Sorry, an error occurred while loading the content.

## Re: [PrimeNumbers] Nash weights

Expand Messages
• Phil (et al) I ve done (mostly in the past to be sure) a lot of work on Nash weights, and adjusted Nash weights. Check out :
Message 1 of 6 , Mar 12, 2001
Phil (et al)

I've done (mostly in the past to be sure) a lot of work on Nash
weights, and adjusted Nash weights. Check out :

www.glasgowg43.freeserve.co.uk/nashdef.htm

for definitions

www.glasgowg43.freeserve.co.uk/nashprim.htm

for high Nash weights

www.glasgowg43.freeserve.co.uk/siernash.htm

for low Nash weights

I have C programs that calculated adjusted or capped Nash weights for
k in ranges and with particular modular forms. Capping just involves
putting a limit on the primes as well as the exponents.

Joe.

______________________________ Reply Separator _________________________________
Subject: [PrimeNumbers] Nash weights
Author: Phil Carmody <fatphil@...> at Internet
Date: 11/03/01 04:21

Can the resident 'Nash weight calculation' expert please step forward!

OK, there are 2 factors involved.
1) absolute exclusion of primes due to explicit factors
e.g. 27*2^n+/-1 will never be divisible by 3
2) being not in the right orbit for other primes
e.g. 27*2^n-1 will only be 4,2,5 mod 7 and 27*2^n+1 will only be 6,4,0 mod 7.
Therefore 7 helps increase prime density for 27..-, but reduces prime density
for 27..+ (it removes 1 in 3 rather than 1 in 7).

Have Nash weights been calculated _in bulk_. I mean real bulk, up to hundreds of
millions?

The reason I ask is that I've seen the applet which calculates the weights for a
particular number, but it struck me that they can be calculated en mass like a
sieve? Has anyone done this?

Phil

Mathematics should not have to involve martyrdom;
Support Eric Weisstein, see http://mathworld.wolfram.com
Find the best deals on the web at AltaVista Shopping!
http://www.shopping.altavista.com

------------------------ Yahoo! Groups Sponsor ---------------------~-~>
Make good on the promise you made at graduation to keep
in touch. Classmates.com has over 14 million registered
high school alumni--chances are you'll find your friends!
http://us.click.yahoo.com/l3joGB/DMUCAA/4ihDAA/BE_UlB/TM
---------------------------------------------------------------------_->

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
The Prime Pages : http://www.primepages.org

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

----------------------------------------------------------------------------
Disclaimer:
This message is intended only for use of the addressee. If this message
was sent to you in error, please notify the sender and delete this message.
Glasgow City Council cannot accept responsibility for viruses, so please
scan attachments. Views expressed in this message do not necessarily reflect
those of the Council who will not necessarily be bound by its contents.

----------------------------------------------------------------------------

----------------------------------------------------------------------------
Disclaimer:
This message is intended only for use of the addressee. If this message
was sent to you in error, please notify the sender and delete this message.
Glasgow City Council cannot accept responsibility for viruses, so please
scan attachments. Views expressed in this message do not necessarily reflect
those of the Council who will not necessarily be bound by its contents.

----------------------------------------------------------------------------
• Hello all. k = 138847 has a standard (negative) Nash weight of 29, which is very respectable for a reasonably small number. The lowest positive Nash weight I
Message 2 of 6 , Mar 12, 2001
Hello all.

k = 138847 has a standard (negative) Nash weight of 29, which is very
respectable for a reasonably small number. The lowest positive Nash
weight I found was 9 (yes, nine), so I'm sure that I could find
something for the negative side in the low teens if I put my mind to
it, though this would take some time with my current computers.

However, if someone could write a very fast program for me, that would
help. How about that Phil. Spookily, I was actually thinking about
asking for this just last week. Great minds think alike. The logic is

Joe.

______________________________ Reply Separator _________________________________
Subject: [PrimeNumbers] Re: Nash weights
Author: d.broadhurst@... at Internet
Date: 12/03/01 01:38

Jack Brennen wrote:

> I have done some extensive calculations looking for high
> Proth weights for both k*2^n+1 and k*2^n-1

I like low weights, too.

They have been studied for k*2^n+1.
But in the Riesel case, k*2^n-1,
I do not know of any lower non-zero
weight than that for k=138847.

138847*2^n-1 is prime for n=33 and for no other n<380,000.

Is there any lower non-zero Nash weight with k<10^6,
for k*2^n +/- 1 ?

David

------------------------ Yahoo! Groups Sponsor ---------------------~-~>
Make good on the promise you made at graduation to keep
in touch. Classmates.com has over 14 million registered
high school alumni--chances are you'll find your friends!
http://us.click.yahoo.com/l3joGB/DMUCAA/4ihDAA/BE_UlB/TM
---------------------------------------------------------------------_->

Unsubscribe by an email to: primenumbers-unsubscribe@egroups.com
The Prime Pages : http://www.primepages.org

Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

----------------------------------------------------------------------------
Disclaimer:
This message is intended only for use of the addressee. If this message
was sent to you in error, please notify the sender and delete this message.
Glasgow City Council cannot accept responsibility for viruses, so please
scan attachments. Views expressed in this message do not necessarily reflect
those of the Council who will not necessarily be bound by its contents.

----------------------------------------------------------------------------

----------------------------------------------------------------------------
Disclaimer:
This message is intended only for use of the addressee. If this message
was sent to you in error, please notify the sender and delete this message.
Glasgow City Council cannot accept responsibility for viruses, so please
scan attachments. Views expressed in this message do not necessarily reflect
those of the Council who will not necessarily be bound by its contents.

----------------------------------------------------------------------------
• ... I find the measurements to be bizarre, in my mind I want a fractional value, and all these integers are out of range, so to speak. I guess that they re
Message 3 of 6 , Mar 12, 2001
On Mon, 12 March 2001, joe.mclean@... wrote:
> k = 138847 has a standard (negative) Nash weight of 29, which is very
> respectable for a reasonably small number. The lowest positive Nash
> weight I found was 9 (yes, nine), so I'm sure that I could find
> something for the negative side in the low teens if I put my mind to
> it, though this would take some time with my current computers.

I find the measurements to be bizarre, in my mind I want a fractional value, and all these integers are out of range, so to speak. I guess that they're scaled, but why should they be?
What is the "average" Nash weight? (not specifying which average, probably geometric). And what if this is normalised to 1?

> However, if someone could write a very fast program for me, that would
> help. How about that Phil. Spookily, I was actually thinking about
> asking for this just last week. Great minds think alike. The logic is
> dead easy, honest.

Jack sent me a mail with a third modifier in it, independent of my first two modifiers. This was to do with (Aurefeulian?) factorisations of prime-power factors of k.

I believe that if I have the definitive expression for a single number, then I can turn that into a (windowed) sieve technique. Who knows, I may even be able to write some "very fast code" for it. It appears to be a O(sqrt(N)) space, O(N) time algorithm, where N is the number itself, not the number of digits.

Code like this must already have been written. I'm sure it;s easier for me to tweak than it is to start from scratch?

Phil

Mathematics should not have to involve martyrdom;
Support Eric Weisstein, see http://mathworld.wolfram.com
Find the best deals on the web at AltaVista Shopping!
http://www.shopping.altavista.com
Your message has been successfully submitted and would be delivered to recipients shortly.