Euclid’s proof of the infinity of primes

There are infinitely many primes: assuming the opposite can quickly be shown to be absurd.

[Rockyzach]

AKA "it doesn't make sense to say that primes are finite because you could always just add +1 to the product of that set of supposedly finite primes and get a new number that is not divisible by any of those primes, however by the fundamental theorem of arithmetic, all natural numbers have to be a product of some set of primes.

The FTOA also states that those prime signatures have to be unique to each natural number. So if you added +1 to a number that is the product of ALL primes, then you would you get a different and larger number that would require more primes to even exist other than the so called "finite set of primes".

[aviralsingh]

Sir make ur voice a little Loud otherwise ur teaching level is awesome 😍😍😍 thanq sir

[miguelnglopes]

If you allow me to make a small suggestion, I'd invest in a better microphone, and place it closer to you.

Do keep up the great work.

[Anteater]

Now cover Galois’s proof that there’s no general formula for the solutions of a quintic equation

[math_travel]

but this is not the exact proof Euclid suggested

[carlsanders]

I do not follow the logic. Adding 1 to any product of primes always gives you an even number. So the target number cannot be a prime and is divisible by 2. How does that prove there are other primes?

[M-F-H]

That's wrong! Euclid's proof is NOT by contradiction, and he does NOT consider the set of ALL primes at the beginning. He does consider ANY set of primes and shows that there must be at least one other prime not in that set.