Transcription
And so it's very um frustrating and annoying that even the most basic questions about primes we still cannot answer definitively.
Um we can we have good guesses uh like so for almost all questions about primes we can predict the answer. uh but we cannot get the 100% mathematical standard of proof for for many of them and one of the most basic questions which is at least 300 years old is called the twin prime conjecture that um uh there should be um so you could show there's infinitely many primes the primes never end you can always find primes bigger than any number you wish but uh we cannot find we cannot say the same yet for prime twins so these are pairs of primes that differ by the closest they can which is two uh for example 11 and 13 um well okay two and three are closer But um but after two all primes are odd. So the the closest you can get is is two.
And so we can observe that every so often you know the primes they they don't seem to obey a pattern. You know some sometimes um the prime gaps are large and sometimes they're small but every so often they they come close to each other and you get a twin and they seem to occur infinitely often you know as we we can find trillions and trillions of these by computer. But we have never been able to prove that they go on forever.
We have this prediction that the primes behave like basically like a random sequence of numbers. um and um random sequences with the if if you have a random sequence of of the same density as the primes, they will hit form twins infinitely often. But the primes are not random. We believe they're what's called pseudo random um that they have no obvious pattern besides the ones that we can we can obviously see such as them being um uh being odd. Yeah. So I mean it's is it's a very likely hypothesis but we can't prove it.