Prime number the 1970s, mathematicians and physicists have speculated that the zeros of the Riemann zeta function are connected to the energy levels of quantum systems. Prime numbers are also significant in quantum information science, thanks to mathematical structures such as mutually unbiased bases and symmetric informationally complete positive-operator-valued measures. The evolutionary strategy used by cicadas of the genus "Magicicada" makes use of prime numbers. These insects spend most of their lives as grubs underground. They only pupate and then emerge from their burrows after 7, 13 or 17 years, at which point they fly about, breed, and then die after a
Prime number theorem limit of the "difference" of the two functions as increases without bound. Instead, the theorem states that approximates in the sense that the relative error of this approximation approaches 0 as increases without bound. The prime number theorem is equivalent to the statement that the th prime number satisfies the asymptotic notation meaning, again, that the relative error of this approximation approaches 0 as increases without bound. For example, the th prime number is , and ()log() rounds to , a relative error of about 6.4%. The prime number theorem is also equivalent to where and are the first and