Rusty returning student stuck on this one proof:

Prove false:

There exists an integer n such that is prime.

I know to do this, I have to prove the universal negation true.

For all integers n such that is not prime.

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- Feb 23rd 2008, 10:34 PMMBoogieFalse Existential
Rusty returning student stuck on this one proof:

Prove false:

There exists an integer n such that is prime.

I know to do this, I have to prove the universal negation true.

For all integers n such that is not prime. - Feb 23rd 2008, 10:44 PMJhevon
- Feb 24th 2008, 05:01 AMMBoogie
oh no -

I had written down so many times, and kept trying to wrong things with it. Is it as simple as this?:

is a sum of two squares which is prime. And because a composite is the product of two primes, is composite? - Feb 24th 2008, 09:32 AMtopsquark
First is not the sum of two squares. is not a perfect square unless n = 0.

Second,

This means that, for any n, is divisible by 3 and is thus a composite number. (A composite number is simply the product of two numbers, neither of which are 1, not necessarily two primes.)

-Dan - Feb 24th 2008, 10:58 AMJhevon
- Feb 24th 2008, 11:03 AMJaneBennet
Not true! 3 is divisible by 3 but 3 is not a composite number!

A positive integer divisible by 3 is not prime only if it’s not equal to 3 itself. It this particular problem, is not prime because 3 divides it**and**is not equal to 1 for any integer*n*. - Feb 24th 2008, 11:19 AMJhevon
- Feb 24th 2008, 07:23 PMMBoogie
wow - yeah I have a problem of getting ahead of myself. Answer was right in front of me the whole time. Thx Jhev and top

- Feb 24th 2008, 07:24 PMJhevon
- Feb 26th 2008, 05:31 AMJaneBennet
I had to learn the hard way too. Once I wanted to prove that, while twin primes exist, you could never have “triple primes” (three consecutive odd primes). I thought I had cool proof in just one line: “Any sequence of three consecutive odd integers must contain a multiple of 3 and so that number in the sequence cannot be prime.” Then someone knocked me off my pedestal by showing me that one set of triple primes does exist: 3, 5, 7. I have learnt my lesson since then! (Evilgrin)