There are infininite number of prime numbers and there are a couple of proofs these are in the linked list below
http://primes.utm.edu/notes/proofs/infinite/index.html
I propose a proof that is simpler
If I prove that if for any n there is a prime > n then I am through
Let us consider n!+1
This does not have any factor from 2 to n and hence it is a prime or in case it is not a prime then prime factor > n.
So for any n there is a prime number> n
Hence proved
3 comments:
Hi Kali. I was about to compliment you on this proof. But I noticed it wasn't quite complete. As it stands, you have only shown that there is a prime that is > n, i.e. that there is an infinitely large prime, but not that there must be an infinite number of primes.
The simplest fix is to change your statement, "So for any n there is a prime number > n", to "So for any n there is a prime number > n and ≤ n! + 1". Obviously your opening assertion must be changed correspondingly.
that is not required.
may be my explanation is not obvious but
there is a prime > n
who cares if if is < n!+ 1 or not
for n we have m > n
if m is new n then one more above it so on infinitely we have infinite primes
I was having an extended senior moment. Your proof is good and I apologise for saying that it wasn't.
Post a Comment