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 values, and places on the rational numbers. The local-global principle allows certain problems over the rational numbers to be solved by piecing together solutions from each of their places, again underlining the importance of primes to number theory. A commutative ring is an algebraic structure where addition, subtraction and multiplication are defined. The integers are a ring, and the prime numbers in the integers have been generalized to rings in two different ways, "prime elements" and "irreducible elements". An element formula_20 of a ring formula_172 is called prime if it is nonzero, has no multiplicative inverse (that is, it is