Second Hardy-Littlewood conjecture
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 means that the number of primes from x + 1 to x + y is always less than or equal to the number of primes from 1 to y.
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.
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