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 a quadratic polynomial that (for integer arguments) is prime infinitely often. Euler's proof that there are infinitely many primes considers the sums of reciprocals of primes, Euler showed that, for any arbitrary real number formula_22, there exists a prime formula_20 for which this sum is bigger than formula_22. This shows that there are infinitely many primes, because if there were finitely many primes the sum would reach its maximum value at the biggest prime rather than growing past every formula_22. The growth rate of this sum is described more precisely by Mertens' second theorem. For comparison, the sum does not