The Student Room Group

Mathematicians, I need YOU! - insane mathematical problems help

So I am currently doing this project, with the title 'What is the significance of prime numbers within online security' - (any input on this would appreciated)

So I'm planning on talking about coding etc, but i want to base it primarily around why are prime numbers so significant.

So wheres the hardcore maths you may be asking?

Well i want to talk about the Riemann Hypothesis, and the effect of this being 'solved' so to speak. Also i was wondering if can link it to any other famous mathematical problems that haven't been solved yet, which if solved, will have huge implications on online security. (Could I include P vs NP?)

Yes I am 'TheALevelStudent' and i know this level of maths is way above my intellectual understanding. But you can't fault curiosity!
(edited 8 years ago)
prime numbers are very useful for security... if you need to choose a 2 digit password then 23 is a good one.
this can be extended to 3 digits ( 139 is good because it looks as if it is not prime but actually is ) and maybe beyond :dontknow:
Reply 2
Avatar for TheBBQ
TheBBQ
21
So what exactly are you asking from people here? Ideas on relevant topics and unsolved problems or do you want explanations?
Original post by the bear
prime numbers are very useful for security... if you need to choose a 2 digit password then 23 is a good one.
this can be extended to 3 digits ( 139 is good because it looks as if it is not prime but actually is ) and maybe beyond :dontknow:


Thanks for your reply!

But I want to get deeper, why is it that they are very useful in terms of mathematics, complex analysis and computability theory
Original post by TheBBQ
So what exactly are you asking from people here? Ideas on relevant topics and unsolved problems or do you want explanations?


Mainly just ideas, but if you are willing to explain some of the more intellectual maths to a mere rookie like me, that would be greatly appreciated!
Original post by TheALevelStudent
Thanks for your reply!

But I want to get deeper, why is it that they are very useful in terms of mathematics, complex analysis and computability theory


this should help:

https://www.quora.com/Why-are-prime-numbers-important-for-computer-security
Reply 6
Avatar for TheBBQ
TheBBQ
21
Original post by TheALevelStudent
Mainly just ideas, but if you are willing to explain some of the more intellectual maths to a mere rookie like me, that would be greatly appreciated!


I would suggest looking at Prime Number Theorem, Prime-counting function, formulae for predicting primes, Goldbach's conjecture, Public-Key cryptography. You may have to get into a bit of group theory for the last one!

I have done real and complex analysis but I have not formally touched on prime numbers, or gone too much into the Riemann zeta function.. the Riemann hypothesis is above me I am afraid.

Is this for the extended project?
(edited 8 years ago)
Original post by TheALevelStudent
So I am currently doing this project, with the title 'What is the significance of prime numbers within online security' - (any input on this would appreciated)

So I'm planning on talking about coding etc, but i want to base it primarily around why are prime numbers so significant.

So wheres the hardcore maths you may be asking?

Well i want to talk about the Riemann Hypothesis, and the effect of this being 'solved' so to speak. Also i was wondering if can link it to any other famous mathematical problems that haven't been solved yet, which if solved, will have huge implications on online security. (Could I include P vs NP?)

Yes I am 'TheALevelStudent' and i know this level of maths is way above my intellectual understanding. But you can't fault curiosity!


I'm not sure if you could really understand much amount the Riemann Hypothesis without a background in Analysis and Number Theory but if I were you I would research on public/private key cryptography and how number theory is used within that field.
Reply 8
Avatar for shamika
shamika
16
Original post by TheALevelStudent
So I am currently doing this project, with the title 'What is the significance of prime numbers within online security' - (any input on this would appreciated)

So I'm planning on talking about coding etc, but i want to base it primarily around why are prime numbers so significant.

So wheres the hardcore maths you may be asking?

Well i want to talk about the Riemann Hypothesis, and the effect of this being 'solved' so to speak. Also i was wondering if can link it to any other famous mathematical problems that haven't been solved yet, which if solved, will have huge implications on online security. (Could I include P vs NP?)

Yes I am 'TheALevelStudent' and i know this level of maths is way above my intellectual understanding. But you can't fault curiosity!


