prime and powers of two

[sullen wraith]

Mersenne numbers [2^n-1] can sometimes be primes, what about for 2^n-7, the first 20 numbers (n>3) are composite, does a prime like this exist?

[marble cave]

Apparently 2^39 - 7 is prime

yeah it is

,w 2^39 - 7 divisors

[dense frost]

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Requested by 6_neruguis

[sullen wraith]

ooh

um

ok

[marble cave]

bro

[sullen wraith]

?

[marble cave]

aaand?

[sullen wraith]

idk

[marble cave]

ok u can see the minimum prime for odd numbers

2^n - k

odd k

lemme see

[sullen wraith]

another question (related), 17 cannot divide 2^n-7, is there infinite prime like this?

[marble cave]

I think so

lol

[rancid pecan]

What do you mean, an "infinite prime"?

[past star]

You may be interested in this.
https://oeis.org/A096822

[sullen wraith]

primes sorry typoed

[rancid pecan]

So you're asking if there are infinitely many primes that don't divide any number of the form 2^n - 7?

[sullen wraith]

yes

I know all mersenne primes bigger than 14 don't

[rancid pecan]

...then if there are infinitely many Mersenne primes, which last I heard we think there are, yes.

Actually, do you have a proof of that?

[sullen wraith]

the maginc sequance of 2 mod (2^n-1) are only powers of 2

Life for 31: 1, 2, 4, 8, 16, 1

*like

[rancid pecan]

"Maginc sequance"?

[sullen wraith]

powers of n mod b

is the magic sequance n mod b