Are there infinitely many primes of the form $(3^{n} - 1)/2$?

Asked Nov 30 '16 at 19:41

Active Nov 30 '16 at 21:36

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I've been trying to show that there are infinitely many primes in the form of $$ \frac {3^n - 1}{2}$$

Up until now I've tried a modified version Euclid's way of proving the infinity of primes but didn't find a solid answer. Do you have a particular way of approaching this problem? Any help will be appreciated.

edited Nov 30 '16 at 19:43

asked Nov 30 '16 at 19:41

theycallmefm

3

Given that we don't know the same for $2^n-1$, it is unlikely that we know it for $(3^n-1)/2$, unless it is in the negative. We also don't know it for $(10^n-1)/9$ - the repunit primes. Basically, this is a hard sort of problem. – Thomas Andrews Nov 30 '16 at 19:44
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Possible duplicate of Prime numbers of the form $(3^n-1)/2$ – CIJ Nov 30 '16 at 19:48
Not at all a duplicate. This is asking if there are infinite primes in the form. The other is to show some of the non-primes in the form. – fleablood Nov 30 '16 at 20:22

Are there infinitely many primes of the form $(3^{n} - 1)/2$?

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