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 concerned with integers. For example, prime ideals in the ring of integers of quadratic number fields can be used in proving quadratic reciprocity, a statement that concerns the existence of square roots modulo integer prime numbers. Early attempts to prove Fermat's Last Theorem led to Kummer's introduction of regular primes, integer prime numbers connected with the failure of unique factorization in the cyclotomic integers. The question of how many integer prime numbers factor into a product of multiple prime ideals in an algebraic number field is addressed by Chebotarev's density theorem, which (when applied to the cyclotomic integers) has Dirichlet's