Is the second Hardy-Littlewood conjecture true? | Manifold

Is the second Hardy-Littlewood conjecture true?

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The second Hardy-Littlewood conjecture says that the prime conting function obeys the triangle inequality, π(x+y) ≤ π(x) + π(y), for x, y ≥ 2. Equivalently, there are always at least as many primes from 1 to x as there are from 1+y to x+y.

It has been proven that only one of the two Hardy-Littlewood conjectures can be true, so this market can't resolve YES if /JosephNoonan/is-the-first-hardylittlewood-conjec resolves YES.

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@FlorisvanDoorn You shouldn't have bet both of these up so high. Only one of the Hardy-Littlewood conjectures can be true.

predicts YES

@JosephNoonan Oh, oops :-)

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