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In a stunning new advance towards the Prime k-Tuple Conjecture, Maynard and Tao have shown that if k is sufficiently large in terms of m, then for an admissible k-tuple of linear forms in ℤ[x], the set contains at least m primes for infinitely many n ∈ ℕ. In this note, we deduce that contains at least m consecutive primes for infinitely many n ∈ ℕ. We answer an old question of Erdős and Turán by producing strings of m + 1 consecutive primes whose successive gaps form an increasing (resp....
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