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 such as the Meissel–Lehmer algorithm can compute exact values of formula_88 faster than it would be possible to list each prime up to formula_1. The prime number theorem states that formula_88 is asymptotic to formula_94, which is denoted as and means that the ratio of formula_88 to the right-hand fraction approaches 1 as formula_1 grows to infinity. This implies that the likelihood that a randomly chosen number less than formula_1 is prime is (approximately) inversely proportional to the number of digits in formula_1. It also implies that the formula_1th prime number is proportional to formula_101 and therefore that the average