Hardy-Littlewood k-tuple conjecture | prime k-tuples conjecture | prime patterns conjecture

The first of the Hardy-Littlewood conjectures. The k-tuple conjecture states that the asymptotic number of prime constellations can be computed explicitly. In particular, unless there is a trivial divisibility condition that stops p, p + a_1, ..., p + a_k from consisting of primes infinitely often, then such prime constellations will occur with an asymptotic density which is computable in terms of a_1, ..., a_k. Let 0

arithmetic progression | Dirichlet's theorem | Hardy-Littlewood conjectures | prime arithmetic progression | prime constellation | prime quadruplet | twin prime conjecture | twin primes | twin primes constant