- The sequences related to Euclid's proof are:

A000945 A000946 A002585 A005265 A005266 A051342

( there are several new ones as well)

A00945 is just the first "related" sequence.

But there have to be two schools of thought

since "proof" isn't working.

1) Euclid's school infinite primes exist

2) modern school of thought : infinite primes don't exist

Unless you can "conclusively" prove no infinite prime exists...

I've seen nothing like that in the posts.

It can be "argued" both ways. Paul Leyland

is good at arguing, but lacks conclusive proofs to go

with it.

It is better to accept that there is more than one possible analytic for

primes

than make "war" over it.

As I said wisdom is a better option.

John Dilick wrote:

>Just a quick comment, then back I go...

--

>

>

>

>>In working with the Euclid proof primes

>>I found that any reasonable number past about 30 primes in the

>>product almost never stops in the factoring step.

>>43 primes in the product was the limit given in the A000945 definition as

>>being a computing limit.

>>

>>

>

>You do realize that A000945 is NOT the sequence we have been discussing

>(namely, the primorial plus one series), right? A000945 is a recursive

>sequence, that defines itself, using a construction similar to the Euclid

>proof. In A000945, A(1)=2, A(x)=the product of all of the previous terms in

>the series plus 1.

>

>The primorials (that is, the product of all primes less than or equal to x)

>plus one is the series generated by the classic Euclid proof, and those HAVE

>been factored completely well beyond the 43rd prime. Also, there is a

>gigantic difference between "can't compute this number with the current

>programs and resources" and "can't compute this number under any

>circumstances". Wagstaff stopped the computation at the 43rd prime in

>*1993*. 10 years has made a huge difference in both hardware and software,

>enough so that even I have factored the primorial+1 series well beyond that

>point. I'm sure others with a better grasp on both theory and programming

>have taken it well beyond the point I have, as well.

>

>

>

>>It is reasonable to assume that an infinite prime might exist ,

>>but could never be computed.

>>

>>

>

>Roger, did you not read Paul Leyland's reply to you, the one that started

>with "What is Infinity?". He explained far better than I have why the

>notion of an infinite prime is absurd.

>

>If you're not going to bother reading the replies, then why are you posting?

>

>John

>

>

>

>

>Unsubscribe by an email to: primenumbers-unsubscribe@yahoogroups.com

>The Prime Pages : http://www.primepages.org/

>

>

>

>Your use of Yahoo! Groups is subject to http://docs.yahoo.com/info/terms/

>

>

>

>

>

Respectfully, Roger L. Bagula

tftn@..., 11759Waterhill Road, Lakeside,Ca 92040-2905,tel: 619-5610814 :

URL : http://home.earthlink.net/~tftn

URL : http://victorian.fortunecity.com/carmelita/435/

[Non-text portions of this message have been removed] - Roger Bagula wrote:

[Philosophical meandering deleted.]

> I don't know if any of this answers you list of questions or not.

No, it does not. Please post again, including my text and at

the appropriate point intersperse your answer to each specific

question that I asked.

> I really don't like to get in such discussions,

That is becoming ever more clear as time goes by.

> since math people seem to ignore any philosophical issues by

Close, but no cigar. Axioms and definitions are the foundations

> defining them away. Axioms and definitions are an answer

> to all their thinking problems?

of mathematical thinking. Rigorously correct logical arguments

are the building blocks placed on the foundations. If you wish to

be considered to be doing mathematics, please use clear and precise

logic.

> As a physical scientist ( chemist, physical scientist)

Ah, so you're not a mathematician and you are not interested in

> I'm not bound by those rules in my thinking.

participating in mathematics. Why, then, are you making so much

noise in an indubitably mathematical forum?

FWIW, my background is in the physical sciences. I have a BA in

chemistry from Oxford and my DPhil was for research in molecular

spectroscopy. I personally don't regard that as an obstacle to

contributing in a small way to a mathematical subject. I'm not

bound by the rules of mathematics any more than you are, but I

choose to follow them when communicating with mathematicians. If

you wish to converse with practitioners of other fields of study,

please do so but, please, do it in a relevant forum elsewhere and

use their rules to do so. Again, FWIW, I'm quite happy to talk

about quantum field theory or geometrodynamics, but not here.

> In other words is science more fundamental

A very good question and one well worth discussing, but not here.

> philosophically than mathematics at a metamathematical level?

It is not (IMO, the moderators may disagree) relevant to the

advertised aims of the forum.

Paul