Question: Whats the hardest problem you have done in maths?

Jake Langham answered on 8 Nov 2017:

The hardest problems I ever did in maths were probably during my university exams. Some of the questions were really difficult. They are a bit tricky to explain because they involve advanced topics that you only learn at university and I didn’t understand them all that well myself!

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I can tell you a really hard problem that is a bit easier to explain though. The question is: “How many pairs of prime numbers are there that differ by 2?” A prime number is one that can’t be divided by anything else to make a whole number. (The first few prime numbers are 2, 3, 5, 7, 11, 13, …. 4 isn’t a prime number because 4 divided by 2 is 2 which is a whole number. 6 isn’t either because 6 divided by 2 is 3 which is also a whole number. Does that make sense?) Here are some pairs of prime numbers that are only 2 apart: 3 and 5, 5 and 7, 11 and 13. Can you find the next pair? Mathematicians don’t know how many pairs there are, even though they’ve been trying to work it out for hundreds of years!