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 corresponds to "congruence" in modular arithmetic: formula_22 and formula_121 are congruent (written formula_122 mod formula_1) when they have the same remainder after division by formula_1. However, in this system of numbers, division by all nonzero numbers is possible if and only if the modulus is prime. For instance, with the prime number formula_125 as modulus, division by formula_28 is possible: formula_127, because clearing denominators by multiplying both sides by formula_28 gives the valid formula formula_129. However, with the composite modulus formula_130, division by formula_28 is impossible. There is no valid solution to formula_132: clearing denominators by multiplying by formula_28 causes