Electrical resistivity and conductivity results in the important concept of "quasineutrality", which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma ("n" = <Z>"n"), but on the scale of the Debye length there can be charge imbalance. In the special case that "double layers" are formed, the charge separation can extend some tens of Debye lengths. The magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density. A common example is to assume that the electrons satisfy the Boltzmann relation: Differentiating this
Lucky numbers of Euler Lucky numbers of Euler Euler's “lucky” numbers are positive integers "n" such that for all integers "k" with , the polynomial produces a prime number. When "k" is equal to "n", the value cannot be prime anymore since is divisible by "n". Since the polynomial can be rewritten as , using the integers "k" with produces the same set of numbers as . Leonhard Euler published the polynomial which produces prime numbers for all integer values of "k" from 1 to 40. Only 7 lucky numbers of Euler exist, namely 1, 2, 3, 5, 11, 17 and 41 . The