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 factorizations are based on Euclid's lemma: If formula_20 is a prime number and formula_20 divides a product formula_33 of integers formula_34 and formula_35, then formula_20 divides formula_34 or formula_20 divides formula_35 (or both). Conversely, if a number formula_20 has the property that when it divides a product it always divides at least one factor of the product, then formula_20 must be prime. There are infinitely many prime numbers. Another way of saying this is that the sequence of prime numbers never ends. This statement is referred to as "Euclid's theorem" in honor of the ancient Greek mathematician Euclid, since the