Talk:Seventeen or Bust
From Wikipedia, the free encyclopedia
Contents |
[edit] Page rename/move discussion
(from Wikipedia:Requested moves)
[edit] Seventeen or bust → Seventeen or Bust
Requesting a swap between article and its redirect. No history at the destination page. The article internally uses "Seventeen or Bust", as does seventeenorbust.com.
- support. Dbenbenn 16:08, 10 Jan 2005 (UTC)
- support Although listing here is a very good way of engaging some scrutiny and obtaining consensus on a proposed move, in practice I think you could have moved this yourself because the only thing at the target location is a redirect with no history. --Tony Sidaway|Talk 16:18, 10 Jan 2005 (UTC)
- Now that the destination page has been cleared, I've unilaterally done the move. Can this entry simply be removed? Dbenbenn 22:50, 10 Jan 2005 (UTC)
- Support retroactively. Neutralitytalk 21:35, Jan 12, 2005 (UTC)
[edit] Trying to prove the remaining sequences contain only composite numbers?
How many mathematicians have actually tried to prove that sequences such as 4847x2n+1, 10223x2n+1 and 19249x2n+1 contain only composite numbers.
By analogy with sequences such as 48w1, 71w7, 38w7, 62w9, 62w7, 51w7 and 32w7 - plus a brief study of my own, I am well aware that for only a very few values do such formulas as 4847x2n+1 have any chance of being prime. This is because, like 71w7, they have what are basically nearly complete covering sets where only a small proportion of numbers remain "uncovered" and needing to be tested.
However, the only way to show that these sequences are likely to contain no primes would be to use theorems analogous to the argument that there are only finitely many Fermat primes. This argument has not or cannot be applied to sequences like 48w1 and 71w7.
Hence, it would be good to find out whether anyone has really tried to prove the impossibility of a prime of the form 4847x2n+1, 10223x2n+1 or 19249x2n+1.
[edit] What is so special about the remaining numbers?
Why do these seventeen (or eight, or however many remain) numbers stand out as possible Sierpinskis? How were the other 70000+ numbers eliminated with comparative ease? Frankie 15:51, 20 December 2005 (UTC)
- For all other positive integers k less than 78,557, somebody has already found a n such that k * 2^n + 1 is prime. The project was named at the point there were seventeen troublesome values of k where no n had yet been found. If the project were started today, it might have been called Eight or bust. --Ghewgill 00:00, 21 December 2005 (UTC)
-
- I grok the definition. I meant is there some other mathematical property shared by these numbers that makes them difficult to test? Or is it simply a pseudo-random fluke of nature, unrelated to all other properties, that these k happen to have unusually high n (or possibly none at all)? Were all the other numbers also tested by brute force (and quickly found to have low n), or were they weeded out in large bunches by more sophisticated methods? Frankie 21:46, 21 December 2005 (UTC)
-
-
- The remaining numbers just generate sequences that have a lot of composite members before the first prime. The are "special" in a similar sense that prime numbers are "special" - they just are that way. I don't know of any correlation to another property of these numbers that makes them particularly more difficult. --Ghewgill 02:14, 22 December 2005 (UTC)
-
-
-
-
- Hence the brute force approch, any other correlation or "specialness" of the numbers would make trying n -> infinity a very silly approach. 202.180.83.6 05:09, 16 February 2006 (UTC)
-
-
Related question: this form of brute force can only prove the negative case, by calculating a counterexample n. How were the positive Sierpinskis proven? Why did that method work for 78557 but not other numbers? Why are people confident that none of the seventeen are actually Sierpinskis? Frankie
