Both arithmetic aficionados and the mathematically challenged will be equally captivated by new research that upends hundreds of years of popular belief about prime numbers. Contrary to what just ...

It is proved that $\lim_{n\rightarrow \infty }inf(p_{n+1}-p_n)\textless 7\times 10^7$, where pn is the n-th prime. Our method is a refinement of the recent work of Goldston, Pintz and Yildirim on the ...

We prove that there are arbitrarily long arithmetic progressions of primes. There are three major ingredients. The first is Szemerédi's theorem, which asserts that any subset of the integers of ...