Is the prime patterns conjecture true?
Is the prime patterns conjecture true?
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Let S be a finite set of integers. Then S is the pattern for a set of prime numbers P if there is some n such that P = { n + s | s ∈ S}.
S is admissible if it doesn't intersect all of the residue classes mod p for any prime p. The prime patterns conjecture states that any finite, admissible set is the pattern for infinitely many sets of primes. In other words, for any admissible S, there are infinitely many values of n for which n + s₁, n + s₂, ..., n + sₖ are all prime (where s₁, s₂, ..., sₖ are the elements of S).
This is a generalization of all of the following conjectures:
/JosephNoonan/is-de-polignacs-conjecture-true
/NcyRocks/are-there-infinitely-many-twin-prim
/JosephNoonan/are-there-infinitely-many-cousin-pr
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What is this?
What is Manifold?
Manifold is the world's largest social prediction market.
Get accurate real-time odds on politics, tech, sports, and more.
Or create your own play-money betting market on any question you care about.
Are our predictions accurate?
Yes! Manifold is very well calibrated, with forecasts on average within 4 percentage points of the true probability. Our probabilities are created by users buying and selling shares of a market.
In the 2022 US midterm elections, we outperformed all other prediction market platforms and were in line with FiveThirtyEight’s performance. Many people who don't like betting still use Manifold to get reliable news.
Why use play money?
Why use play money?Mana (Ṁ) is the play-money currency used to bet on Manifold. It cannot be converted to cash. All users start with Ṁ1,000 for free.
Play money means it's much easier for anyone anywhere in the world to get started and try out forecasting without any risk. It also means there's more freedom to create and bet on any type of question.
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