Another mistake at 14:00 : 2^(2^6) + 1 is not divisible by 641. It should be 2^(2^5) + 1 (which equals 641×6700417). Instead, 2^(2^6) + 1 can be prime factorized into 274177×67280421310721.
I notice "Euler" is mentioned instead of "Euclid", several times. It's a mistake I make and nice to see one of the top mathematicians in the world has the same issue :)
So much jargon. Is it not easier to say that the list of primes is endless because the lowest factor greater than 1 of p!+1 must be a prime number and must be greater than p?
for 3(p1 to pn)-1, if it's a prime, then it's also 3n+2, that's good. if it's not a prime, it must contain a prime factor greater than (p1 to pn), if the factor is in 3n+2 that's also good. if it's in 3n+1, then we have (3m+1)k = 3(p1 to pn) - 1 3mk+k=3(p1 to pn) - 1 so k is -1 in Z3. Since 3m+1 is greater (p1 to pn) so k is no more than 3 and k is positive integer. k can only be 2. then 3 *m*2 = 3(p1 to pn) - 3. m*2 = (p1 to pn) - 1 . left is even right is odd since p1 =2 the 1st prime. so contradiction. is my idea right? i hope anyone can help to check
I agree so much about his lexicography discussion
Thanks Prof. Borcherds. Please keep on doing lectures like that. They calm me down during these strange times.
Another mistake at 14:00 : 2^(2^6) + 1 is not divisible by 641. It should be 2^(2^5) + 1 (which equals 641×6700417). Instead, 2^(2^6) + 1 can be prime factorized into 274177×67280421310721.
Thanks! This is indeed a mistake by me.
@@richarde.borcherds7998 Thank you professor for your video series! Really appreciate it.
I notice "Euler" is mentioned instead of "Euclid", several times. It's a mistake I make and nice to see one of the top mathematicians in the world has the same issue :)
So much jargon. Is it not easier to say that the list of primes is endless because the lowest factor greater than 1 of p!+1 must be a prime number and must be greater than p?
I hate to correct Prof. Borcherds, but 1807 = 13*139 (39 is not prime, or coprime to 1806).
Oh no! Euclid's algorithm doesn't work!
@@brettaspivey 🤣 Clearly not what I meant, but thank you for the laugh.
@Dave I hate to correct Dave, but you clearly meant 1807 when you wrote 1806.
@@SaveSoilSaveSoil You are correct, thank you.
Thanks! I've added a note about it.
Thankyou
8:21 "A lot of examples in politics that I'm not gonna mentioned... is Pluto a planet?" I think I almost hear "Is a fetus a human being?" lol
for 3(p1 to pn)-1, if it's a prime, then it's also 3n+2, that's good. if it's not a prime, it must contain a prime factor greater than (p1 to pn), if the factor is in 3n+2 that's also good. if it's in 3n+1, then we have (3m+1)k = 3(p1 to pn) - 1 3mk+k=3(p1 to pn) - 1 so k is -1 in Z3. Since 3m+1 is greater (p1 to pn) so k is no more than 3 and k is positive integer. k can only be 2. then 3 *m*2 = 3(p1 to pn) - 3. m*2 = (p1 to pn) - 1 . left is even right is odd since p1 =2 the 1st prime. so contradiction. is my idea right? i hope anyone can help to check
Use a dot for multiplication!!!!
Why are you using numerals and glyphs, thats not euclid you silly goose