5, 13 and 137 are Pythagorean Primes - Numberphile
Professor Laurence Eaves on Pythagorean Primes - and why 5, 13 and 137 are three of his favourites!? More links & stuff in full description below ↓↓↓ Fine ...
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LAURENCE EAVES: Right. Well, I was born on May, which is the fifth month, and on the 13th day of May. Mathematically, that's vaguely interesting because these are both Pythagorean primes. Right, OK. Well, if we look at 5, then we can write 5 as the sum of two squares. So 1 squared plus 2 squared is equal to 5. Now if we take 13-- see if we can work that one out. Well, 13 is 9 plus 4, so 4 is just 2 squared. And 3 squared is 9. So that gives me-- now, the next one, 17. We can do that as well, because 17 is 4 squared plus 1 squared, which is another Pythagorean prime. Pythagorean-- we've all heard of Pythagoras, who was a very famous mathematician. So why do these numbers bear his name? Well, if we remember our right-angle triangle. So we've got a right trian...
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LAURENCE EAVES: Right. Well, I was born on May, which is the fifth month, and on the 13th day of May. Mathematically, that's vaguely interesting because these are both Pythagorean primes. Right, OK. Well, if we look at 5, then we can write 5 as the sum of two squares. So 1 squared plus 2 squared is equal to 5. Now if we take 13-- see if we can work that one out. Well, 13 is 9 plus 4, so 4 is just 2 squared. And 3 squared is 9. So that gives me-- now, the next one, 17. We can do that as well, because 17 is 4 squared plus 1 squared, which is another Pythagorean prime. Pythagorean-- we've all heard of Pythagoras, who was a very famous mathematician. So why do these numbers bear his name? Well, if we remember our right-angle triangle. So we've got a right trian...
