Math

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1: Goldbach's Conjecture is a famous conjecture that has never been proven true or false. The conjecture states that every even number, except 2, can be written as the sum of two prime numbers. For example, 16 can be written as 5+11.
1 a: Write the first six even numbers greater than 2 as the sum of two prime numbers.
1 b: Write 100 as the sum of two primes.
1 c: The number 2 is a prime number. Can an even number greater than 4 be written as the sum of two prime numbers if you use 2 as one of the primes? Explain why or why not.

  • Math -

    1a: the numbers are 4, 6, 8, 10, 12, and 14. 4 = 2 + 2; 6 = 3 + 3; 8 = 5 + 3; 10 = 5 + 5; 12 = 7 + 5.

    If you don't know how to do this, it's probably because you don't understand prime numbers so well. Prime numbers are numbers only divisible by 1 and itself (so you know automatically the number will be odd - not divisible by 2!). There are infinite prime numbers, but it really helps to know a good set of them. You can Google it, but here are some in order to get you started: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, etc. See a pattern?

    onto...

    1b: 100 = 39 + 61. How do I know this? It really takes some guesswork, trial and error, and familiarity with prime numbers. I'm sure you'll get there soon!

    1c: Absolutely not! The question specifies an even number. Now think, 'how do I get an even number as a result of addition?' The only way you can do this is add two even numbers or two odd numbers (try a few examples...). All prime numbers except 2 are odd (bc even numbers are always multiples of 2), and an even number + an odd number is always odd. Thus, 2 + a different prime number will always equal an odd number - never an even number.


    Hope this helps. This is an interesting conjecture!

  • Math -

    Thank you so much

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