Andrica's conjecture, Brocard's conjecture, Legendre's conjecture, and Oppermann's conjecture all suggest that the largest gaps between primes from formula_69 to formula_1 should be at most approximately formula_71 a result that is known to follow from the Riemann hypothesis, while the much stronger Cramér conjecture sets the largest gap size at formula_72 Prime gaps can be generalized to prime formula_73-tuples, patterns in the differences between more than two prime numbers. Their infinitude and density are the subject of the first Hardy–Littlewood conjecture, which can be motivated by the heuristic that the prime numbers behave similarly to a random sequence of numbers with density given by the prime number theorem.