Is the largest prime number greater than the largest natural number?

If n! can be defined as the product of all the natural numbers from 1 to n, then n!+1, will be the product of a natural number greater than n as it's largest divisor, no matter how large a number n is.

Example

1!+1= 2 which is larger than 1, 2!+1 equals 3 which is greater than 2. 3!+1 equals 7 which is greater than 3. 4!+1 equals 5*5 which is greater than 4.

And so on.

And more importantly who gives a f**k? 

I'm not sure I'm understanding this correctly but looking from your example, this wouldn't work since 4!+1 would equal 25 and 25 is not a prime number

Prime factorization

It's a square number

5!+1=121=11*11 and 11 is greater than 5, etc.

Yep

I was talking about how the largest prime number would not be larger than the largest natural number with this theory

All primes are also natural numbers.  But there is no largest natural number.  If we assume n is the largest, then n + 1 is also natural, but we assumed n was the largest.  This is  a contradiction, so our original assumption was false and there is no largest.

The significance of n! + 1 is that it is used in Euclid's proof that there is no largest prime.

Assume there is a largest prime, N.  Then, multiply all numbers up to N, to get N!.  Then add 1.  N! + 1 is a natural number, so it is either prime or composite.  It cannot be prime because it is larger than what we assumed was the largest prime.  So this means N! + 1 is composite.  Since every composite number has a prime factorization, we can divide N! + 1 by some prime less than or equal to N.  

N! is a multiple of every number up to and including N, but N! + 1 is one larger than a multiple of all those numbers so it cannot be a multiple of any of them.  But then, according to our assumptions, we have a number (N! + 1) which is neither prime nor composite.  This is impossible, so our original assumption, that there was a largest prime, is false.

Nope, if n! is defined as the product of all the Counting Numbers from 1 to n, then n!+1 will be a new  Counting Number greater than n

Being that n!+1 is a product of a Counting Number different than any that could be counting with the product n!

talkingcat90 is correct. It has been known (and mathematically proven) for more than 2200 years that the number of primes is infinite... there IS NO largest prime number.