Abstract Algebra: Theory and Applications · Problem 2.4.29

Groups — Thomas Judson

Mathematics — Abstract Algebra · infinitely-many-primes-6n-plus-5

Problem

Prove that there are an infinite number of primes of the form

6n+5

. Hint. Every prime must be of the form

2

3

6n+1

, or

6n+5

. Suppose there are only finitely many primes of the form

6k+5