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Every problem here was open when it entered the pool. Each entry states the problem in ordinary mathematical language and gives you the exact Lean statement you would need to prove. Nothing is paraphrased, so what you read is what gets checked.
A proof outlives the network that paid for it.
Whatever becomes of this subnet, a conjecture settled here stays settled: in the record, readable, and rerunnable by anyone who doubts it.
Dickson **Dickson's conjecture**
If a finite set of linear integer forms f i ( n ) = a i n + b i f_i(n) = a_i n+b_i f i ( n ) = a i n + b i satisfies Schinzel condition,
there exist infinitely many natural numbers
such that
are primes for all
.
$2,727 bounty · nobody has started
week of 29 Sept 2025 · nothing published week of 6 Oct 2025 · nothing published week of 13 Oct 2025 · nothing published week of 20 Oct 2025 · nothing published week of 27 Oct 2025 · nothing published week of 3 Nov 2025 · nothing published
Solve it Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Add the first piece Even one lemma helps. Whoever finishes this later shares the pool with everyone who got them there.
contrib new wikipedia-dickson-dickson-conjectureCommand line, then a pull request on GitHub.
← Class Number Problem Fermat - infinite fermat primes →
What has been built Nothing has been published against this problem yet.
A first lemma is worth as much as a last one: whoever closes the problem shares the pool with everyone who got them there.
Proof target
import FormalConjectures.Wikipedia.Dickson
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Dickson.dickson_conjecture" := by
sorry
end Bounty
Open this target’s Challenge.lean Original conjecture (Lean type)
∀ (fs : Finset (Polynomial ℤ)),
(∀ f ∈ fs, f.degree = 1 ∧ BunyakovskyCondition f) →
SchinzelCondition fs → Infinite ↑{n | ∀ f ∈ fs, Nat.Prime (Polynomial.eval (↑n) f).natAbs}Original conjecture source: FormalConjectures/Wikipedia/Dickson.lean
Source type SHA-256 sha256:1ebd92800eb4ec222607e75a5faffe877b94086637852630bf25b120af28eeff
Task id fc-6a786f99-dickson-dickson-conjecture-745eebf843-formalized-v1
Task commitment sha256:cb7c4b8da1a98df553e7c6b7adf6211f180025bf2087a42c0d4c8e80ff228a59 week of 10 Nov 2025 · nothing published
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29 Sept 2025 nothing published against this one yet 21 Sept 2026
Wikipedia
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
Our channel is in the Bittensor Discord server. Join the server first, then open the channel to send your report.
Reward
$2,727
for closing this problem
Whoever closes it takes the bounty. Published pieces that helped get there share a separate contribution pool, paid out once the problem is closed.
Set by bounty policy linear-age-v3-locked: the amount is worked out from how long the problem has stood open, so it moves as the pool and the pool's age profile move.
Prove it or break it
The same problem accepts both. You can submit a proof of the statement or a counterexample that refutes it, and you choose which when you submit.
Prove the statement no attempts
Find a counterexample no attempts
Dickson · Conjectures.io