- Bill Krys wrote:

> but what about the other half of the conjecture that

Also false, I believe. Consider the prime q=103.

> all primes may be generated

I can see no way of writing either 51 or 52

in the form p^a+p^b.

David (not Dave:-) - To: Alan Powell <powella@...>

Copies to: primenumbers@yahoogroups.com

From: Bill Krys <billkrys@...>

Date sent: Sat, 30 Jun 2001 06:16:28 -0700 (PDT)

Subject: [PrimeNumbers] What about perimetric prime sieve/generator = 2(2^(n-k)+2^k) )

> Dear Alan et al,

2*(2^(8-1)+2^1)-1 factor : 7

>

> can you find any for me that don't work for

> e=2(2^(n-k)+2^k)?

2*(2^(8-1)+2^1)+1 factor : 3

2*(2^(8-4)+2^4)-1 factor : 3

2*(2^(8-4)+2^4)+1 factor : 5

2*(2^(9-1)+2^1)-1 factor : 5

2*(2^(9-1)+2^1)+1 factor : 11

2*(2^(9-3)+2^3)-1 factor : 11

2*(2^(9-3)+2^3)+1 factor : 5

2*(2^(10-1)+2^1)-1 factor : 13

2*(2^(10-1)+2^1)+1 factor : 3

2*(2^(10-4)+2^4)-1 factor : 3

2*(2^(10-4)+2^4)+1 factor : 7

>

Michael Hartley : Michael.Hartley@...

> > At 03:07 AM 6/30/01, you wrote:

> > >take a prime number (p), raise it to any power (n),

> > >make a rectangle out of that number (with sides

> > >p^(n-k) and p^k). Calculate the perimeter of that

> > >rectangle. Add or subtract 1. At least one of these

> > >will be a prime number ... I think. At any rate,

> > all

> > >the primes may be generated this way ... I think.

> >

> >

>

>

> =====

> Bill Krys

> Email: billkrys@...

> Toronto, Canada (currently: Beijing, China)

>

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>

Head, Department of Information Technology,

Sepang Institute of Technology

+---Q-u-o-t-a-b-l-e---Q-u-o-t-e----------------------------------

"If you entertain a thought, it becomes an attitude..." - To: d.broadhurst@...

Copies to: primenumbers@yahoogroups.com

From: Bill Krys <billkrys@...>

Date sent: Sun, 1 Jul 2001 08:33:19 -0700 (PDT)

Subject: Re: [PrimeNumbers] Re: sieve = 2(p^(n-k)+p^k)

> Okay, Dave,

Yes. 103 cannot be written 2(p^k + p^(n-k))+/-1 for any prime p,

>

> but what about the other half of the conjecture that

> all primes may be generated from 1 in such manner,

> despite creating many composites? Can you find a

> counter example?

integers n >= k >= 0.

Proof: Left as an exercise to the reader.

Puzzle: Find the _next_ such prime...

[ PS - I almost embarrassed myself by saying "Yes. 31 cannot..." ]

>

Michael Hartley : Michael.Hartley@...

> Bill

>

> =====

> Bill Krys

> Email: billkrys@...

> Toronto, Canada (currently: Beijing, China)

>

> __________________________________________________

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>

>

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>

>

Head, Department of Information Technology,

Sepang Institute of Technology

+---Q-u-o-t-a-b-l-e---Q-u-o-t-e----------------------------------

"If you entertain an attitude, it becomes an action..." > Puzzle: Find the _next_ such prime...

103,139,151,157,199,223,233,239,241,307,311,313,353,367,373,379,

409,419,421,431,433,439,443,463,571,593,599,601,607,619,631,643,

659,661,673,683,727,733,739,743,751,757,809,811,823,827,829,853,

857,859,877,883,911,919,941,947,953,967,991,997...- Next puzzle: Why is EIS sequence

ID Number: A033227

Sequence: 43,103*,139*,157*,181,277,367*,439*,523,547,

607*,673*,751*,823*,991*,997*...

Name: Primes of form x^2+39*y^2.

such a fecund source of exceptions to Bill's conjecture?

[*] 11 of the first 16 elements are non-Krys