Random number generator in approx. Random number generator online

Numbers accompany us everywhere - room home and apartments, telephone, car, passport, plastic card, dates, email passwords. We choose some combinations of numbers themselves, but most we get randomly. Without giving yourself in this report, we use the numbers generated by random every day. If we are inventing pinsodes, then unique credit or salary card codes are generated by reliable systems that exclude access to passwords. Random number generators provide protection in areas requiring speed processing, security and independent data processing.

The process of generating pseudo-random numbers is subordinate to certain laws and is used quite a long time, for example, when conducting lotteries. In the recent past, the draws were carried out using lothotrones or lots. Now in many countries, winning numbers of state lotteries are determined by the set of generated random numbers.

Benefits of the Fashion

So, the random number generator is an independent modern mechanism for random determination of the combinations of numbers. The uniqueness and perfection of this method are impossible to external interference in the process. The generator is a complex of programs built, for example, on noise diodes. The device forms the stream of random noise, the current values \u200b\u200bof which are converted into numbers and constitute a combination.

The generation of numbers provides an instant result - the compilation of a combination takes several seconds. If we talk about the lotteries, the participants can immediately find out if the ticket number coincided with the winning. This allows the circulation as often as participants want this. But the main advantage of the method in unpredictability and inability to calculate the algorithm of the selection of numbers.

How is the generation of pseudo-random numbers

In fact, random numbers are not accidental - the row begins with a given number and is generated by the algorithm. The pseudo-random number generator (GPSR or PRNG - Pseudorandom Number Generator) - and there is an algorithm that generates a sequence, at first glance, not related numbers subordinated to the usually uniform distribution. In computer science, pseudo-random numbers are used in many applications: in cryptography, simulation modeling, Monta Carlo method, etc. The quality of the result depends on the GPSF properties.

The source of generation can be physical noise from cosmic radiation to noise in the resistor, but such network security applications are almost not used. In cryptographic applications, special algorithms that generate sequences that cannot be statistically random are used. However, the correctly selected algorithm allows you to get rows of numbers passing by most accidents. The repetition period in such sequences is more than the operating interval from which the numbers are taken.

Many modern processors contain GPSh, for example, in RDRAND. As an alternative, sets of random numbers are created published in one-time notebook (dictionary). The source of the numbers in this case is limited and does not provide full network security.

History GPSH

The prototype of the random number generator can be considered the Desktop game Senez, common in ancient Egypt in 3500 BC. Under the conditions, two players participated, the moves were determined by throwing four flat black and white sticks - they were the similarity of the GPH of the time. The sticks were thrown at the same time, and the glasses were counted: if one fell up the white side, 1 point and an additional move, two white - two points and so on. The maximum result of five points received a player who threw four chopsticks in the black side.

Nowadays, Ernie generator was used for many years in the UK during lottery draws. Two basic methods for generating winning numbers: linear congruent and additive congruent. These and other methods are based on the principle of chance of choice and are provided by software, infinitely producing numbers, guess the sequence of which is impossible.

GPSF functions continuously, for example, in slot machines. According to the laws of the United States, this is a prerequisite that must comply with all software providers.

Etc., and is used by accountholders to attract a new audience in the community.

The result of such drawers often depends on the user's goodness, since the recipient of the prize is determined randomly.

For this definition, the organizers of the raffle almost always use a random number generator online or pre-installed, spreading free.

Choice

Quite often to choose such a generator may be difficult, since their functionality is quite different - some it is significantly limited, others are quite wide.

It is implemented quite a large number of such services, but the complexity is that they differ in the scope of action.

Many, for example, are tied with their functionality to a specific social network (for example, many generators applications work only with references to this).

The most simple generators simply determine the random number in the specified range.

This is convenient because it does not associate the result with a certain post, and therefore can be used in the draws outside the social network and in various other situations.

There is no other application in essence.

Tip! When choosing the most suitable generator, it is important to take into account that for what purposes it will be used.

