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 of 1859, and he succeeded in proving a slightly weaker form of the asymptotic law, namely, that if the limit of as goes to infinity exists at all, then it is necessarily equal to one. He was able to prove unconditionally that this ratio is bounded above and below by two explicitly given constants near 1, for all sufficiently large . Although Chebyshev's paper did not prove the Prime Number Theorem, his estimates for were strong enough for him to prove Bertrand's postulate that there exists a prime number between and for any integer . An important paper concerning the