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We know that all primes greater than $3$ are of form $6n+1$ or $6n-1,$ but how do I prove that there are infinitely many of the form $6n+1$? Please prove it without Dirichlet's theorem.

Note: This question is not a duplicate of Proving an infinite number of primes of the form 6n+1; there people are discussing about $6n-1$.

J. W. Tanner
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1 Answers1

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Due to Dirichlet's theorem on arithmetic progressions, the arithmetic progression $$a_0=1\quad\quad a_{n}=1+6n$$ contains infinitely many primes since gcd$(1,6)=1$. Can you end it from here?

Dr. Mathva
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