Specifications

For the fastest process of choosing the optimal online service generation of random numbers in the table below, the main technical characteristics and functionality of such applications are given.

Read more All applications discussed in the table are described below.

Randstuff

You can use this application online by reference to its official website http://randstuff.ru/number/.

This is a simple generator of random numbers, different than quick and stable work.

It is successfully implemented both in the format of a separate independent application on the official website and in the form of an application.

The feature of this service is that it can choose a random number from both the specified range and from a specific list of numbers that can be specified on the site.

• Stable and fast work;
• The absence of direct binding to the social network;
• You can choose both one and several numbers;
• You can choose only among the specified numbers.

User reviews about this application are as follows: "Determine through this service winners in groups in contact. Thank you, "You are the best", "I use only this service."

Cast Lots.

This application provides a simple functional generator, implemented on the official website, in the form of an VKontakte application.

There is also a generator widget for insertion to its site.

The main difference from the previous described application is that it allows you to disable the repetition of the result.

Note that, ideally, the density curve of the distribution of random numbers would look like shown in Fig. 22.3. That is, in the perfect case, the same number of points fall into each interval: N. i. = N./k. where N. - Total number of points, k. - the number of intervals, i. \u003d 1, ..., k. .

It should be remembered that the generation of an arbitrary random number consists of two stages:

• generation of a normalized random number (that is, evenly distributed from 0 to 1);
• transformation of normalized random numbers r. i. in random numbers x. i. which are distributed over the necessary user (arbitrary) law distribution or in the required interval.

Generators of random numbers by the method of obtaining numbers are divided into:

• physical;
• tabular;
• algorithmic.

Physical GSH

An example of a physical stage can serve: coin ("Eagle" - 1, "Rushka" - 0); dice; divided into sectors with numbers drum with arrow; The noise alternator (GS), which is used as a noisy thermal device, for example, a transistor (Fig. 22.4-22.5).

Table GSH

Table GCMs as a source of random numbers use specially compiled tables containing proven non-corrosive, that is, in no way depend on each other, the numbers. In tab. 22.1 shows a small fragment of such a table. Coming down the table from left to right from top to bottom, you can get evenly distributed from 0 to 1 random numbers with the desired number of placked signs (in our example we use for each number three characters). Since the numbers in the table do not depend on each other, the table can be passed in different ways, for example, from top to bottom, or right to left, or, say, you can choose numbers on even positions.

The advantage of this method is that it gives indeed random numbers, as the table contains proven uncorrelated numbers. Method disadvantages: To store a large number of numbers, a lot of memory is required; Big difficulty of generating and verifying such tables, repeats when using the table no longer guarantee the randomness of the numerical sequence, which means that the reliability of the result.

There is a table containing 500 absolutely random proven numbers (taken from the book I. G. Venetsky, V. I. Venetskaya "The main mathematicheological and statistical concepts and formulas in economic analysis").

Algorithmic GSH

The numbers generated by these GSH are always pseudo-random (or quasonic), that is, each subsequent generated number depends on the previous one:

r. i. + 1 = f.(r. i.) .

The sequences composed of such numbers form a loop, that is, there is a cycle, repeating the infinite number of times. Repeated cycles are called periods.

The advantage of the Data GSH is the speed; Generators practically do not require memory resources, compact. Disadvantages: Numbers cannot be fully called random, since there is a dependence between them, as well as the presence of periods in the sequence of quasonic numbers.

Consider several algorithmic methods for obtaining HSH:

• method of middle squares;
• method of middlework;
• mixing method;
• linear congruent method.

Method of middle squares

There is some four-digit number R.0. This number is built into the square and is entered in R.one . Next R.1 takes the middle (four middle digits) - a new random number - and recorded in R.0. Then the procedure is repeated (see Fig. 22.6). Note that in fact, as a random number, it is necessary to take ghij., but 0.Ghij. - with the onion with the left zero and decimal point. This fact is reflected in fig. 22.6, and on subsequent similar drawings.

