The Oldest Unsolved Problem in Math

this is a video about the oldest unsolved problem in math it dates back 2,000 years some of the brightest mathematicians of all time have tried to crack it but all of them failed in the year 2000 the Italian mathematician Pier Georgio Oda Freddy listed it among four of the most pressing open problems at the time solving this problem could be as simple as finding a single number so mathematicians have used computers and checked numbers up 210 to the power of 2,200 but so far they've come up empty-handed why do you think this problem has captured the imaginations of so many mathematicians it's old it's simple it's beautiful what what else could you want so the problem is this do any odd perfect numbers exist so what is a perfect number well take the number six for example you can divide it by 1 2 3 and six but let's ignore six because that's the number itself and now we're left with just the proper divisors if you add them all up you find that they add to six which is the number itself so numbers like this are called perfect you can also try this with other numbers like 10 10 has the proper divisors 1 2 and 5 if you add those up you only get eight so 10 is not a perfect number now you can repeat this for all other numbers and what you find is that most numbers either overshoot or undershoot between one and 100 only 6 and 28 are perfect numbers go up to 10,000 and you find the next two perfect numbers 496 and 8,128 these were the only perfect numbers known by the ancient Greeks and they would be the only known ones for over a thousand years if only we could find a pattern that makes these numbers then we could use that to predict more of them so what do these numbers have in common well one thing to notice is that each next perfect number is one digit longer than the number that came before it another thing they share is that the ending digit alternates between six and 8 which also means they are all even but here's where things get really weird you can write six as the sum of 1 + 2 + 3 and 28 as the sum of 1 ...