Talk:Riesel number
From Wikipedia, the free encyclopedia
 |
|||||
| Mathematics rating: | Stub Class | Low Priority | Field: Number theory | ||
| Please update this rating as the article progresses, or if the rating is inaccurate. Please also add comments to suggest improvements to the article. | |||||
[edit] Covering Set
"To show that a number is a Riesel number, one must find a 'covering set'. A covering set is a set of small prime numbers that will divide any member of a sequence, so called because it is said to 'cover' that sequence."
There are at least three necessary conditions for that statement:
- there's no such thing as a nonconstructive proof that a number is Riesel
- one can define "small"
- every Riesel number even has a finite covering set - can't there be one whose sequence of smallest factors is unbounded?
Does anybody have a proof of any of these statements? -- Smjg 16:54, 14 September 2005 (UTC)
- I suppose "small" here would simply be finite. Depending on the exact definition of covering set used, I could see an argument for them, but if the definition is that broad (lacking a proof of your first and third points) then I can't see any justification for talking about them, because they could be too unwieldy to work with. I've changed the wording in the article to reflect the possibility of nonconstructive proofs; anyone with proofs for your first or third points should add them to the article. CRGreathouse 22:50, 25 May 2006 (UTC)
