Tuesday, February 8, 2011

2011/014) Proof of existence of infinite prime numbers.

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



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3 comments:

  1. ChrisJuly 28, 2012 at 9:02 PM

    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.

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  2. kaliprasad July 30, 2012 at 7:35 PM

    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

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  3. ChrisAugust 17, 2012 at 11:30 PM

    I was having an extended senior moment. Your proof is good and I apologise for saying that it wasn't.

    ReplyDelete