> What would be the consequences if Mr. X would have a formula to calculate

from

> a given prime the whole ordered series of the subsequent primes one after

the other?

Any of the freely or costly available CAS have this function already

implemented, it's called nextprime()

(and explicit formulas do exist, although those which remain readable are

much less efficient than those which are less "explicit" but rather written

as algorithm).

I admit that most nextprime() functions use pseudo-primality tests (for

which no counter example is known and which are less likely to yield a

false positive than the probability of an error due to the computer

hardware).

But does this make a difference for this discussion? If so, in which

respect?

> 1- Would we need to solve the Riemann hypothesis

Depends on what you mean by "need".

I don't think that existence of the nextprime() function (or formula)

implies the RH.

> 2- Would we need to solve all the mountain of conjectures around the

primes?

Having a formula which yields all primes one after the other

does not yield a response to many conjectures, I think.

> Indeed one major point of discussion was to remind:

>

> 3- What where Euler, Riemann, and all the many great mathematicians

seeking for?

I did not catch what you reminded about this.

(Personally I think they were and are seeking better understanding of

several quite distinct mathematical problems, among which might be the

understanding of the structure of the set of prime numbers.

But even knowing all of the latter (even if it was "all at once" and not

"one after the other")

does not mean to understand much about the structure.

That's quite similar with other branches of science:

Even a most complete set of measurements is not equivalent to an

explanation or understanding.)

Regards,

Maximilian

> Look foward.

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