## Prime number enigma could be solved by simple networks

发布时间：2019-03-15 04:11:01来源：未知点击：

By Jacob Aron IS THERE a pattern behind prime numbers? This is one of the biggest questions in mathematics. Now networks that reproduce relationships between primes and non-primes could point the way to an answer. Primes are numbers that are only perfectly divisible by themselves and by 1. They can be thought of as the building blocks of numbers, because any non-prime – or composite – can be generated by multiplying primes together. But they remain mysterious: no one has been able to find a pattern in the way prime numbers are distributed among the composites. To investigate, Marián Boguñá of the University of Barcelona, Spain, and his colleagues turned the numbers from 2 to 1 billion into a network by linking composites to their prime building blocks. They also devised a way to generate similar networks using other simple rules to link the numbers, and wondered if they could get these networks to reproduce the pattern of links between primes and composites. Their rules depend on probabilities, so the generated networks are different each time. On average, the researchers found that the webs are very close to the real network of primes and composites. Previous work made it possible to estimate how many primes there are below a certain number, but this is the first time a model has reproduced the relationships between primes and composites. The next step will be to generate more prime-like networks. Testing theories about the real primes has been difficult because there was no other similar system before this research. “There is only one set of primes, but with their technique you can produce a thousand different networks,” says Dave Platt of the University of Bristol, UK. This might even help tackle a problem called the Riemann hypothesis, a proof of which is worth $1 million. This article appeared in print under the headline “Prime numbers emerge from simple network” More on these topics: