Odd numbers as a sum of 3 primes

Prove that if every even natural number greater than 2 is a sum of two prime numbers ( Goldbach conjucture), then every odd number greater than 5 is a sum of three prime numbers.

Proof:

1. Let every number in the Set of Natural numbers greater than 2 be ‘m’
2. m = 2 + 2n [ 2n => Even number]

3. But based on the Goldbach conjucture, m is a sum of 2 primes.
Let p and q be the two primes

m = (2 + 2n) = p + q

4. Let O be the odd number greater than 5
O = m + 3
Note : Since m is greater than 2, so O > 5

5. But m is a sum of 2 primes, so O can be expressed as a sum of 2 primes + 3.
Also, 3 is a prime!

O = p + q + 3

O is expressed as sum of 3 primes.

Advertisements
This entry was posted in Uncategorized. Bookmark the permalink.

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 )

Twitter picture

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

Facebook photo

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

Google+ photo

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

Connecting to %s