Is Dickson's conjecture true?
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Dickson's conjecture states that for any finite set of tuples of integers (aᵢ, bᵢ) with the aᵢ all positive, there are infinitely many values of n such that aᵢn + bᵢ is prime for all i, unless there is a specific prime number p that always divides one of the linear forms aᵢn + bᵢ for any value of n.
Dickson's conjecture implies all the following conjectures:
/JosephNoonan/is-de-polignacs-conjecture-true
/JosephNoonan/is-the-first-hardylittlewood-conjec (at least according to OEIS wiki, though there's no citation for this, and it's not obvious how it follows)
/JosephNoonan/is-the-prime-patterns-conjecture-tr
/NcyRocks/are-there-infinitely-many-twin-prim
/JosephNoonan/are-there-infinitely-many-cousin-pr
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