primes themselves, with weighted by . The term is roughly analogous to a second-order correction accounting for squares of primes. Equivalent for prime k-tuples An equivalent definition of Skewes' number exists for prime k-tuples (). Let denote a prime (k + 1)-tuple, the number of primes below such that are all prime, let and let denote its Hardy-Littlewood constant (see First Hardy-Littlewood conjecture). Then the first prime that violates the Hardy-Littlewood inequality for the (k + 1)-tuple , i.e., the first prime such that (if such a prime exists) is the Skewes number for The table below shows the currently known Skewes numbers for prime k-tuples: The Skewes number (if it exists) for sexy primes is still unknown. It is also unknown whether all admissible k-tuples have a corresponding Skewes number. References . . External links Large numbers Number theory Large integers