Dickson's conjecture

Dickson's conjecture

In number theory, a branch of mathematics, Dickson's conjecture is the conjecture stated by Dickson (1904) that for a finite set of linear forms a1 + nb1, a2 + nb2, ..., ak + nbk with bi ≥ 1, there are infinitely many positive integers n for which they are all prime, unless there is a congruence condition preventing this (Ribenboim 1996, 6.I). The case k = 1 is Dirichlet's theorem.

Two special cases are well known conjectures: there are infinitely many twin primes (n and n + 2 are primes), and there are infinitely many Sophie Germain primes (n and 2n + 1 are primes).

Dickson's conjecture is further extended by Schinzel's hypothesis H.

See also

References


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