Re: antiprimes ??????????????

the primes belong to a diophantine set.

a certain polynomial in more than 1 variable for
wich
the positive imputs give positive and negative
outputs.

if we consider only the positive imputs and the
positive outputs ; then those positive outputs are
exactly the primes.

but what about the negative outputs ???
or the negative imputs ???

couldnt we learn a lot about them ???

and isnt there a way bye studying them , we might
conclude things about their "opposites " the
primes
??

so i call these negative imputs and negative
outputs

" antiprimes " (not to be confused with negative
primes or composites )

an interesting idea with hopefully some
consequences
in the study of number theory.

also note that there are at least 2 polynomials
known
that generate the primes in the way i mentioned.

so they also generate antiprimes.

so you could further categorize the antiprimes
easily.


greets
tommy1729

It is certainly well known that the set of prime
numbers is an enumerable and hence a diophantine
set.


i like it , that you dont need to look that up :-)

This was proved by Matiyasevich back in 1970 spoiling
a positive answer to Hilbert's 10th problem.

yes he spoiled hilbert but gave wonderfull things instead too.

he's one of my favorite mathematicians !!! :-)

a no-nonsence type of guy ! :-)

unlike cantor set theory.

nice of you to repeat , but i already know that.

i believe he knew the result before 1970 unofficially however thats off topic.


It is also well known that there is at least one
polynomial P(x_1,...x_n) with integer coefficients
such that the set of prime numbers coincides with the
range of positive values taken on by P as x_1,...,x_n
range over the positive integers. This was proved by
James, J.P.
et al. back in 1976.

at least 3 actually.


Several of such polynomials have been constructed
explicitly ever since. In particular James, J.P. et
al. constructed such a polynomial with the property
that all of its negative values are composite.

and there is another of my great "examples"

i dont know a polynomial with that property of giving positive primes and negative composites.

you dont mean all primes and all composites i assume ?

would like to see that polynomial.

james rules , and i dont mean harris :p



So not all polynomials with the above property are
suitable to define "antiprimes" the way you "defined"
them (i.e. "not to be confused with negative primes
or composites").

my definition is open and vague , not wrong.

i was talking about "any" polynomial giving primes for positive output.



Hope this helps
Michael

maybe , thanks anyway

tommy1729
.

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