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 Dusart proved: The proof by de la Vallée Poussin implies the following. For every , there is an such that for all , As a consequence of the prime number theorem, one gets an asymptotic expression for the th prime number, denoted by : A better approximation is Again considering the th prime number , this gives an estimate of ; the first 5 digits match and relative error is about 0.00005%. Rosser's theorem states that This can be improved by the following pair of bounds: The table compares exact values of to the two approximations and . The last