Prime numbers...just how many are there? And how do we know? If we look at the first few we get the following sequence:2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ...
Seemingly no real rhyme or reason, but what can we say about them? Well to start with we have the Fundamental Theorem of Arithmetic...sounds grand no? It's actually pretty simple (we use it every time we do factor trees!) and it's just that every number can be written as a unique product of primes...
Seemingly no real rhyme or reason, but what can we say about them? Well to start with we have the Fundamental Theorem of Arithmetic...sounds grand no? It's actually pretty simple (we use it every time we do factor trees!) and it's just that every number can be written as a unique product of primes...
e.g. 180 = 2 x 2 x 3 x 3 x 5
We can use this to help calculate the number of primes in total...Start by assuming that there are only a finite number of primes who knows how many? 100? 1000? 1000000000? We're not sure so let's just say n...
Multiply these n primes together and then add 1...now what is the unique product of primes that make this number? It doesn't divide by any of our n primes (as we have + 1 on the end) and so we either have a new prime or there is a prime not in our list that divides into our number...
Both of these outcomes give us an extra prime not on our list...so how many primes are there?
No comments:
Post a Comment