00:03
So in this problem, we're presented with a conjecture by a famous mathematician.
00:08
That conjecture says that every even number greater than two can be written as a sum of two prime numbers.
00:17
They're asking us to find the next five even numbers as the sum of two primes.
00:25
So just to recall a little bit of vocabulary here, a sum means that we're adding.
00:34
And then a prime number is a number whose only factors are one and itself.
00:41
So like, for example, a prime number that two is prime because it's only factors are one and two.
00:48
Might be helpful for this problem to list out the first few prime numbers so that we have it as a reference when we're finding the sums for all the even numbers.
00:58
So two is a prime number.
01:00
Three is a prime number because it's only factors are one and three.
01:03
5 is a prime number.
01:07
6 is not prime because it has factors of 2 and 3, but 7 is prime because 7 only has factors of 1 and 7.
01:18
8, 9, 10 are not prime because they have lots of factors, but 11 is prime, and 12 is not prime but 13 is.
01:36
This should be enough prime numbers to be able to do those first 5 even numbers.
01:42
So let's look at the first even number there you did was four, so we're going to do six next.
01:50
So we want to find two prime numbers here that add to six...