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Old 2015-10-13, 19:49   #28
Batalov's Avatar
Mar 2008

11·881 Posts

Originally Posted by kalikidoom View Post

I mean... isn't that at least a proof that there's an infinate amout of them?

Try it with how meny primes you like... and with how meny 2^....-1 you like... it always works
This is not a good sentence or an argument.
First you need to make it understandable.

1. "It always works for me to go outside without a jacket when I see sun in the window." Nothing to argue about here. "It always works (for you)." Fine! And no one can say - "wait, what if there is rain later in the day?" You've already answered - "It always works (for you)", whatever it means. Maybe the rain works for you; who are we to judge?..
2. "If I see sun in the window, then there will be no rain today (and therefore I go out without the jacket)."
The latter is in fact an argument - it has a premise and it has a conclusion. It is not a true argument, though, because everyone can point out a lot of cases, when you see the sun in the window and there will be rain one hour later.

Now, compare:
(1) what you wrote is some (charitably speaking) ..."opinion". It is your opinion and it doesn't matter that a) it doesn't mean anything to others, b) it cannot be verified (there is no "if", there is no "then"...) Nothing to discuss there.
(2) We can assume that what you actually wanted to write was "If n is prime, then 2^n-1 is (always) prime". That is in fact an argument - it has a premise and it has a conclusion. It is not a true argument, because n=11 is prime, but 2^n-1 is not prime.
(3) We can only guess that furthermore you wanted to write this: "If n is prime and 2^n-1 is prime, then 2^(2^n-1)-1 is (always) prime". Which however is also false: n=13 is prime and 2^n-1=8191 is prime, but 2^(2^n-1)-1 is composite (because 338193759479 divides it).

So, therefore if you wanted to say "(2)" or "(3)" then what you wanted to say was false; and you cannot use it to build into any theories. (In logic, there is a rule: "from false, anything follows". In other words, when you have a false statement it is as good as no statement at all.)

If you wanted to say "(1)", then it simply is meaningless and cannot be meaningfully discussed.

Last fiddled with by Batalov on 2015-10-13 at 19:51
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