Disadvantages of the method: 1) if at some iteration the number R.0 will be equal to zero, the generator degenerates, so the right choice of the initial value is important. R.0; 2) the generator will repeat the sequence through M. n. steps (at best), where n. - The bit rate R.0 , M. - Base of the number system.

For example in fig. 22.6: if the number R.0 will be represented in the binary number system, the sequence of pseudo-random numbers will repeat after 2 4 \u003d 16 steps. Note that the repetition of the sequence can occur before, if the initial number is selected unsuccessfully.

The method described above was proposed by John von Neumanan and refers to 1946. Since this method was unreliable, he was very quickly refused.

Method of middle work

Number R.0 multiplied by R.1, from the result R.2 Middle extracted R.2 * (this is another random number) and is multiplied by R.one . According to this scheme, all subsequent random numbers are calculated (see Fig. 22.7).

Mixing method

In the mixing method, the cyclic shift operations are used to the left and right. The idea of \u200b\u200bthe method is as follows. Let the initial number be stored in the cell R.0. Cyclically shifting the contents of the cell to the left by 1/4 of the cell length, we get a new number R.0 *. In the same way, cyclically shifting the contents of the cell R.0 to the right on 1/4 cell length, we get the second number R.0 **. Sum of numbers R.0 * I. R.0 ** gives a new random number R.one . Further R.1 is entered in R.0, and the entire sequence of operations is repeated (see Fig. 22.8).

Note that the number obtained as a result of summation R.0 * I. R.0 ** may not be fully in the cell R.one . In this case, unnecessary discharges should be discarded from the resulting number. We will explain it for fig. 22.8, where all cells are represented by eight binary discharges. Let be R.0 * = 10010001 2 = 145 10 , R.0 ** = 10100001 2 = 161 10 , then R.0 * + R.0 ** = 100110010 2 = 306 10 . As you can see, the number 306 takes 9 discharges (in the binary number system), and the cell R.1 (like R.0) can accommodate the maximum of 8 digits. Therefore, before entering the value in R.1 It is necessary to remove one "extra", the extreme left bit from among the 306, as a result of which R.1 will not be 306, A 00110010 2 \u003d 50 10. We also note that in such languages \u200b\u200blike Pascal, "Cutting" of unnecessary bits when the cell is overflowed automatically in accordance with the specified variable type.

Linear congruent method

The linear congruent method is one of the simplest and most common procedures that simulate random numbers. This method uses the MOD operation ( x., y.), returning the remainder from dividing the first argument to the second. Each subsequent random number is calculated on the basis of the previous random number according to the following formula:

r. i. + 1 \u003d MOD ( k. · r. i. + b., M.) .

The sequence of random numbers obtained using this formula is called linear congruent sequence. Many authors call a linear congruent sequence when b. = 0 multiplicative congruent method, and when b. ≠ 0 — mixed congruent method.

For a high-quality generator, you must select suitable coefficients. Need to M. it was quite large since the period cannot have more M. Elements. On the other hand, the division used in this method is a rather slow operation, so the binary computing machine will be logical M. = 2 N. Because in this case the destruction from the division is reduced inside the computer to the binary logical operation "and". Also widespread the choice of the greatest simple number M. less than 2 N. : In special literature it is proved that in this case the younger discharges of the resulting accidental number r. i. + 1 behave just as accidentally, as well as senior, which positively affects the entire sequence of random numbers in general. As an example, you can bring one of numbers Mermesennaequal to 2 31 - 1, and thus M. \u003d 2 31 - 1.

One of the requirements for linear congruent sequences is as much length of the period. The length of the period depends on the values M. , k. and b. . Theorem that we give below allows you to determine whether the maximum length period is possible for specific values M. , k. and b. .

Theorem. Linear congruent sequence determined by numbers M. , k. , b. and r. 0, has a period of length M. Then and only when:

• numbers b. and M. Mutually simple;
• k. - 1 more paint p. For each simple p. Divider M. ;
• k. - 1 multiple 4, if M. Mark 4.

