"In April 2013, Yitang Zhang proved the existence of a finite bound B such that there are infinitely many pairs of distinct primes which differ by no more than B... In November, inspired by Zhang’s extraordinary breakthrough, James Maynard dramatically slashed this bound to 600, by a substantially easier method. Both Maynard, and Terry Tao who had independently developed the same idea, were able to extend their proofs to show that for any given integer m >= 1 there exists a bound B_m such that there are infinitely many intervals of length B_m containing at least m distinct primes. We will also prove this much stronger result herein, even showing that one can take B_m = e^(8m+5)." Andrew Granville has made available a pdf of this paper: http://www.dms.umontreal.ca/~andrew/CEBBrochureFinal.pdf