Is the first Hardy-Littlewood conjecture true? | Manifold

Is the first Hardy-Littlewood conjecture true?

6

Ṁ130Ṁ376

2101

90%

chance

1H

6H

1D

1W

1M

ALL

The first Hardy-Littlewood conjecture, also called the k-tuple conjecture, gives an asymptotic formula for the number of primes p ≤ x such that p, p + a₁, p + a₂, ..., p + aₖ are all prime, for any tuple (a₁, a₂, ..., aₖ).

For the exact formula, see: https://mathworld.wolfram.com/k-TupleConjecture.html

k-Tuple Conjecture -- from Wolfram MathWorld

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<m_1<m_2<...<m_k, then the k-tuple conjecture predicts that the...

Market context

Get

1,000

to start trading!

People are also trading

Is the second Hardy-Littlewood conjecture true?

Is Legendre's conjecture correct?

Is Hadwiger's conjecture true?

Is Goodman's Conjecture true?

Is the Hodge conjecture true?

Is Haborth's Conjecture true?

Is Dickson's conjecture true?

Is the Birch and Swinnerton-Dyer conjecture true?

Is Rudin's conjecture true?

Is the strong Rudin's conjecture true?

Related questions

Is the second Hardy-Littlewood conjecture true?

Is Legendre's conjecture correct?

Is Hadwiger's conjecture true?

Is Goodman's Conjecture true?

Is the Hodge conjecture true?

Is Haborth's Conjecture true?

Is Dickson's conjecture true?

Is the Birch and Swinnerton-Dyer conjecture true?

Is Rudin's conjecture true?

Is the strong Rudin's conjecture true?

© Manifold Markets, Inc.•Terms•Privacy