Finally, in conclusion, consider a couple of examples of using a linear congruent method to generate random numbers.

It was found that a number of pseudo-random numbers generated on the basis of data from Example 1 will be repeated every M./ 4 numbers. Number q. set arbitrarily before the start of computing, however, it should be borne in mind that the range of random at large k. (and therefore q. ). The result can be somewhat improved if b. Eldight I. k. \u003d 1 + 4 · q. - In this case, the row will be repeated through every M. numbers. After long searches k. Researchers stopped at 69069 and 71365.

The random number generator using data from Example 2 will issue random non-repeating numbers with a period of 7 million.

The multiplicative method of generating pseudo-random numbers was proposed by D. G. Lechmerom (D. H. Lehmer) in 1949.

Checking the quality of the generator

The quality of operation of the entire system and the accuracy of the results depends on the quality of the work of HSH. Therefore, the random sequence generated by the amount of GSH should satisfy a number of criteria.

Checks are available two types:

• checks on the uniformity of the distribution;
• checks for statistical independence.

Distribution Uniform Checks

1) HSH should produce close to the following values \u200b\u200bof statistical parameters characteristic of a uniform accidental law:

2) Frequency Test

The frequency test allows you to find out how many numbers got into the interval (m. r. – σ r. ; m. r. + σ r.) that is, (0.5 - 0.2887; 0.5 + 0.2887) or, ultimately, (0.2113; 0.7887). Since 0.7887 - 0.2113 \u003d 0.5774, we conclude that about 57.7% of all random numbers falling on this interval should be included in this interval (see Fig. 22.9).

It should also be borne in mind that the number of numbers in the interval (0; 0.5) should be approximately equal to the number of numbers in the interval (0.5; 1).

3) Check by the criterion "chi-square"

The criterion "chi-square" (χ 2 -criteria) is one of the most famous statistical criteria; It is the main method used in combination with other criteria. The criterion "Hee-square" was proposed in 1900 by Karl Pearson. His wonderful work is considered as the foundation of modern mathematical statistics.

For our case, checking on the criterion of "chi-square" will allow how we created real GSH is close to the standard of all soles, that is, whether it satisfies the requirement of uniform distribution or not.

Frequency diagram reference GSH is presented in Fig. 22.10. Since the law of distribution of the reference GSH is uniform, then (theoretical) probability p. i. Finding numbers B. i. interval (all of these intervals k. ) Equal p. i. = 1/k. . And thus in each of k. Intervals will hit smooth by p. i. · N. numbers ( N. - Total number of generated numbers).

Real GSH will issue numbers distributed (and not necessarily evenly!) By k. intervals and in each interval will fall n. i. numbers (in total n. 1 + n. 2 + ... + n. k. = N. ). How do we determine how well the test it is good and close to the reference? It is quite logical to consider the squares of the differences between the number of numbers n. i. and "reference" p. i. · N. . Moving them, and as a result we get:

χ 2 exp. \u003d ( n. 1 - p. one · N.) 2 + (n. 2 - p. 2 · N.) 2 + ... + ( n. k. – p. k. · N.) 2 .

From this formula, it follows that the smaller the difference in each of the terms (and therefore, and the less the value of χ 2 exp.), The stronger the law of the distribution of random numbers generated by the real GSH, is uniform.

In the previous expression, each of the terms is attributed to the same weight (equal to 1), which can actually do not correspond to reality; Therefore, for the Statistics "Hee-Square" it is necessary to carry out the normalization of each i. -to the foundation by sharing it on p. i. · N. :

Finally, we write the resulting expression more compact and simplify it:

We got the value of the criterion "Chi-Square" for experimental data.

In tab. 22.2 are given theoretical the values \u200b\u200bof "chi-square" (χ 2 theorem.), where ν = N. - 1 is the number of degrees of freedom, p. - this is a trustful probability set by the user, which indicates how much stage must meet the requirements of the uniform distribution, or p. — this is the likelihood that the experimental value of χ 2 exp. There will be less to theoretical (theoretical) χ 2 Theorem. or equal to Him.

