proof of Legendre Conjecture lead to a proof of Riemann Hypothesis? #691 Correcting Math
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From: Archimedes Plutonium on 17 Jul 2010 13:06 --- quoting from Wikipedia --- Riemann's hypothesis is concerned with the zeroes of the æ-function (i.e., s such that æ(s) = 0). The connection to prime numbers is that it essentially says that the primes are as regularly distributed as possible. From a physical viewpoint, it roughly states that the irregularity in the distribution of primes only comes from random noise. From a mathematical viewpoint, it roughly states that the asymptotic distribution of primes (about 1/ log x of numbers less than x are primes, the prime number theorem) also holds for much shorter intervals of length about the square root of x (for intervals near x). This hypothesis is generally believed to be correct. In particular, the simplest assumption is that primes should have no significant irregularities without good reason. --- end quoting from Wikipedia --- Maybe, just maybe I have a proof of the Riemann Hypothesis. Funny how a correction of the Indirect Method Euclid Infinitude of Primes proof-- that the Euclid Numbers of P-1 and P+1 are necessarily primes in that method yields the proof of the Riemann Hypothesis. The proof of the Legendre Conjecture is easily begot from the idea that both n^2 +1 and (n+1)^2 -1 lie between n^2 and (n+1)^2 and are prime using the Indirect Euclid IP method. So if the Riemann Hypothesis is a further demand or restriction of having a prime existing in a much smaller interval about number x, well, the Indirect Euclid IP can fulfill that demand. Archimedes Plutonium http://www.iw.net/~a_plutonium/ whole entire Universe is just one big atom where dots of the electron-dot-cloud are galaxies |