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24998[PrimeNumbers] What if Mr. X would have a formula for the prime series?

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  • Maximilian Hasler
    Apr 4 8:42 AM
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      > 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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