### Pseudo-random numbers

Pseudo-random numbers are generated by software algorithms and have a predictable pattern, although it may be difficult to detect. They appear to be random, but they are generated by a mathematical formula that has a deterministic nature. This means that if the same algorithm and seed value are used, the same sequence of numbers will be generated. Pseudo-random numbers are generated quickly and efficiently, and they are suitable for applications that require randomness but do **not require high security**. For example, they can be used in simulations, video games, or random number generation for online polls.

### True random numbers

True random numbers, on the other hand, are generated by physical processes and have no predictable pattern. True randomness is necessary for applications that **require high security**, such as cryptography. True random numbers are generated using various physical phenomena, such as radioactive decay, atmospheric noise, or electronic circuit noise. These sources of randomness are used to generate unpredictable and unbiased numbers that cannot be reproduced or predicted. True random number generators typically require specialized hardware and are often slower than pseudo-random number generators.

### How to distinguish?

One way to distinguish between pseudo-random and true random numbers is to use **statistical tests**. Statistical tests can analyze the generated sequence of numbers and determine whether they are random or not. Pseudo-random numbers can pass many statistical tests, but true random numbers will pass all statistical tests, as they have no predictable pattern or correlation between the numbers. Therefore, true random number generators are essential for applications that require high levels of security, such as in the generation of cryptographic keys, passwords, or for secure communication channels.

### Quantum random number generators

In recent years, new methods of generating random numbers have been developed, such as quantum random number generators. Quantum random number generators use the random behavior of quantum particles, such as photons or electrons, to generate truly random numbers. These generators are not based on deterministic algorithms or physical processes, but rather on the inherent randomness of quantum phenomena. Quantum random number generators are still in their early stages of development, but they hold great promise for improving the efficiency and security of random number generation.