk) 19:05, 28 July 2011 (UTC)

Your first edit was correct. I have reinstated it and added an accessdate so readers can see when the source contained the limit we mention. The Wayback Machine shows that it wasn't Weisstein's first update since our old 2006 limit. PrimeHunter (talk) 22:59, 28 July 2011 (UTC)

Infinitely many Smarandache primes?[edit]

The page says "It is conjectured there are infinitely many Smarandache primes." Who conjectured this and why? Is there any good reason to believe that two very sparse, unrelated sets of numbers have infinite intersection? Sxdcer (talk) 04:09, 26 September 2016 (UTC)

@Sxdcer: Considering the prime number theorem I wouldn't call the primes very sparse. A random number near x has chance 1/log(x) of being prime. The sum of 1/log(Sm(n)) taken over all Smarandache numbers Sm(n)) is infinite. There is no known reason to think Smarandache numbers behave significantly differently from random numbers when primality is concerned, so it's expected there are infinitely many primes. The sum only converges slowly to infinite so it seems very plausible that it's just a coincidence that no primes have been found yet. PrimeHunter (talk) 11:13, 26 September 2016 (UTC)