Prime Numbers, Composite Numbers, Prime Factorisation

All integers (whole numbers), which are greater than 1, are either prime numbers or composite numbers.

Prime numbers have exactly two factors, one of which is 1 and the other is the number itself, eg. 3=3x1, 5=5x1.

For this reason 1 is not prime. It only has one factor, 1.

Composite numbers can always be factorised into prime numbers:

4 = 2x2, 6=2x3, 8=2x2x2, 9=3x3, 10=2x5, 12=2x2x3

How many prime factors a number has, has got nothing to do with the size of the number.

360=2x2x2x3x3x5 361=19x19

Goldbach's Conjecture

Christian Goldbach was a mathematician who lived between 1690 and 1764.

He came up with his conjecture in 1742. It was a conjecture because he could not prove it, nor disprove it.

It is still a conjecture because it is still not proved, or disproved!

Goldbach's Conjecture

Any even number, greater than 2, can be written as the sum of 2 prime numbers.

Starting with 4=2+2, how far can you get?

                 6 = 3+3

                 8 = 3+5

               10 = 3+7 = 5+5, so there are

                                     two possible sums

                12 = 5+7

                14 = 3+11 = 7+7

                16 = 3+13 = 5+11

Less well known is the second part of the conjecture:

All odd numbers, > 1, are either prime or the sum of three prime numbers.

           9 = 3+3+3

         15 = 5+5+5

         21 = 7+7+7

         25 = 3+9+12

         27 = 9+9+9

         33 = 11+11+11

         35 = 7+11+17

 

 

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