the proof is by contradiction...
Suppose the exist only finite primes.
Let the set of primes be equat to P={2,3,5,7,11,13,17,19,.....p_k}, where k is a natural number.
Now consider a composite number, lets define the nuber as D, I use the D to identify the divisors of the primes,
D=2*3*5*7*11*13*17*19*.....*p_k +1, by our assumtion of D as a composite, P|D, which is a contradiction due to the fact that 1 is not a prime, so since P does not devide D, implies that there exist another prime after p_k.
Poor lay out. You introduce new entities without explaining what they are, also you have already used them for something else (or worse still you are using an extended notion of divisibility without explanantion).
You do not explaing what results, theorems or notions you are using at the key point in the argument.
5/10
CB
Please quote what you are replying to, otherwise we will just be guessing if we respond.
You responded 3+ days after the question was asked and replied to, plenty of time to do what the previous posters suggested and see a proof that actually proves what was required.
CB