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 ...

Learning basic math facts is a critical step that allows children to progress efficiently to higher levels of mathematical thinking. If a middle-school student cannot quickly recall basic facts like 2 ...

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 ...