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 corresponds to "congruence" in modular arithmetic: formula_22 and formula_121 are congruent (written formula_122 mod formula_1) when they have the same remainder after division by formula_1. However, in this system of numbers, division by all nonzero numbers is possible if and only if the modulus is prime. For instance, with the prime number formula_125 as modulus, division by formula_28 is possible: formula_127, because clearing denominators by multiplying both sides by formula_28 gives the valid formula formula_129. However, with the composite modulus formula_130, division by formula_28 is impossible. There is no valid solution to formula_132: clearing denominators by multiplying by formula_28 causes