- Anybody up to checking some calculations??

Sure would be appreciated.

See http://www.opertech.com/primes/residues.html

in particular the value of C2 (think it is a little large)

Tom - On the k-tuples, have just finished an update of the permissible

patterns site www.opertech.com/primes/k-tuples.html

At the site the trophies (contradiction patterns/super dense

constellations) are listed up to packing 100 additional primes in an

interval. In fact 17 additional prime can be packed in an interval of

length of just 8509 integers.

The chart at www.opertech.com/primes/kpiwchart.html shows the crossover

(s) and the growth.

It is estimated that all intervals of more than 5980 integers can

demonstrate a super-dense condition.

Enjoy

Thomas J Engelsma - Dear Tom, Thank you very much for your crackajack work.

About your “An admissible k-tuple of 447 primes can be created in an interval of 3159 integers,

while p(3159) = 446.”,

can I realize:

An admissible 447-tuple has been created in an interval of 3159 integers, while p(3159) = 446?

It is not:

An admissible prime 447-tuple has been created in an interval of 3159 integers,while p(3159) = 446.

Where we call a k-tuple is admissible, if it does not cover all congruence classes modulo any

prime p, we call the k-tuple a prime k-tuple when all of its components are primes by Daniel M. Gordon and Gene Rodemich.

So that: if the original k-tuple conjecture is true, then Hardy-Littlewood conjecture

p(x+y) - p(x) <= p (y)

is fails with a value of y = 3159.

In my paper I try prove that admissible prime k-tuples are infinite rather then admissible k-tuples will infinitely often be simultaneously primes. The original k-tuple conjecture may not true, example the prime of the form n^2-1.

Could you read my paper please and we will discuss some interesting problem.

Fengsui Liu.

Tom <tom@...> 写道： On the k-tuples, have just finished an update of the permissible

patterns site www.opertech.com/primes/k-tuples.html

At the site the trophies (contradiction patterns/super dense

constellations) are listed up to packing 100 additional primes in an

interval. In fact 17 additional prime can be packed in an interval of

length of just 8509 integers.

The chart at www.opertech.com/primes/kpiwchart.html shows the crossover

(s) and the growth.

It is estimated that all intervals of more than 5980 integers can

demonstrate a super-dense condition.

Enjoy

Thomas J Engelsma

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[Non-text portions of this message have been removed] - --- primenumbers@yahoogroups.com wrote:

From: "Tom" <tom@...>>

Wonderful work, Tom. One I wish I'd been part of!

> On the k-tuples, have just finished an update of the permissible

> patterns site www.opertech.com/primes/k-tuples.html

> At the site the trophies (contradiction patterns/super dense

> constellations) are listed up to packing 100 additional primes in an

> interval. In fact 17 additional prime can be packed in an interval of

> length of just 8509 integers.

> The chart at www.opertech.com/primes/kpiwchart.html shows the crossover

I absolutely will!

> (s) and the growth.

> It is estimated that all intervals of more than 5980 integers can

> demonstrate a super-dense condition.

>

> Enjoy

I of course blindly accept the "possible therefore happens" approach in such

'linear' matters (i.e. this does not in any way apply to pseudoprime existance

questions). It's just a shame that there will probably never be any possibilty

of the human race actually finding such a tuple. I don't know if QC can reduce

the problem to a triviality, but I don't have much faith in QC either!

Are you still pushing the green zone to the right, or has your program hit an

architectural brick wall now?

Phil

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http://mail.yahoo.com - Are you still pushing the green zone to the right, or has your

program hit an architectural brick wall now?

Phil,

On the chart, the green zone is from exhautive searching, and cannot

(will not) be improved. The assembler program I wrote had a ceiling

of 2047. When I move to a 64-bit machine I intend to run the

exhaustive search some more. My initial calculations say I should be

able to run up to 2250 before I get exponentially stopped.

The red zone is in constant change above 3900, some lucky finds

below that. The updates page

http://www.opertech.com/primes/updates.html shows the changes.

These changes are in the 2047 to 8509 range.

The trophy case www.opertech.com/primes/trophycase.html shows

the first instance currently known for each additional prime. And

you can see the widths are being improved.

Fengsui Liu,

The work I have done is to find permissible patterns of primes not

the primes themselves.

Thank-you for the interest.

Thomas J Engelsma