Talk:Seventeen or Bust

Page rename/move discussion

(from Wikipedia:Requested moves)

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. Neutrality^talk 21:35, Jan 12, 2005 (UTC)

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 48_w1, 71_w7, 38_w7, 62_w9, 62_w7, 51_w7 and 32_w7 - 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 71_w7, 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 48_w1 and 71_w7.

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. — Preceding unsigned comment added by 203.194.49.116 (talk) 05:08, 13 June 2005 (UTC)

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)

Different k's have different weights. This is basically a measure of what portion of numbers with that k have small factors. High-weight k's, on average, produce more primes per n range than low-weight k's do (because they produce a larger number of testable candidates), and so typically have their first prime at a lower n. The seventeen k's that would remain at such a high n are (statistically speaking: almost certainly) very low-weight k's. You can see more info at http://www.mersenneforum.org/showthread.php?t=18818 and example of very low weight and very high weight k's (different bases and Riesel/Sierp differences are irrelevant at this level of discussion). As for whether a certain k will be high or low weight, I think it's basically a pseudo-random fluke. — Mini-Geek ^(talk) 19:16, 11 December 2013 (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

This page might answer some of your questions. Qutezuce 20:58, 16 February 2006 (UTC)

degree symbol in table

What is the reason for the "°" symbol in the first column of the table? Bubba73 (talk), 05:10, 19 June 2009 (UTC)

I don't know. The column was created like that by a Russian editor.[1] Could this be some Russian notation? PrimeHunter (talk) 10:14, 19 June 2009 (UTC)

I don't see a reason for it, so I'll take them out. Bubba73 (talk), 14:43, 19 June 2009 (UTC)

67607

They've found that 67607 + 2¹⁶³⁸⁹ is prime. 116.14.21.167 (talk) 12:57, 24 March 2010 (UTC)

If so, this is not a prime that matters to this project. Bubba73 ^{(You talkin' to me?)}, 02:15, 29 May 2010 (UTC)

It's mentioned at http://www.seventeenorbust.com/. It's a prime found for the dual Sierpinski problem: What is the smallest odd k such that k + 2ⁿ is composite for all n. 67607 + 2¹⁶³⁸⁹ is the smallest prime for k = 67607. It was found to be a probable prime in 2002 by Jim Fougeron, and later proved prime. It only has limited relevance to the Seventeen or Bust project which works on the "normal" (not dual) Sierpinski problem, and hasn't yet found a prime of form 67607·2ⁿ+1. PrimeHunter (talk) 02:47, 29 May 2010 (UTC)

Thanks, I didn't know about the dual problem. Bubba73 ^{(You talkin' to me?)}, 03:05, 29 May 2010 (UTC)