🧵 Untitled Thread
Anonymous at Tue, 22 Oct 2024 15:04:12 UTC No. 16444201
do we know there aren't any more primes between the new largest prime and now second largest prime? perhaps one that isn't some power of 2 minus 1?
Anonymous at Tue, 22 Oct 2024 15:08:15 UTC No. 16444204
>>16444201
No, we do not. There could be several.
Anonymous at Tue, 22 Oct 2024 15:09:21 UTC No. 16444207
>>16444201
https://en.wikipedia.org/wiki/Prime
Anonymous at Tue, 22 Oct 2024 16:18:00 UTC No. 16444290
>>16444201
why do you care? like really, why do you guys care about prime numbers? what habe they ever done for you? I understand that if you're a cryptographist you need to know about prime numbers to do your job, but why does John, 53, cashier at a supermarket, care about prime numbers so much? what's the appeal?
Anonymous at Tue, 22 Oct 2024 17:00:24 UTC No. 16444339
>>16444290
aesthetics. John the supermarket cashier most likely doesn’t have the brain to appreciate aesthetics, just like (You).
Anonymous at Tue, 22 Oct 2024 17:55:05 UTC No. 16444405
there (most likely) are a shitbillion
the reason the largest known prime is a mersenne prime is because those are a bit easier to search for and verify than any old prime
it will take you longer to take random extremely long [large enough] numbers, and verify they're prime, than it will to increase powers of 2 until long enough, and verify that that is prime.
Anonymous at Tue, 22 Oct 2024 18:15:37 UTC No. 16444446
Do mathematicians know what the biggest prime is yet? Or an upper bound?
Anonymous at Tue, 22 Oct 2024 18:56:11 UTC No. 16444514
>>16444290
He is so bored at his job that he started to wonder about prime numbers, even his age being a prime number.
Anonymous at Tue, 22 Oct 2024 18:57:39 UTC No. 16444517
>>16444446
give me your biggest prime p.
p! + 1 is either prime, or has prime factors larger than p.
fundamental theory of arithmatic.
🗑️ Anonymous at Tue, 22 Oct 2024 19:07:39 UTC No. 16444533
>>16444517
That's actually pretty cool. I guess it has to do with the fact that the square root of p!+1 must be greater than p.
Anonymous at Tue, 22 Oct 2024 19:09:06 UTC No. 16444537
>>16444446
>>16444533
this proof >>16444517 is over 2000 years old btw…
Anonymous at Tue, 22 Oct 2024 19:10:18 UTC No. 16444539
>>16444517
So let's say p!+1 is not prime. Sure it has factors greater than p but how do you know that at least one of those factors is a prime?
Anonymous at Tue, 22 Oct 2024 19:12:17 UTC No. 16444541
>>16444539
mathematical induction and the fact that the factorial includes all numbers up to and including p
Anonymous at Tue, 22 Oct 2024 19:40:02 UTC No. 16444590
>>16444541
Oh yeah now I think I got it and it's cool. By adding 1 to the number p!, all the numbers less than or equal to p are disqualified for being factors of p!+1, and yet it has factors by definition. And one of them must be prime because the factor of a factor is a factor of the original number and you can't keep factoring factors forever so you must arrive at a prime factor, which then is also a factor of the original p!+1. People think maths is hard but this is surprisingly simple stuff.