What Are The Orders Of Colors In Cubefield

Prime Numbers and Safety Case

During the elementary school or in later primary school years, you come across in prime numbers and these numbers are associated with the idea of \u200b\u200bbuilding blocks with which all the natural numbers, by the multiplication .
It then goes on to show the criteria for divisibility by prime numbers smaller and so are taught to factor numbers.
Factoring numbers: a problem that you learn to deal with children.
Factoring numbers: a problem that computers can not solve.
There is no contradiction in the two previous statements. Indeed we are accustomed to dealing with very small numbers. 120, 1345, 5 billion ... are small numbers in our daily lives as they might appear larger. We intend to say that factoring a number of two, three, ten digits may actually be a breeze. But it can be difficult to factor a hundred digits? Meanwhile, we can conceive the magnitude of such a number? Just to help the intuition, if we had a lot of pens can be expressed with a a hundred-digit number ... we could give away a billion billion each atom in the universe and we still have a huge stock!
Then, if we take two prime numbers of fifty, sixty digits each and multiply them together we get a very large number. Well, it would be as simple as factoring factorization 120? Of course not, but how difficult would it? How long does it take a computer to find the first two that make it up? It 'clear that this time depends on the number of primes that can be found in that range, that is, those who are first in the range of numbers that have fifty or sixty figures. There are more than the computer has to "riddle".
There are more than there are nell'uiniverso atoms.
So it is almost impossible to solve the problem, a PC would take centuries.
E 'is based on what the security of credit cards, banks, transactions: a hacker who wants to access a protected area should almost be able to find the first two making up a number (public key easily recognizable) of one hundred, one hundred and twenty figures. It can not!
I am often asked "but what good math background ?"... well, this argument is one of my favorite responses.
E 'thanks to mathematics that can be spending with your credit card and be sure that no one, that is genius, you can access your account. Without primes our economy would be back a hundred years.