Cullen and Woodall altering on Prime Pages

jasong · 2008-01-13, 22:08

Okay, I understand that if a k in k*2^n+/-1 is even than k can be halved and n increased by one. But since Cullen and Woodall numbers are based on the idea that k and n are the same number, doesn't Prime Pages policy defeat the purpose of the people doing the search in the first place?

Brian-E · 2008-01-15, 21:50

Quote:

Originally Posted by jasong

Okay, I understand that if a k in k*2^n+/-1 is even than k can be halved and n increased by one. But since Cullen and Woodall numbers are based on the idea that k and n are the same number, doesn't Prime Pages policy defeat the purpose of the people doing the search in the first place?

I'm risking looking silly here, but I have to admit I have no idea what you mean, Jason. But I am intrigued.

What is this Prime Pages policy?
Brian.

jasong · 2008-01-16, 10:30

Quote:

Originally Posted by Brian-E

I'm risking looking silly here, but I have to admit I have no idea what you mean, Jason. But I am intrigued.

What is this Prime Pages policy?
Brian.

I'm not sure how much you understand, so I'll expand the scope of the question a bit. Cullen and Woodall numbers are numbers of the form n*2^n+ or -1, Cullen is the plus numbers, Woodall is the minus.

With Prime Pages, they've noted that if k is even, then k*2^n+1=(k/2)*2^(n+1)+1. This is normally a fabulous simplification. The problem is the whole point of the Cullen and Woodall projects is that k and n are the same number, when you do the math trick, it's just a regular equation.

If there's something quirky about an equation, and simplifying takes away the obviousness of the quirkiness, than you've defeated the whole point of finding it in the first place.

Brian-E · 2008-01-16, 10:54

But isn't the point of the exercise to factorise the Cullen and Woodall numbers and to find the very rare primes, not to discover the alternative representations of the numbers?

Edit: Ah, are you wondering why Prime Pages doesn't list the numbers with the k equal to the n? I think because it lists other numbers of the form k*2^n +/- 1 which are not Cullen/Woodall as well, and the policy is to "simplify" all such numbers so that n is as large as possible. This makes it indeed less simple-looking in the case of the special Cullen/Woodall, but by standardising in that way they make it less likely that someone will make a mistake by analysing a number which has in fact already been tested but written in a different form.

axn · 2008-01-17, 06:02

To be fair, Prime Pages' prime (pardon the pun) purpose is to act as a repository of top primes. It is always a good idea to "normalize" the expression of a prime to a standard form so that you don't end up with multiple representations of the same prime.

The secondary purpose of classifying the primes is achieved thru the archival tags. IMO, these policies are entirely appropriate for a catalog such as this.

I can see why seeing the original "non-normalized" representation might be useful, but I just don't think it is prime page's responsibility.

jasong · 2008-01-18, 01:23

Quote:

Originally Posted by axn1

I can see why seeing the original "non-normalized" representation might be useful, but I just don't think it is prime page's responsibility.

lol, I'd temporarily forgotten Prime Pages was a volunteer project, and he probably wasn't personally involved in the Cullen Woodall search.

Jasong knows he has too much free time, but isn't sure how to rectify the situation.

xilman · 2008-01-18, 08:16

Quote:

Originally Posted by jasong

Jasong knows he has too much free time, but isn't sure how to rectify the situation.

Quote:

Originally Posted by jasong

Too bad I'm not a programmer, sounds like a Linux and Windows version could be relatively easily made, given sufficient skills.

I think you answered your own question. Spend your free time acquiring the necessary skills.

Paul

jasong · 2008-01-24, 00:11

Quote:

Originally Posted by xilman

I think you answered your own question. Spend your free time acquiring the necessary skills.

Paul

Well, ( :) smiley face mood applies to entire post), to be honest, when I wrote that, I was thinking more along the lines of a more robust social life. But now that you mention it, I bought a book a couple months ago called Getting Things Done. It's supposed to be a fantastic book for those who want to organize their lives better. It's dry as hell, but it seems like a very good book for people who intend to restructure their lives.

One of my goals, in terms of reorganizing my life, is to learn some programming skills. I haven't even gotten a third of the way through the book because, as I said, it's dry as hell, so all I've really done for the moment is made a list of things I want to purchase and start asking around for old PDAs I could use once I have a system set up to monitor goals.

Xyzzy · 2008-01-24, 14:01

Quote:

...and start asking around for old PDAs I could use once I have a system set up to monitor goals.

A note pad and a pen works great for us.

Simplify.

jasong · 2008-01-25, 01:51

Quote:

Originally Posted by Xyzzy

A note pad and a pen works great for us.

Simplify.

I'm obsessive-compulsive, so if I added a PDA with these habits, it would reduce a lot of stress.

2008-01-13, 22:08	#1
jasong "Jason Goatcher" Mar 2005 3·7·167 Posts	Cullen and Woodall altering on Prime Pages Okay, I understand that if a k in k*2^n+/-1 is even than k can be halved and n increased by one. But since Cullen and Woodall numbers are based on the idea that k and n are the same number, doesn't Prime Pages policy defeat the purpose of the people doing the search in the first place?

2008-01-16, 10:54	#4
Brian-E "Brian" Jul 2007 The Netherlands 2×11×149 Posts	But isn't the point of the exercise to factorise the Cullen and Woodall numbers and to find the very rare primes, not to discover the alternative representations of the numbers? Edit: Ah, are you wondering why Prime Pages doesn't list the numbers with the k equal to the n? I think because it lists other numbers of the form k2^n +/- 1 which are not Cullen/Woodall as well, and the policy is to "simplify" all such numbers so that n is as large as possible. This makes it indeed less simple-looking in the case of the special Cullen/Woodall, but by standardising in that way they make it less likely that someone will make a mistake by analysing a number which has in fact already been tested but written in a different form. Last fiddled with by Brian-E on 2008-01-16 at 11:04 Reason: Suddenly guessed what you are getting at.*

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2008-01-17, 06:02	#5
axn Jun 2003 43×127 Posts	To be fair, Prime Pages' prime (pardon the pun) purpose is to act as a repository of top primes. It is always a good idea to "normalize" the expression of a prime to a standard form so that you don't end up with multiple representations of the same prime. The secondary purpose of classifying the primes is achieved thru the archival tags. IMO, these policies are entirely appropriate for a catalog such as this. I can see why seeing the original "non-normalized" representation might be useful, but I just don't think it is prime page's responsibility.