Prime free sequence.

[Wacky]

Originally Posted by David John Hill Jr

i felt uncomfortable with
3) The *theorem*..........
in English, and might ask Dr Silverman to apply his criticism.
Is it correct to apply what I think I read that all the inverses cannot be found
in a three dimensional partial differential system, to the english used?

John,
I'm "uncomfortable" with your question. (I don't understand what it is that you are asking).

When Dr. Silverman said "The *theorem* ...", I believe that he was indicating that that which follows is a (proven) theorem rather than a postulate or something else. Since the theorem relates to the number of elements in a set, I don't see the connection to partial differential systems or your question (Except, from other material, we know that a 1 to 1 correspondence establishes one, of possibly many, mapping that has an inverse)

So, would you please try to restate your question.

[David John Hill Jr]

My question is more rhetorical , (to english) and applies to the
'basic concept', 'the 'theorem'',instead of 'a theorem'.
I dont think it worth going into the mathematics of all of three,from the point of view of my comment.(Not to clutter this thread with the mathematics of
English)

I might add that my opinion(only), is that it will (future tense)be possible to determine a sequence void of primes, simply by avoiding primes, if such can be set up.This is how I interpreted the initial question,which has
diverged to other considerations, as is.

[Wacky]

Originally Posted by David John Hill Jr

My question is more rhetorical , (to english) and applies to the 'basic concept', 'the 'theorem'',instead of 'a theorem'.

So are you complaining that a particular theorem is not a "basic concept"?

In Mathematics, as in physics, and other things, "basic concept" is ill-defined.
When viewed a one level, certain things are basic. However, there is a branch of study that presumes that these concepts are not sufficiently basic and establishes them from some "more fundamental concepts".

Or are you contending that there is more than one theorem which states that "a set can NOT be put into 1-1 correspondence with the set containing all of its subsets"?

[ewmayer]

So would DJH's conjecture that the stars are really just giant Mersenne numbers in disguise remain just that, or has enough evidence been amassed to support it that it can now assume the title of Theorem? I simply shan't be able to sleep until this has been clarified.