- Sindelar wrote:
> > I'm lost here. Seems like a convoluted approach.

Andersen wrote:

> You asked for comments on your statement (which is an unproven

Jens, I think I may have offended you by writing "I'm lost here. Seems

> guess). I briefly showed that it would follow from a well-known

> and trusted conjecture, sometimes called the prime k-tuple

> conjecture

> (that name is sometimes restricted to special cases). Of course

> it's

> less "convoluted" to not relate your guess to anything else like

> previously studied things. If you want something unconvoluted

> (but not very useful by itself) then here it is: I guess your guess

> is

> right.

like a convoluted approach." Looking back at this, I can see that it can

be taken as arrogant criticism. Gad, that is not what I meant it to be. I

should have written "I am unable to follow your explanation. It seems

complicated to me because I know nothing about admissible prime

constellations, but I accept your opinion". I regret my choice of words

and hope you accept my sincere apology.

Sindelar wrote in regard to Green and Tao:>>>To me, this is a very broad claim covering any type of (PAP-k, n).

Jens can you explain your answer a bit more?

Andersen wrote:> Just to be clear: My "No" was only to your second sentence:

(PAP-k, n=0))"

> "I would interpret Green and Tao as covering this type. (meaning

>

Jens thank you. Nothing more to explain. You made it clear that the Green

> You defined (PAP-k, n) as a PAP-k with n primes between each of

> the k-1 pairs of successive primes in the AP. Tao and Green don't

> mention this concept of equal prime counts and their theorem says

> nothing about your (PAP-k, n) for n=0 or any other n value.

> I don't know what else you want me to explain.

> All I can say is that the theorem simply doesn't say it.

and Tao theorem does not apply to type (PAP-k, n=0 or greater). And thank

you for an example of a (PAP-8, 5). Don't know how you calculated that so

quickly. I was beginning to think there might be a limit on k.

Bill Sindelar

[Non-text portions of this message have been removed] - Bill Sindelar wrote:
> I used Pari-gp for this. For every set of k consecutive primes, which has

I would expect your method to be much slower based on how

> n skipped consecutive primes between its adjacent terms, after an

> inputted integer, it checks if the terms of that set are in arithmetic

> progression. Jens, is this slower than your approach with your tuplet

> finder?

"randomly" consecutive prime gaps appear to be distributed.

> If one could prove the above assumption, would that also prove

No, and also no to the only-part. Your assumption says nothing

> that all admissible prime constellations have infinitely many occurrences

> as you put it, or only those that have a (PAP-k, n) subset?

about the existence of specific differences between primes,

so it says nothing about any admissible constellation.

> This suggested trying this assumption which is just a fancy way of

.....

> defining a (PAP-k, n):

> It works but is more

"computationally complicated" refers to something computational,

> computationally complicated. What do you think?

for example the time to compute something with a given algorithm.

You have made another formulation of your conjecture but not

described an algorithm so "computationally complicated" is a

concept which does not apply.

I don't have time to discuss more.

--

Jens Kruse Andersen