For those who don't wish to read all the news fluff to hear about a mathematical discovery:[1] Abstract. We show that there exists pairs of consecutive primes

For those who don't wish to read all the news fluff to hear about a mathematical discovery:[1] Abstract. We show that there exists pairs of consecutive primes less than x whose difference is larger than t(1+o(1))(log x)(log log x)(log log log log x)(log log log x)⁻² for any fixed t. This answers a well-known question of Erdős. Their "key proposition", as stated, is:[2] Proposition 5. Fix δ > 0. Let m < Uz⁻¹(log₂ x)⁻² be even and let Iₘ ⊆ [x/2, x] be an interval of at least δ|ℝₘ| log x. Then for x > x₀ (δ, C_U) there exists a choice of residue classes aₙ (mod n) for each prime n ∈ Iₘ such that p ∈ ℝₘ ⇒ p ≡ aₙ (mod n) for some prime n ∈ Iₘ. [1]: Here is the paper linked: http://arxiv.org/pdf/1408.5110v1.pdf http://arxiv.org/pdf/1408.5110v1.pdf (strangely, while the news article mentions two papers, both links go to the same one in both the original and Wired articles ...). [2]: I changed all instances of q to n in this so that I could type most of the subscripts, but any errors are mine.