Table of solutions, 1 ≤ n ≤ 20
If more than one optimal solution exists, all are shown. ==Special cases==
Special cases
Only 26 optimal packings are thought to be rigid (with no circles able to "rattle"). Numbers in bold are prime: • Proven for n = 1, 2, 3, 4, 5, 6, 7, 10, 11, 12, 13, 14, 19 • Conjectured for n = 15, 16, 17, 18, 22, 23, 27, 30, 31, 33, 37, 61, 91 Of these, solutions for n = 2, 3, 4, 7, 19, and 37 achieve a packing density greater than any smaller number > 1. (Higher density records all have rattles.) ==See also==