Small gaps between primes exist

In the preprint 3, Goldston, Pintz, and Yıldırım established, among other things, equation ₍p₍+₁-pₙ pₙ=0, equation with pₙ the nth prime. In the present article, which is essentially self-contained, we shall develop a simplified account of the method used in 3. We include a short expository last section.