Talk:Carol number

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[edit] Why?

This article does not even attempt to explain, why are integers of the form "4^n - 2^(n+1) - 1" of any particular interest to anyone? And who is Cletus Emmanuel and why did he name the numbers "Carol numbers" — who is this Carol person, anyway? --ZeroOne 16:19, 28 September 2006 (UTC)

Emmanuel is a professional mathematician who researched these numbers in connection to primality testing. Carol is a personal friend of his (Eric Weisstein of Mathworld thus calls the naming an "arbitrary dubbing.") As for why they are interesting to anyone, the article does need to explain this. I know they are interesting to professional mathematicians, but I don't always understand why professional mathematicians find interesting some of the things they study. PrimeFan 23:26, 28 September 2006 (UTC)

Is there evidence that Cletus Emmanuel is a professional mathematician, or that Carol numbers (and the similar Kynea numbers) are interesting to professional mathematicians? I think the first public use of the names and mention of the forms is from February 2002 in [1] where Emmanuel writes "The Most interesting formula I've looked at is Cp = 4^p - 2^(p+1) - 1(Here Cp is a Carol Number)", and in the last post: "Also, there is another set of numbers called Kynea Numbers. They are of the form K[p]= 4^p + 2^(p+1) - 1. They have exactly the same properties as Carol Numbers."

Emmanuel gave the impression that they were existing names and continued to use the names for two years, getting a few others to use the names. Then in February 2004 in [2] he revealed a secret: It was himself who had named the numbers and they were named after personal acquaintances:

"Carol G. Kirnon is my best female friend in the whole wide world. She was the first girl to steal my heart when we were in high school. Therefore, since math is my love and she is my love, I named the first set of numbers after her. The second set, and really the second set, because I encountered them days after is named for the baby girl that had the greatest inpact on my life so far, Kynea R. Griffith (she is ten years old now). I hope some day when people talk about Carol and Kynea numbers, they will know a little bit about the two."

There is no sign that Carol and Kynea have any relation to the numbers (other than knowing the namer) or to mathematics. Somebody contacted MathWorld with the history of the numbers, and the articles at http://mathworld.wolfram.com/CarolNumber.html and http://mathworld.wolfram.com/KyneaNumber.html were replaced with a link to http://mathworld.wolfram.com/Near-SquarePrime.html. That article does not use the names "Carol number" and "Kynea number", but it says about numbers of those forms that are prime:

"(arbitrarily dubbed Carol primes by their original investigator in reference to a personal acquaintance)"

"(arbitrarily dubbed Kynea primes by their original investigator in reference to a personal acquaintance)"

PrimeHunter 01:32, 2 August 2007 (UTC)

Maybe I was wrong about Emmanuel being a professional mathematician. I have verified that now at Mathworld CarolNumber.html has been turned into what we would call a redirect. The OEIS sequence was submitted by Weisstein himself; I'd like to think that Neil Sloane would've questioned the nomenclature. Also, I tried looking it up in Google Scholar but only came up with results that appear to have no relevance to this topic. PrimeFan 22:08, 2 August 2007 (UTC)

In January 2004 [3] Emmanuel said he planned to submit a paper about Carol and Kynea numbers to a journal. I haven't heard of any result and his mail doesn't sound like something a professional mathematician would write. OEIS has around 130000 integer sequences and appear to accept almost anything. I don't think OEIS would question a name from Weisstein who submitted it before he changed his own site, and I guess before he learned of the origin of the names.

I'm in a small dispute with an IP and a just created SPA. It doesn't make sense to me to say that somebody "discovered" or "found" numbers of the form 4ⁿ − 2^{n + 1} − 1, and the added "source" in [4] does not source anything. Emmanuel named them and studied them but nobody "discovered" them. He discovered some primes of that form but not the numbers themselves. "Arbitrarily dubbing" a form of number as Weisstein calls it is not the same as somebody who discovers a species or asteroid and then names it. PrimeHunter 23:40, 2 August 2007 (UTC)

I don't thik that's an issue for us anymore. The issue is whether or not the OEIS has enshrined this usage of the term or Wikipedia has. If Wikipedia has, then I think we should take action to try to reverse that. But if the OEIS has, then it's out of our hands. Anton Mravcek 00:09, 3 August 2007 (UTC)

My last paragraph about the word "discovered" was referring to the specific edit [5] which I think should be reverted, but I have already done it a few times. Whether Carol numbers and Kynea numbers notable subjects and those names should be used is another matter. PrimeHunter 01:13, 3 August 2007 (UTC)

Update on the planned paper Emmanuel mentioned in January 2004. He just wrote this to the mail list where he introduced Carol/Kynea numbers in 2002: "I am now ready to publish Carol/Kynea numbers. How do i go about doing that/ What journal should I submit to/ Is there a special format?".[6] That sounds like an amateur mathematician who hasn't published anything before. PrimeHunter 00:23, 15 August 2007 (UTC)