- 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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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