Number partitions, prime numbers, and Godel Incompleteness approach to partition theorem

Numbers as a formal system: axioms

This is an attempt to prove that there can never be an exact formula for the say nth prime or for that matter the no. of partitions for number n. 

  • 0 and 1 exists
  •  addition is a way of adding 1 to an existing number
  • 0 is the identity element for repeated addtion operation
  • Primes is special type of number, which has exactly one partition where all the constituent numbers are equal(in this case 1).

I might be missing something, but i think next step would be to prove that having an “exact closed form formula” for prime would be the equivalent of proving one of the axioms.

Then from Godel’s incompleteness theorem we have proved our premise.

One thought on “Number partitions, prime numbers, and Godel Incompleteness approach to partition theorem

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google photo

You are commenting using your Google account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.