This is a preview. Log in through your library . Abstract Some newly-discovered arithmetic progressions of primes are presented, including five length twenty-one and one of length twenty-two. Journal ...

Sequences of integers exist with any possible upper density and lower density which do not contain an infinitely long arithmetic progression. Journal Information This monthly journal, begun in 1950, ...

A pair of mathematicians has solved the first chunk of one of the most famous conjectures about the additive properties of whole numbers. Proposed more than 60 years ago by the legendary Hungarian ...

The original version of this story appeared in Quanta Magazine. The simplest ideas in mathematics can also be the most perplexing. Take addition. It’s a straightforward operation: One of the first ...

A new proof marks the first progress in decades on a problem about how order emerges from disorder. In February, Sah and Sawhney announced yet another joint accomplishment. With James Leng, a graduate ...