Dirichlet's theorem
Jenna Nieminen
and
Pi Han Goh
contributed
This wiki is incomplete.
Dirichlet's theorem is a theorem in number theory, which states that for any two coprime positive integers \(a\) and \(d\), there exists an infinite amount of positive integers \(n\) for which \(an + d \) is a prime number.
\[97!\; n + d\] Find the smallest integer \(d > 1\), such that the number above is prime for an infinite number of integers \(n\).
Notation:
\(!\) denotes the factorial notation. For example, \(10! = 1\times2\times3\times\cdots\times10 \).
Cite as:
Dirichlet's theorem.
Brilliant.org.
Retrieved from
https://brilliant.org/wiki/dirichlets-theorem/