Numeros aleatorios

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Introduction to Randomness and Random Numbers
RANDOM.ORG is a true random number service that generates randomness via atmospheric noise. This page explains why it's hard (and interesting) to get a computer to generate proper random numbers.
Random numbers are useful for a variety of purposes, such as generating data encryption keys, simulating and modeling complex phenomena and for selectingrandom samples from larger data sets. They have also been used aesthetically, for example in literature and music, and are of course ever popular for games and gambling. When discussing single numbers, a random number is one that is drawn from a set of possible values, each of which is equally probable, i.e., a uniform distribution. When discussing a sequence of random numbers, each number drawnmust be statistically independent of the others.
With the advent of computers, programmers recognized the need for a means of introducing randomness into a computer program. However, surprising as it may seem, it is difficult to get a computer to do something by chance. A computer follows its instructions blindly and is therefore completely predictable. (A computer that doesn't follow itsinstructions in this manner is broken.) There are two main approaches to generating random numbers using a computer: Pseudo-Random Number Generators (PRNGs) and True Random Number Generators (TRNGs). The approaches have quite different characteristics and each has its pros and cons.
Pseudo-Random Number Generators (PRNGs)
As the word ‘pseudo’ suggests, pseudo-random numbers are not random in the way youmight expect, at least not if you're used to dice rolls or lottery tickets. Essentially, PRNGs are algorithms that use mathematical formulae or simply precalculated tables to produce sequences of numbers that appear random. A good example of a PRNG is the linear congruential method. A good deal of research has gone into pseudo-random number theory, and modern algorithms for generatingpseudo-random numbers are so good that the numbers look exactly like they were really random.
The basic difference between PRNGs and TRNGs is easy to understand if you compare computer-generated random numbers to rolls of a die. Because PRNGs generate random numbers by using mathematical formulae or precalculated lists, using one corresponds to someone rolling a die many times and writing down the results.Whenever you ask for a die roll, you get the next on the list. Effectively, the numbers appear random, but they are really predetermined. TRNGs work by getting a computer to actually roll the die — or, more commonly, use some other physical phenomenon that is easier to connect to a computer than a die is.

PRNGs are efficient, meaning they can produce many numbers in a short time, anddeterministic, meaning that a given sequence of numbers can be reproduced at a later date if the starting point in the sequence is known. Efficiency is a nice characteristic if your application needs many numbers, and determinism is handy if you need to replay the same sequence of numbers again at a later stage. PRNGs are typically also periodic, which means that the sequence will eventually repeat itself.While periodicity is hardly ever a desirable characteristic, modern PRNGs have a period that is so long that it can be ignored for most practical purposes.
These characteristics make PRNGs suitable for applications where many numbers are required and where it is useful that the same sequence can be replayed easily. Popular examples of such applications are simulation and modeling applications.PRNGs are not suitable for applications where it is important that the numbers are really unpredictable, such as data encryption and gambling.
It should be noted that even though good PRNG algorithms exist, they aren't always used, and it's easy to get nasty surprises. Take the example of the popular web programming language PHP. If you use PHP for GNU/Linux, chances are you will be perfectly...
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