Sunday, January 24, 2010

Prime Numbers:Textbook p8 #24

I agree with the claim. An even number can never be a prime number as all even numbers are divisible by 2. So prime numbers are always odd numbers(not assuming all odd numbers are primes, eg.9. But instead of 9+9=18, we can have 5+5+5+3+18). So, when we add up 2 similar odd numbers(or 4 or 6 or 8, etc.), the resulting answer will be an even number(adding 2 similar numbers is like multiplying the number by 2, which will result in an even number). That is why every even number greater than 2 can be expressed as a sum of prime numbers.
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1 comment:

  1. Loh Kwai YinJanuary 24, 2010 at 7:27 PM

    Zhi Chao

    Indeed, the number 18 can be expressed as the sum of two prime numbers, 5 and 13.

    While we can add up 2 prime numbers to result an even number, how do we know that all even numbers are 'covered' by the pairs of odd numbers that are added together?

    Check out the Goldbach Conjecture :D

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