rav3n_pl pisze: The Riemann hypothesis implies results about the distribution of prime numbers.
Zdanie oczywiście prawdziwe jeśli dobrze rozumiemy słowo
rozkład, tylko jak ono się ma do metody łatwego/szybkiego wynajdywania dużych liczb pierwszych? Nijak.
https://math.stackexchange.com/question ... accomplish
[..]the Riemann Hypothesis is mostly about the distribution of prime numbers.
The idea is that mathematicians have some very good approximations (emphasis on approximate)
for the density of the primes (so you give me an integer, and I can use these approximate functions to tell you roughly how many primes are between 0 [really 2] and that integer).
The reason we use these approximations is that no [known] function exists that efficiently and perfectly computes the number of primes less than a given integer (we're talking numbers with literally millions of zeros). Since we can't determine the exact values (again, I'm simplifying a lot of this) the problem mathematicians want to know is exactly HOW good are these approximations.
This is where the Riemann Hypothesis comes in to play. For well over a century, mathematicians have known that a special form of the polylogarithm function (again, more fun math if you're bored) is a really great approximation for the prime counting function (and it's way easier to compute).
The Riemann Hypothesis, if true, would guarantee a far greater bound on the difference between this approximation and the real value. In other words, the importance of the Riemann Hypothesis is that it tells us a lot about how chaotic the primes numbers really are. That's an incredibly high-level explanation and the Riemann Hypothesis deals with literally hundreds of other concepts, but the main point is understanding the distribution of the primes.
Udowodnienie hipotezy w żaden sposób nie ułatwi nam wyznaczania liczb pierwszych.