Acceptable believes p. from 10% to 90%.

If χ 2 exp. Many more χ 2 Theorem. (i.e p. - Great), then the generator does not satisfy the requirement of uniform distribution, since the observed values n. i. too far go away from theoretical p. i. · N. and cannot be considered random. In other words, such a large confidence interval is established that the restrictions on the numbers become very non-fasteners, the requirements for the numbers are weak. This will be observed a very large absolute error.

Yes, D. Knut in his book "The Art of Programming" noticed that there is χ 2 exp. Little too, in general, it is not good, although it seems, at first glance, it is remarkably from the point of view of uniformity. Indeed, take a number of numbers 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, ... - they are ideal from the point of view of uniformity, and χ 2 exp. It will be practically zero, but you can hardly recognize them by random.

If χ 2 exp. Many less than χ 2 Theores. (i.e p. - Little), then the generator does not satisfy the requirement of random uniform distribution, since the observed values n. i. too close to theoretical p. i. · N. and cannot be considered random.

But if χ 2 exp. Lies in a certain range, between two values \u200b\u200bof χ 2 theore. that correspond, for example, p. \u003d 25% and p. \u003d 50%, then we can assume that the values \u200b\u200bof random numbers generated by the sensor are quite random.

In addition, it is necessary to keep in mind that all values p. i. · N. Must be large enough, for example more than 5 (clarified by empirically). Only then (with a fairly large statistical sample), the conditions for conducting the experiment can be considered satisfactory.

So, the verification procedure has the following form.

Checks for statistical independence

1) checking for the frequency of appearance numbers in the sequence

Consider an example. Random number 0.2463389991 consists of digits 2463389991, and the number 0.5467766618 consists of numbers 5467766618. Connecting a sequence of numbers, we have: 24633899915467766618.

It is clear that theoretical probability p. i. Dropping i. The numbers (from 0 to 9) are 0.1.

2) Checking the emergence of the series from the same digits

Denote by n. L. Number of episodes of the same in a row length numbers L. . It is necessary to check everything L. from 1 to m. where m. - This is a user specified number: the maximum number of identical numbers in the series.

In the example "24633899915467766618" found 2 series of 2 (33 and 77), i.e. n. 2 \u003d 2 and 2 series length 3 (999 and 666), that is n. 3 = 2 .

The probability of the appearance of a series of length in L. equal to: p. L. \u003d 9 · 10 - L. (Theoretical). That is, the probability of the appearance of a series of length in one character is equal to: p. 1 \u003d 0.9 (theoretical). The probability of the appearance of a series of two characters long is equal to: p. 2 \u003d 0.09 (theoretical). The probability of the appearance of a series of three characters long is: p. 3 \u003d 0.009 (theoretical).

For example, the probability of the appearance of a series of length in one character is equal p. L. \u003d 0.9, since only one character from 10 can meet, and all the characters 9 (zero is not considered). And the likelihood that in a row will meet two identical symbols "XX" equal to 0.1 · 0.1 · 9, that is, the probability of 0.1 that the symbol "X" appears in the first position, is multiplied by the probability of 0.1 that the same symbol appears in the second position "X" and multiplied by the number of such combinations 9.

The frequency of the series is calculated by the previously disassembled formula of the "chi-square" formula using values p. L. .

Note: The generator can be checked multiple times, but the checks do not have the property of completeness and do not ensure that the generator displays random numbers. For example, a generator issuing a sequence 12345678912345 ... When checking will be considered ideal, which is obviously not quite so.

In conclusion, we note that the Third Head of the Book of Donald E. Knuta "The Art of Programming" (Volume 2) is fully devoted to the study of random numbers. It studies various methods for generating random numbers, statistical criteria for chance, as well as the transformation of uniformly distributed random numbers to other types of random variables. The presentation of this material is paid more than two hundred pages.

The herorator of random numbers for lottery tickets is provided free of charge in the format "As is" ("As IS"). The developer does not bear any responsibility for the material and intangible loss of script users. You can use this service at your own risk. However, what, and the risk you do not take exactly :-).

