Is there any demonstration that there are an infinite amount of primes of the form $6ab-1$ being $a$ and $b$ integers?
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5How is this any different from trying to prove that there are an infinite number of primes that can be written in the form $6n - 1,$ $n$ an integer? – K. Jiang Jun 12 '16 at 02:14
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There are infinitely many primes of the form $6n - 1$. – Jun 12 '16 at 02:14
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@K.Jiang : something looks like a subtle difference, but cant put my finger on it – jimjim Jun 12 '16 at 02:22
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I believe there is no difference. Still, even though I know that there are infinitely many 6n + 1 primes, does that imply that there are infinitely many 6n-1 primes? – Marroja Jun 12 '16 at 02:24
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Well, since $n = 1 \times n$, no, there's no difference. But, if you don't allow $a$ or $b$ to be $1$, I don't think it's an immediate corollary. – pjs36 Jun 12 '16 at 02:28
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Yes; this is a special case of Dirichlet's theorem, which states that the arithmetic progression $b, a+b, 2a+b, …$ contains an infinite number of primes except when $a$ and $b$ have a common factor larger than 1.
For your question we take $a=6, b=5$.

MJD
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