A new research has resorted to the concept of integer partitions to make it much easier to discover new prime numbers.
An innovative discovery of a team of mathematicians is transforming the way we understand prime numbers – the fundamental blocks of arithmetic.
For centuries these numbers, which are only divisible by 1 and themselves, fascinate mathematicians. However, despite their apparent simplicity, prime numbers become increasingly difficult to identify As they increase, and their distribution among the integers remains a mystery.
In a recent article in Proceedings of the National Academy of Sciences USA, Mathematics Ken Ono (University of Virginia), William Craig (US Naval Academy) and Jan-Willem Van Ittersum (University of Colony) presented a new method for detecting prime numbers, resorting to an ancient mathematical concept: The partitions of integers.
Partitions – ways to express a number as The sum of smaller integers – They may seem simple at first glance. For example, number 5 has seven possible partitions, such as 4+1 or 3+2. However, ono and his colleagues have shown that partition functions can be used in a sophisticated way to reveal if a number is cousin, reports.
At the center of the approach are Diophantin Equations – Algebraic equations with entire solutions – involving partition functions. Researchers have proved that there are endless equations of this type capable of identifying prime numbers. One of the examples presented in the article includes a complex polynomial equation with constant and partition functions that returns zero only when the number inserted is cousin. As one says: “It is almost as if our work offer infinite new definitions what it is to be cousin. ”
The discovery represents a change in the face of traditional methods, which depend on factory – technique that quickly becomes impractical to very large numbers. The largest cousin number currently known have More than 41 million digits – Far beyond the range of basic tests.
Although this discovery does not solve classic puzzles such as the conjecture of twin cousins or Goldbach, it is a significant advance. As Ken Ono concludes: “This result is an example of how far we have come to understand the complex nature of cousins - and how far we can still go.”
