Textbook: Brainworks (p8) Q24(b) A mathematician proposed that "Every even number greater than 2 can be expressed as a sum of two prime numbers." Do you agree? Why?
Yes, I do agree because I was able to express the even numbers (which I anyhow pick for myself to try out) as a sum of two prime numbers. Then I went online and found the information below.
Why Does Every Even Number Greater Than 2 Can Be Expressed As A Sum Of 2 Prime Numbers?
Even numbers have several ways to be the sum of two prime numbers. For example, the number 36 can be shown as '5+31', '7+29', or '17+19'. By looking at these examples, it appears that the higher the even number, the more pair of prime numbers there are that add up to it.
There is an assumption that says that every even number can be expressed as the sum of two prime numbers at least in one way. This assumption is called as Goldbach's conjecture, after Christian Goldbach, a Prussian mathematician who propounded it. it remains to be one of the most ancient problems that is yet not completely solved in the field of mathematics. The conjecture basically states that every even integer that is greater than the number 2 can be expressed as the sum of two primes.
There is an assumption that says that every even number can be expressed as the sum of two prime numbers at least in one way. This assumption is called as Goldbach's conjecture, after Christian Goldbach, a Prussian mathematician who propounded it. it remains to be one of the most ancient problems that is yet not completely solved in the field of mathematics. The conjecture basically states that every even integer that is greater than the number 2 can be expressed as the sum of two primes.
Cited from: http://www.blurtit.com/q710414.html
Lai Ziying
Well done! You found the Goldbach Conjecture.
ReplyDeleteIn the first paragraph, you mentioned "it appears that the higher the even number, the more pair of prime numbers there are that add up to it". However, you only used one number "36" (from the website) to illustrate that the even number could be expressed in more than one pair of prime numbers. What would you do to justify your claim that the higher the even number, there are more pairs of prime numbers? Try using other numbers to test it out.