Large Gaps between Primes - Numberphile
James Maynard on discoveries about large gaps between prime numbers. More links & stuff in full description below ↓↓↓ More Maynard videos: http://bit.ly/JamesMaynard Prime Playlist:...
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It's a fairly natural question. If you're looking at the sequence of prime numbers, so, P1 is 2, P2 is 3, and so on, how big do these gaps get? And we know that, actually, the gaps can get pretty big. So there's a very high school argument, that if you take the numbers 1 times 2 times 3, up to, say, times 100, and then you look at this number plus 2, this is going to be a multiple of 2, because 2 is a multiple of 2, and this first big number of product of numbers between 1 and a hundred is multiple of 2. Another way that mathematicians might write this is 100 exclamation mark plus 2. So this is, multiply all numbers up to 100 together, and then add 2. But then exactly the same argument means that 100 factorial plus 3 is going to be a multiple of ...
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It's a fairly natural question. If you're looking at the sequence of prime numbers, so, P1 is 2, P2 is 3, and so on, how big do these gaps get? And we know that, actually, the gaps can get pretty big. So there's a very high school argument, that if you take the numbers 1 times 2 times 3, up to, say, times 100, and then you look at this number plus 2, this is going to be a multiple of 2, because 2 is a multiple of 2, and this first big number of product of numbers between 1 and a hundred is multiple of 2. Another way that mathematicians might write this is 100 exclamation mark plus 2. So this is, multiply all numbers up to 100 together, and then add 2. But then exactly the same argument means that 100 factorial plus 3 is going to be a multiple of ...
