 In November 2013, Maynard gave a different proof of Yitang Zhang's theorem that there are bounded gaps between primes, and resolved a longstanding conjecture by showing that for any formula_1 there are infinitely many intervals of bounded length containing formula_1 prime numbers.This work can be seen as progress on the Hardy–Littlewood formula_1-tuples conjecture as it establishes that "a positive proportion of admissible formula_1-tuples satisfy the prime formula_1-tuples conjecture
for every formula_1.