Primes, primes everywhere!
Mathematicians get closer to solving one of the greatest problems in number theory.
Mathematicians from the US, Hungary and Turkey just might be one step closer towards the impossible. One of the greatest problems in number theory is determining whether the number of prime tuples, prime numbers which lie very close to each other, is infinite. In short, “are there an infinite number of prime tuples which lie next to each other?”
The authors present a mathematical technique which shows that there are an infinite number of prime tuples within 16 or less from each other. While this does not fully solvethe long-standing problem, the research published in Annals of Mathematics at least offers a “partial solution”.
Prime numbers are divisible only by themselves and 1. For example, 2, 3 and 5 are all prime since they can only be divided by themselves and 1. Whereas 4 is not, since it can bedivided by itself, 1 and 2. This makes it seem that there are less primes than there are positive integers; however, mathematics can tell us that there are as many prime numbers as there are positive integers.
However, as the size of the number increases, the distance between adjacent prime numbers also increases. This means that the chance that any given number is prime decreases as the size of the number increases. The research indicates that even with a decreasing probability of finding two primes close to one-and-other, primes with very close neighbours are still infinitely many. A weird result, since this means that prime tuples are as numerous as the set of positive integers.
