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.
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