/sci/ - Science & Math

[Anonymous No.11322246]

Why are prime numbers '"interesting" in number theory/ math in general?

[Anonymous No.11322266]

>>11322246
Because it shows that without intermediate steps, humans really are clueless. A big brain species would've concluded by now that the complexity of the pattern is defined by the system that computes it. Prime numbers will always require eclectic validation. Computing the next based solely on the previous will never work because of the bounded associativity at play.

[Anonymous No.11322268]

>>11322246
loads upon loads of interesting stuff involves multiplying numbers

[Anonymous No.11322278]

>>11322266
gibberish

[Anonymous No.11322291]

>>11322246
Why particles are "interesting" in quantum electrodynamics/ physics in general?

[Anonymous No.11322300]

>>11322278
>complexity of [calculating] the pattern to the prime numbers depends on the machine you use to compute it
>Prime numbers will always require an assortment of individual factor checking to ensure they really are prime
>Computing the next prime number after a previous prime number based solely on that previous prime number is impossible because the current prime number probably requires information encoded in other prime numbers far back in the sequence.

hope that helps brainlet-anon

[Anonymous No.11322319]

>>11322300
Please translate into non-autistic

[Anonymous No.11322329]

>>11322319
check sieve algorithms, he is trying to sound smart talking about their properties by making it vague.

[Anonymous No.11322337]

>>11322300
>>11322319
He's saying that they while they appear to be simple and interesting from a human perspective, because it is computationally difficult to compute one from the last they are not (well he says impossible, but this is objectively wrong so giving the benefit of the doubt I assume he simply means difficult without some form of computing previous terms).

This is obviously wrong, computational complexity is worth study, but there are innumerable contexts in which it does not correlate to the ease of finding results nor how broad the application of those results are.

>>11322246
Prime numbers are interesting because they are fundamental to the relationship between an integer's additive and multiplicative properties. This relationship remains to be the source of a disproportionate amount of the difficulty still faced by modern number theory. As a matter of fact many of the problems which do not appear to have anything to do with primes per se are still difficult precisely because of this difficulty in resolving additive and multiplicative properties, e.g. Collatz Conjecture.

[Anonymous No.11322347]

>>11322246
It's like, once you figure out how to tie your shoelaces without your mum helping you, the challenge will become less interesting, and you will start to look for something else to interest you. This will happen to you someday too, dear anon.

[Anonymous No.11322352]

>>11322337
Yeah I meant to say impossible if it requires information encoded in a previous prime number from a pure continuity perspective (encodings needs to be preserved, prime numbers have a diversity of encodings). But the only exceptions to this are at the start of the sequence, which is irrelevant.

>This is obviously wrong, computational complexity is worth study, but there are innumerable contexts in which it does not correlate to the ease of finding results nor how broad the application of those results are.

Low brainwave answer. If prime numbers could be calculated from the interference pattern of EMR waves, you'd be a very rich man.

[Anonymous No.11322371]

>>11322352
That isn't how information works, a single prime number perfectly "encodes" every previous one, it is obviously trivial to write a program that takes a single prime number and gives the next, the fact that the implementation details don't match whatever intuition you have about continuity has no formal basis and is irrelevant.

[Anonymous No.11322387]

>>11322371
t. 2

[Anonymous No.11322392]

>>11322371
>low IQ and angry, the post

[Anonymous No.11322410]

>>11322371
If each number in a sequence must match a set of independent conditions proportional to the length of the sequence when sampled, with no further abstraction, then each number is not dependant on each other- just the conditions.

If the conditions themselves are deterministic and predictable based on the results of previous conditions, then you now have two choices- either each number is independent and very slow to compute- or you are reliant on the results of the conditions encoded into previous numbers.

[Anonymous No.11322444]

>>11322246
it's very useful for encryption, since it takes exponential time (I think) to factor a number, you can choose two random primes, convert them to binary and do operations to them like bitwise XOR in private key and public key cryptography. Since it takes a lot longer to factor a number to find what code you're using for encryption than to generate two random primes it is a very useful and is the way how they store and transmit and store important banking information worldwide.

[Anonymous No.11322465]

>>11322444
Yes, to factor a number into primes takes exponential time (fast). But it is not known whether it is possible in polynomial time (even faster). Which is the basic reason why something like an ATM can function.

[Anonymous No.11322471]

[Anonymous No.11322481]

>>11322465
exponential time is (slow)

[Anonymous No.11322482]

Wow, a bunch of autistic replies and not a single correct one.

Answering the question: because they are very simple in their definition, yet they are completely random. You have to compute the last N-1 primes in order to get the Nth prime, meaning it's just very hard to pin down their locations in general.

[Anonymous No.11322493]

>>11322482
>not just checking <= root n
i shiggy

[Anonymous No.11322494]

>>11322482
>yet they are completely random

[Anonymous No.11322495]

>>11322482
Once again, the crackpots have descended on /sci/

[Anonymous No.11322503]

>>11322494
>>11322495
>th-they are interesting because of the riemann hypothesis?

ok so why is the riemann hypothesis interesting

>be-because of prime numbers

You people are pathetic and lack basic understanding of mathematics

[Anonymous No.11322522]

>>11322503
No we are not pathetic, nor do we lack understanding of mathematics. But we can clearly identify someone who is and who does. Very nice creativity in figuring out insults though, for a twelve year old.

[Anonymous No.11322530]

>>11322503
>ok so why is the riemann hypothesis interesting

$1M, nerd.

[Anonymous No.11322537]

>>11322522
Sure, buddy

[Anonymous No.11322540]

>>11322337
>Prime numbers are interesting because they are fundamental to the relationship between an integer's additive and multiplicative properties.
What.
I don't understand this part, I've read these lines more than once.

[Anonymous No.11322652]

>>11322540
he just took his first abstract algebra classes and heard something about primes there

[Anonymous No.11322663]

>>11322300
In English, doc

[Anonymous No.11322676]

>>11322537
Srsly, you need to go study, or else you are f***cked. Right now, you clearly have no idea.

[Anonymous No.11322740]

>>11322676
If mememaster Terence Tao says the same thing maybe you will take the idea that primes are random more seriously?

https://www.youtube.com/watch?v=PtsrAw1LR3E

[Anonymous No.11322781]

>>11322740
he used word randomness (I remember he worked on some patterns emerging in random matrices and how it correlated with zeta function), but never proved nor attempted to prove that the sequence of primes is random (by any standard randomness definition), because he has basic math education and seen prime number theorem.

[Anonymous No.11322786]

>>11322781
You seem like a math academic (graduate student or other) to me, only this way you could be this cocky and short-sighted simultaneously. Sure m8, primes are not random and statements in lesser areas invoving primes is what makes them interesting

[Anonymous No.11322927]

I have paper on primes.

I found generator, that seriously spits out EVERY prime number conseccutive.

It is interesting?

[Anonymous No.11322932]

>>11322246
Prime numbers get you all the math hoes and bitches anon.

[Anonymous No.11322941]

>>11322927
what's the last one?

[Anonymous No.11323831]

>>11322927
not closed form though

[Anonymous No.11323845]

>>11322300
but there are ways to calculate the next prime just by being given the previous one. It's just that the algorithm is so complex that it takes much less time to do "tricks" like 2^n-1 and check afterwards than actually calculate that far.

The problem is nobody has invented a "fast" algorithm for easily solving the next prime. And actually that's not even the problem because most mathematicians are pretty sure it doesn't exist, it's just proving that nobody has proven there ISN'T a way to do it.