Let pn be the n-th prime number and ${x_n} = p_{n + 1}^{n + 1}/p_n^n$. We show that the sequence (xn)n ≥ N is not monotonie for any integer N > 1 and that the series $\sum\limits_{n = 1}^{ + \infty } ...

One of the curious properties of mathematics is its beauty. But exactly what mathematicians mean by beauty is hard to capture. Perhaps the most famous example is Euler’s relation, e iπ + 1 = 0, which ...

What is your favorite number? For many people, it may be an irrational number such as pi (π), Euler’s number (e) or the square root of 2. Even among the natural numbers (positive integers), there are ...

Mathematicians have been studying the distribution of prime numbers for thousands of years. Recent results about a curious kind of prime offer a new take on how spread out they can be. You may have ...

The discovery may aid research in both mathematics and materials science. “Prime numbers have beautiful structural properties, including unexpected order, hyperuniformity and effective limit-periodic ...

Prime numbers, whole numbers greater than one with only two factors (one and themselves), are fundamental in mathematics. They serve as building blocks for all other whole numbers, a concept known as ...