Random numbers for lottery tickets online

This software (GPSF on the JS) is a pseudo-random number generator implemented by JavaScript programming language capabilities. The generator issues a uniform distribution of random numbers.

This allows you to knock out the Wedge Wedge on the HSH with a uniform distribution from the lottery company to respond random numbers with a uniform distribution. This approach eliminates the player's subjectivity, since people have certain preferences in choosing numbers and numbers (the birthdays of relatives, memorable dates, years, etc.), which affect the selection of numbers manually.

Free tool helps players pick up random numbers for lotteries. In the random generator script, there is a set of pre-confined modes for Gosloto 5 of 36, 6 of 45, 7 of 49, 4 of 20, Sportlio 6 of 49. You can select the generation mode of random numbers with free settings for other lottery options.

Forecasts Winning Lottery

The random number generator with a uniform distribution can serve as a horoscope on the lottery draw, however, the likelihood that the forecast will be raised by the low. But still, the use of a random number generator has a good probability of winning compared to many other lottery game strategies and additionally frees you from the mucke of a complex choice of happy numbers and combinations. For our part, I do not advise you to succumb to the temptation and buy paid predictions, it is better to spend this money on the textbook on the combinatorics. From it you can learn a lot of interesting things, for example, the probability of winning Jack-Pota in Gosloto 5 of 36 Sociorates 1 to 376 992 . And the probability of getting a minimum prize, guessing 2 numbers, is 1 to 8 . The same probabilities of the winnings have a forecast based on our GSH.

On the Internet there are requests for random numbers for the lottery, taking into account past editions. But provided that the Lottery uses the HSH with a uniform distribution and the probability of falling out of a particular combination does not depend on the circulation to the circulation, then trying to take into account the results of past erases meaningless. And this is quite logical, as the lottery companies are not beneficial for participants to increase the likelihood of their winning simple methods.

There are often conversations that the organizers of the lotteries are fascinated by the results. But in fact, there is no point in this, even, on the contrary, if the lottery companies had influenced the lottery results, it would be possible to find a winning strategy, but until it was possible to anyone. Therefore, the arrangers of lotteries are just very profitable that the balls fall out with a uniform probability. By the way, the estimated return of the lottery 5 of 36 is 34.7%. Thus, a lottery company remains 65.3% of revenue from the sale of tickets, some of the funds (usually half) is deducted to the formation of Jack Pot, the rest of the money goes to organizational expenses, advertising and net profit of the company. Statistics on the resources These numbers perfectly confirms.

Hence the conclusion - do not buy meaningless forecasts, use the free generator of random numbers, take care of your nerves. Let our random numbers become happy numbers for you. Good mood and a good day!

The submitted online generator of random numbers operates on the basis of the pseudo-random numbers built into the JavaScript with a uniform distribution. An integers are generated. By default, 10 random numbers are displayed in the range of 100 ... 999, the numbers are separated by spaces.

Basic settings for generator random numbers:

• Amount of numbers
• Range of numbers
• Type of separator
• On / Off Repeat Removal Function (numbers)

The total amount is formally limited to 1000, the maximum number is 1 billion. Separate options: Space, comma, semicolon.

Now you know exactly where and how on the Internet get a free sequence of random numbers in a given range.

Options for using random numbers generator

The random number generator (HSH on JS with a uniform distribution) is useful to SMM specialists and owners of groups and communities on social networks Istagram, Facebook, VKontakte, classmates to determine the winners of lotteries, competitions and prizes.

The random number generator allows the prizes drawing among an arbitrary number of participants with a given number of winners. Competitions can be carried out without reposts and comments - you yourself ask the number of participants and the interval of generation of random numbers. You can get a set of random numbers online and can be free on this site, and you do not need to put any application on your smartphone or a program on a computer.

Also, the generator of random numbers online can be used to simulate a flipping of coins or playing bones. But however, we have separate specialized services for these cases.