Põhiarvu

Põhiarvu is a mathematical concept in the field of combinatorics, specifically in the study of pseudorandom number generation. It is a measure used to determine the uniformity of a sequence of numbers, and is often used in cryptographic and randomness-related applications.

The concept of põhiarvu was introduced by Estonia's mathematician Helmut Võhmann in the late 20th century. The name itself is derived from the Estonian language, with "põhi" meaning "main" or "primary" and "arvu" meaning "number". It is also known as the "basic number" or "primary number" in English-speaking countries.

The põhiarvu of a sequence of numbers is defined as the ratio of the number of pairs of elements in the sequence that are separated by a distance of one position, to the total number of pairs of elements in the sequence. A sequence with a high põhiarvu is considered to be well-distributed and pseudorandom, meaning that it appears to be randomly generated but is actually deterministic.

The põhiarvu has been widely used in various applications including cryptography, statistical analysis and simulation-based methods. However, its usage has also been met with some criticism due to its apparent brittleness in certain situations.

There are several methods for calculating the põhiarvu, with the most common one involving the calculation of the autocorrelation function. The autocorrelation function measures the similarity between the original sequence and a time-shifted version of the original sequence.

Researchers have argued that the põhiarvu offers a faster and more straightforward method for checking the quality of random number sequences. However, further research is needed to understand the deeper implications and limitations of this concept.