Is Dickson's conjecture true?
4
110Ṁ2222101
92%
chance
1H
6H
1D
1W
1M
ALL
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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