Formula for primesIn number theory, a formula for primes is a formula generating the prime numbers, exactly and without exception. No such formula which is efficiently computable is known. A number of constraints are known, showing what such a "formula" can and cannot be. A simple formula is for positive integer , where is the floor function, which rounds down to the nearest integer. By Wilson's theorem, is prime if and only if . Thus, when is prime, the first factor in the product becomes one, and the formula produces the prime number .
Grid-tie inverterA grid-tie inverter converts direct current (DC) into an alternating current (AC) suitable for injecting into an electrical power grid, normally 120 V RMS at 60 Hz or 240 V RMS at 50 Hz. Grid-tie inverters are used between local electrical power generators: solar panel, wind turbine, hydro-electric, and the grid. To inject electrical power efficiently and safely into the grid, grid-tie inverters must accurately match the voltage, frequency and phase of the grid sine wave AC waveform.
Wilson primeIn number theory, a Wilson prime is a prime number such that divides , where "" denotes the factorial function; compare this with Wilson's theorem, which states that every prime divides . Both are named for 18th-century English mathematician John Wilson; in 1770, Edward Waring credited the theorem to Wilson, although it had been stated centuries earlier by Ibn al-Haytham. The only known Wilson primes are 5, 13, and 563 . Costa et al. write that "the case is trivial", and credit the observation that 13 is a Wilson prime to .
