Three Mathematics Problems

[Countolaf]

Try to prove the following:

1) Every even integer greater than 2 can be written as the sum of two primes. (The same prime may be used twice.) (Goldbach Conjecture)

2) There are no non-zero integers x, y, and z such that x^n + y^n = z^n in which n is an integer greater than 2. (Fermat's Last Theorem) (Has proof)

3) The real part of any non-trivial zero of the Riemann zeta function is ½. (Riemann hypothesis) ($1,000,000 prize offered by the Clay Mathematics Institute for a proof)

[Fox Mc Cloud]

1.
Integer = 2,4,6,8... ?

They can be written as:

4 = 2 + 2
6 = 3 + 3
8 = 3 + 5
10 = 3 + 7
12 = 5 + 7
Then use the next primes to make integer numbers: 11, 13, 17, 23...

[Countolaf]

But will there be enough primes to make all even integers?

[Fox Mc Cloud]

not really...