Talk:Weird number

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How can the Schnirelmann density of the set of weird numbers be positive? The defintion given of Schnirelmann density is such that if the set does not contain 1 its density is zero. Molinari 01:44, 15 Apr 2005 (UTC)

I think it is an error. UPINT 2nd ed (Guy 1994) says only "Erdös showed that their density is positive", which I think must be referring to Natural density. Hv 16:39, 13 July 2005 (UTC)


The placement of the trivia in no way detracts from the mathematical content of the page, so why remove it? Other major pages have trivia sections, so I doubt there's an actual precedent against it.

I second this. It's definitely not "subtrivial" especially due to the heavy symbolism, especially numerical, that they put into their music. Thavron 04:04, 10 August 2006 (UTC)

[edit] Lower bound for odd weird numbers

I took out the claim "if any [odd weird numbers exist], they must be greater than 10^18 (as noted by Bob Hearn in a July 2005 posting to the SeqFans mailing list)" since it was insufficiently sourced, due to the fact that the result is not published (as far as I can tell). I replaced it with the rather trivial lower bound 10^6 given by Benkoski and Erdos. If anyone knows a better published lower bound, please add it. Thanks. Doctormatt 18:45, 25 August 2007 (UTC)

If you must: the 10^6 result is ridiculously trivial. Frankly I don't think you can expect to find a published result on this, since even the 10^18 bound is too trivial to be accepted as a paper in any mathematical journal. Considering that fact, I think that a reference to Sloane's encyclopedia is more than sufficient -- but as a WP:0RR devotee I will leave it.
Hmm. Perhaps some undergraduate journal would accept such a result?
CRGreathouse (t | c) 03:20, 12 October 2007 (UTC)
The 10^6 bound is not the point of the Erdos paper. An improved bound could be simply part of a paper proving something significant. Thanks for not reverting. Doctormatt 05:59, 12 October 2007 (UTC)
That was a 1974 paper, I believe. Searching JSTOR and a few other databases from 1975 on, I wasn't able to find a single paper mentioning "weird numbers" in this context. (JSTOR had half a dozen ads and 2-3 papers from undergraduate journals calling various transcendentals "weird"; Academic Search Complete pulled up only a newspaper article which was similarly unrelated.)
CRGreathouse (t | c) 13:04, 12 October 2007 (UTC)
Guy lists this paper (in section B2 of Unsolved Problems in NT):
  • Sidney Kravitz, A search for large weird numbers, J. Recreational Math., 9 (1976-77) 82-85.
I think that might be worth a look (unfortunately we don't have JRM at my institution). MathSciNet also lists this:
  • On primitive weird numbers. A collection of manuscripts related to the Fibonacci sequence, pp. 162--166, Fibonacci Assoc., Santa Clara, Calif., 1980.
which might also be worth a look (this isn't in our library either...) Doctormatt 14:50, 12 October 2007 (UTC)
I'll see if I can locate either. My library, like yours, doesn't have the Journal of Recreational Mathematics, but I should be able to get a copy somehow. I'm not even sure what the other one is but I'll ask after it.
As clarification, I added only the 10^17 bound from the OEIS, not the 10^18 bound from the seqfans list. I still feel the 10^17 result is proper, regardless of the 10^18 bound's propriety. (I didn't know about the 10^18 bound at all until I looked in the history after my addition.)
CRGreathouse (t | c) 16:52, 12 October 2007 (UTC)
I've requested the Kravitz article by interlibrary loan. Doctormatt 17:17, 17 October 2007 (UTC)
I did the same thing earlier today.
I was able to find one reference -- CN Friedman, "Sums of Divisors and Egyptian Fractions",Journal of Number Theory (1993) -- which shows the weak lower bound of 232 ≈ 4×109. The result is attributed to "M. Mossinghoff at University of Texas - Austin".
CRGreathouse (t | c) 03:20, 19 October 2007 (UTC)
Great, I'll check out that paper. I got the Kravitz article: no mention of odd weird numbers, just a method for generating large even ones. I added his results to the article. The "large" weird number he gives is clearly outdated - I think it's high time that someone publish a paper with some modern weird number calculations... Doctormatt 04:32, 19 October 2007 (UTC)
Yes, I did not consider the search to 10^18 worth publishing. But I will investigate the options. If nothing else I can make my code available. Actually there were several tricks required to get to 10^18; even checking a single candidate odd weird (to see whether it is semiperfect) in this range is extremely slow if done naively, and of course the vast majority of the space must be weeded out before explicit checking. Bobhearn 00:11, 31 October 2007 (UTC)
UPINT would be a likely place to get this to be a published result. I know the author posts to seqfan occasionally, but I'm not sure how assiduously he reads it. Hv (talk) 13:06, 20 January 2008 (UTC)

[edit] 1976 paper

What's the point in the quoted result from the 1976 paper concerning very large weird numbers, given that if N is weird, Np is weird for all p>sigma(N) ? So taking p=M#44 (the largest known prime), we get a much larger weird number using any other weird number (provided its divisors' sum does not exceed M#44). — MFH:Talk 17:47, 4 April 2008 (UTC)