Does anybody know chain of prime numbers?


#1

Does anybody know chain of prime numbers and based on what this is developed?


#2

Actuallyt, IDK, but you know primes are the base of numbers. RSA helps us win the WW2, maybe the chain of prime numbers will help you win WW3.


#3

I think many Encryption Algorithms uses prime numbers. For more details I guess you need someone more professional.


#4

Hmm,hope ww3 won’t happen


#5

So I came to this forum in search of some professionals


#6

Do you mean Cunningham chain?


#7

In the world of Number Theory, there are a lot of hypothesizes instead of those famous ones. For some of these hypothesizes, certain type of the prime numbers are important.
I can give an example here, the Sierpinski Number, an odd natural number k such that k * 2^n + 1 is composite. Here is the wiki http://en.wikipedia.org/wiki/Sierpinski_number.
The reason why I give this example is that we all know the Second Kind Cunningham Chain is just like n+1, 2n+1 ,…, 2^k*n + 1. Do you guys think they look same.
As for bi-twins, till now, people can not even give a proof whether there are infinite pairs of bi-twins or not.
So we really need to get more primes, and we want to get something from all these primes.


#8

Hey, that is so brain-burning… Can you elaborate it?


#9

Primes are used as fundamental numbers for things like cryptography. This is because they have no numbers that divide them evenly. There are unanswered questions about how dense the prime numbers are and there is no existing theorem for how to systematically find every single prime, aside from guess and check. There are some theorems for finding chains of primes, but they are necessarily incomplete, meaning that they miss some. This provides opportunity for mathematicians and crypto fans alike to find new primes and new theorems for chains of primes.


#10

Sorry for that. But mathematical things are always like that, I can not make everyone clear for these tedious notations and hypothesizes.
The idea I want to show you is just as Nagalim said, prime is kind of the foundation in the math world, it is necessary to find more prime number for mathematical research.