Given a sequence a1, a2, . . . of integers, one can form the sequence |a1 – a2|, |a2, a3|, . . .. Gilbreath’s conjecture is that if you start with the sequence of the primes and iterate this consecutive differencing procedure, then the first term of every sequence (besides the initial one) is a 1. We prove the conclusion of Gilbreath’s conjecture for a suitably random initial sequence instead of the primes.
This video is part of the Webinar in Additive Combinatorics series, and this is their YouTube channel.
