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Minimal BlocksSuppose we define an ordering on the points of the plane by saying that (x_{1},y_{1}) <= (x_{2},y_{2}) if and only if x_{1} <= x_{2} and y_{1} <= y_{2}. The ordering is only partial, i.e., doesn't apply to all pairs of points, but then when it does apply we can probably all agree with the result. Under that ordering, a set of points won't necessarily have a minimum, but it will have a minimal set, a set of points such that every other point is larger than at least one of them. Here's the minimal set for the points that are centers of 3×3 blocks.
Actually, that's only half the minimal set … you can get the other half by reflecting about the line y = x. Next, here are the coordinates, reflected to fit the convention that x < y.
Which of these is the “real” first block is a matter of taste. However … if we measure using the function min(x,y), the first block is the first one I found, but under any other reasonable measure—max(x,y), x+y, sqrt(x^{2}+y^{2})—the first block is (1275,1309). Finally, here are three nice nonminimal blocks that I happened to notice.

See AlsoNext Block, The Odds and Ends @ July (2004) 