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 .
Prime quadrupletIn number theory, a prime quadruplet (sometimes called prime quadruple) is a set of four prime numbers of the form {p,\ p+2,\ p+6,\ p+8}. This represents the closest possible grouping of four primes larger than 3, and is the only prime constellation of length 4. The first eight prime quadruplets are: {5, 7, 11, 13}, {11, 13, 17, 19}, {101, 103, 107, 109}, {191, 193, 197, 199}, {821, 823, 827, 829}, {1481, 1483, 1487, 1489}, {1871, 1873, 1877, 1879}, {2081, 2083, 2087, 2089} All prime quadruplets except {5, 7, 11, 13} are of the form {30n + 11, 30n + 13, 30n + 17, 30n + 19} for some integer n.
