Intro to Dirichlet's Theorem

Explanations 4

• Infinitude of Primes: Special Case 4n−14n-14n−1 We have seen some proofs of infinitude of primes. Another important theorem related to infinitude of primes is Dirichlet's theore…

  By amaterasu

• Dirichlet's theorem in prime number theory concerns prime numbers in arithmetic progressions a,a+m,a+2m,…a,a+m,a+2m,\ldotsa,a+m,a+2m,…. (Here, aaa and m>1m>1m>1 are integers.) W…

  By Kada Williams, Alex Federspiel

• In the question, the last two options tried to connect Dirichlet's theorem with the number of primes in the progression. Try to prove the following statement, which may seem sur…

  By Kada Williams

• Theorem There are infinitely many primes of the form 4k+14k+14k+1. Try to prove it yourself. We will post the proof later. Warning There is a catch in this proof. And the exerci…

  By amaterasu, Victor Wang