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 instance the Solovay–Strassen primality test on a given number formula_20 chooses a number formula_34 randomly from formula_42 to formula_210 and uses modular exponentiation to check whether formula_211 is divisible by formula_20. If so, it answers yes and otherwise it answers no. If formula_20 really is prime, it will always answer yes, but if formula_20 is composite then it answers yes with probability at most 1/2 and no with probability at least 1/2. If this test is repeated formula_1 times on the same number, the probability that a composite number could pass the test every time is at most formula_216. Because