- --- In primenumbers@yahoogroups.com, w_sindelar@... wrote:

> Jens can you explain your answer a bit more?

I'll try.

Are you aware of the concept of "admissible constellations?" For

example, twin primes, x and x+2, are believed to occur infinitely

often. A triplet of the form x, x+2, x+4 is not admissible because

one of these numbers always divisible by 3. Hence (3, 5, 7) is the

only example - a finite number. However x, x+2, x+6 is admissible and

is believed to be prime infinitely often.

Jens point is that you can construct an admissible constellation that

has all kn-1 primes in fixed locations so the the arithmetic

progression and primes between are honored. This is more restrictive

than your rules require, but would be an example as long as none of

the the other values within the constellation's range are also prime.

Jen's further point is that you could further restrict the

constellation so that the intermediate values were divisible by

selected primes, and hence composite. Again more restrictive than you

rules, but it would qualify as an example. Finally, from the

constellation conjecture there would be an infinite number of these

constellation, each and every one an example.

For example, x, x+2, x+6, x+8, x+12 is an example of admissible

constellation that has 3 primes in arithmetic progression with(al

least) one prime between them. In this case there is exactly one

prime because x+4 and x+10 must be divisible by 3. In general, we

would need to jiggle the start point as x=ay+b for selected fixed

values if a and b to ensure the omitted points are composite.

Finally, every example that you find can could be reverse-engineered

to such an admissible constellation, so this search would be a subset

of a search for examples of admissible constellations.

William Lipp

Poohbah of OddPerfect.org - 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