1) RH being solved doesn't necessarily have a major impact on cryptography and hence online security. The only way I can think it would is if the method to solve RH told us something new about primes, which in turn can be used to crack codes previously difficult

2) why on earth are you trying to talk about P vs NP at the same time as RH? You need to have a serious think about what precisely you want to focus your project on. It's far better to focus a project on a narrower area and research / explain that well, then to try to mention all famous unsolved maths problems.
Original post by the bear


Thanks for this, I've come across a lot articles on this website related to the topic, but weirdly not this one which has a direct link lol! - very much appreciated
Original post by TheBBQ
I would suggest looking at Prime Number Theorem, Prime-counting function, formulae for predicting primes, Goldbach's conjecture, Public-Key cryptography. You may have to get into a bit of group theory for the last one!

I have done real and complex analysis but I have not formally touched on prime numbers, or gone too much into the Riemann zeta function.. the Riemann hypothesis is above me I am afraid.

Is this for the extended project?


Wow thanks, thats exactly the kind of information i was looking for!

-and yep, it is!
Original post by Louisb19
I'm not sure if you could really understand much amount the Riemann Hypothesis without a background in Analysis and Number Theory but if I were you I would research on public/private key cryptography and how number theory is used within that field.


Ive been searching riemann hypothesis for dummies on google lmao. From what i have gathered, i kind of understand its principle, but of course none of the maths behind it. The focus of my project is to fundamentally show how significant maths is in the real world.

Thanks for your input, i will deffinaley look into cryptography and number theory!
Original post by shamika
1) RH being solved doesn't necessarily have a major impact on cryptography and hence online security. The only way I can think it would is if the method to solve RH told us something new about primes, which in turn can be used to crack codes previously difficult

2) why on earth are you trying to talk about P vs NP at the same time as RH? You need to have a serious think about what precisely you want to focus your project on. It's far better to focus a project on a narrower area and research / explain that well, then to try to mention all famous unsolved maths problems.


1) I thought RH was linked to providing us with an understanding of how primes are distributed along the number line, therefore linking it to cryptography. Is this not correct?

2) Forgive me of my naivety, i just get a bit excited when it comes to maths lmao. Out of the topics mentioned by other users, which one would you say would be the best research most given my situation?
Original post by TheALevelStudent
1) I thought RH was linked to providing us with an understanding of how primes are distributed along the number line, therefore linking it to cryptography. Is this not correct?

2) Forgive me of my naivety, i just get a bit excited when it comes to maths lmao. Out of the topics mentioned by other users, which one would you say would be the best research most given my situation?


RH does tell you something about the distribution of primes, but not everything to do with primes has something to do with security. As for topics to research, why don't you google a bit yourself? That way you're genuinely learning how various bits of maths is helpful for cryptography and you can shape your own project?
Original post by shamika
RH does tell you something about the distribution of primes, but not everything to do with primes has something to do with security. As for topics to research, why don't you google a bit yourself? That way you're genuinely learning how various bits of maths is helpful for cryptography and you can shape your own project?


Understanding the distribution of primes along the number line would make it easier for 'hackers' to basically 'hack'?

Ive googled around quite a lot actually, all I'm asking for is some guidance into which way i should take this project : /
Reply 15
Avatar for TheBBQ
TheBBQ
21
Original post by TheALevelStudent
Wow thanks, thats exactly the kind of information i was looking for!

-and yep, it is!


If you're going to write any formulae etc in your EP then I suggest looking up a LaTeX document editor such as overleaf and taking an hour or two getting familiar with it. Came very handy during my Physics lab reports :biggrin:
Original post by TheALevelStudent
Understanding the distribution of primes along the number line would make it easier for 'hackers' to basically 'hack'?


Why?

Ive googled around quite a lot actually, all I'm asking for is some guidance into which way i should take this project : /


Well what precisely have you googled? I've already given you a recommendation - focus on a particular area and explain that well
Original post by TheBBQ
If you're going to write any formulae etc in your EP then I suggest looking up a LaTeX document editor such as overleaf and taking an hour or two getting familiar with it. Came very handy during my Physics lab reports :biggrin:


Thanks I will do! I imagine i would have to use some sort of formula somewhere along the line

Quick Reply

Related discussions

Latest

Trending

Trending

Articles for you