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Is there any demonstration that there are an infinite amount of primes of the form $6ab-1$ being $a$ and $b$ integers?

JMP
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Marroja
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    How 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
  • There are infinitely many primes of the form $6n - 1$. –  Jun 12 '16 at 02:14
  • @K.Jiang : something looks like a subtle difference, but cant put my finger on it – jimjim Jun 12 '16 at 02:22
  • 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
  • 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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