N-Cluster

A Lattice Point configuration with no three points Collinear and no four Concyclic. An example is the 6-cluster (0, 0), (132, $-720$), (546, $-272$), (960, $-720$), (1155, 540), (546, 1120). Call the Radius of the smallest Circle centered at one of the points of an N-cluster which contains all the points in the N-cluster the Extent. Noll and Bell (1989) found 91 nonequivalent prime 6-clusters of Extent less than $20937$, but found no 7-clusters.

References

Guy, R. K. Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, p. 187, 1994.

Noll, L. C. and Bell, D. I. ``$n$-clusters for $1<n<7$.'' Math. Comput. 53, 439-444, 1989.