Prime quadruplet 23620, 152141, 1028789, 7188960, 51672312, 381226246, 2873279651 . The constant representing the sum of the reciprocals of all prime quadruplets, Brun's constant for prime quadruplets, denoted by "B", is the sum of the reciprocals of all prime quadruplets: with value: This constant should not be confused with the Brun's constant for cousin primes, prime pairs of the form ("p", "p" + 4), which is also written as "B". The prime quadruplet {11, 13, 17, 19} is alleged to appear on the Ishango bone although this is disputed. Excluding the first prime quadruplet, the shortest possible distance between two quadruplets {"p",
Prime number theorem column, , is the average prime gap below . The value for was originally computed assuming the Riemann hypothesis; it has since been verified unconditionally. There is an analogue of the prime number theorem that describes the "distribution" of irreducible polynomials over a finite field; the form it takes is strikingly similar to the case of the classical prime number theorem. To state it precisely, let be the finite field with elements, for some fixed , and let be the number of monic "irreducible" polynomials over whose degree is equal to . That is, we are looking at polynomials with