The Riemann Hypothesis will imply that Nature’s prime number dice are fair.

If I toss a coin 1,000,000 times it is unlikely to land heads exactly 500,000 times. How big can the deviation be before we might suspect that the coin is biased. If the error is within the square root of 1,000,000 either way, statisticians regard this as a fair coin.

Gauss’s guess was based on the prime number dice landing on the prime side exactly once out of every log(N) throws. The way the dice really landed is given by the staircase of primes. Riemann’s music tells us the error between these two. The louder a note, the bigger the error between Gauss’s guess and the real number of primes.

The loudness of the note is determined by the east-west coordinate of each point at sea-level. Riemann guessed that every note will have east-west coordinate equal to 1/2. This will cause an error of N1/2=squareroot of N.

So if every point at sea-level is on the critical line, the error between Gauss’s guess and the true number of primes is square root of N. THE PRIME NUMBER DICE ARE NOT BIASED.