The Second Hardy-Littlewood Conjecture concerns the number of primes in intervals.
If pi(x) is the number of primes up to and including x then the conjecture states:
- pi(x + y) <= pi(x) + pi(y)
- where x, y >= 2.
This is probably false in general as it is inconsistent with the first Hardy-Littlewood conjecture, but the first violation is likely to occur for very large values of x and y.