## Hardy-Littlewood Conjectures

The first Hardy-Littlewood conjecture is called the k-Tuple Conjecture. It states that the asymptotic number of Prime Constellations can be computed explicitly.

The second Hardy-Littlewood conjecture states that

for all and , where is the Prime Counting Function. Although it is not obvious, Richards (1974) proved that this conjecture is incompatible with the first Hardy-Littlewood conjecture.

Richards, I. On the Incompatibility of Two Conjectures Concerning Primes.'' Bull. Amer. Math. Soc. 80, 419-438, 1974.