Unsolved problems in number theory | Conjectures about prime numbers

Dickson's conjecture

In number theory, a branch of mathematics, Dickson's conjecture is the conjecture stated by Dickson that for a finite set of linear forms a1 + b1n, a2 + b2n, ..., ak + bkn with bi ≥ 1, there are infinitely many positive integers n for which they are all prime, unless there is a congruence condition preventing this . The case k = 1 is Dirichlet's theorem. Two other special cases are well-known conjectures: there are infinitely many twin primes (n and 2 + n are primes), and there are infinitely many Sophie Germain primes (n and 1 + 2n are primes). Dickson's conjecture is further extended by Schinzel's hypothesis H. (Wikipedia).

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Related pages

Dirichlet's theorem on arithmetic progressions | Prime number | Green–Tao theorem | Prime triplet | Primes in arithmetic progression | Bunyakovsky conjecture | Sophie Germain prime | Twin prime | Modular arithmetic | Number theory | Schinzel's hypothesis H | First Hardy–Littlewood conjecture